1
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Nayak AK, Das SL, Misbah C. Endothelial calcium dynamics elicited by ATP release from red blood cells. Sci Rep 2024; 14:13550. [PMID: 38866785 DOI: 10.1038/s41598-024-63306-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 05/27/2024] [Indexed: 06/14/2024] Open
Abstract
Red blood cells (RBCs) exhibit an interesting response to hydrodynamic flow, releasing adenosine triphosphate (ATP). Subsequently, these liberated ATP molecules initiate a crucial interaction with endothelial cells (ECs), thereby setting off a cascade involving the release of calcium ions (Ca2 + ). Ca2 + exerts control over a plethora of cellular functions, and acts as a mediator for dilation and contraction of blood vessel walls. This study focuses on the relationship between RBC dynamics and Ca2 + dynamics, based on numerical simulations under Poiseuille flow within a linear two-dimensional channel. It is found that the concentration of ATP depends upon a variety of factors, including RBC density, channel width, and the vigor of the flow. The results of our investigation reveals several features. Firstly, the peak amplitude of Ca2 + per EC escalates in direct proportion to the augmentation of RBC concentration. Secondly, increasing the flow strength induces a reduction in the time taken to reach the peak of Ca2 + concentration, under the condition of a constant channel width. Additionally, when flow strength remains constant, an increase in channel width corresponds to an elevation in calcium peak amplitude, coupled with a decrease in peak time. This implies that Ca2 + signals should transition from relatively unconstrained channels to more confined pathways within real vascular networks. This notion gains support from our examination of calcium propagation in a linear channel. In this scenario, the localized Ca2 + release initiates a propagating wave that gradually encompasses the entire channel. Notably, our computed propagation speed agrees with observations.
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Affiliation(s)
| | - Sovan Lal Das
- Physical and Chemical Biology Laboratory, and Department of Mechanical Engineering, Indian Institute of Technology Palakkad, Palakkad, 678623, India
| | - Chaouqi Misbah
- CNRS, LIPhy, Université Grenoble Alpes, 38000, Grenoble, France.
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2
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Kabacaoğlu G, Lushi E. Cross-stream migration of a vesicle in vortical flows. Phys Rev E 2023; 107:044608. [PMID: 37198778 DOI: 10.1103/physreve.107.044608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Accepted: 04/03/2023] [Indexed: 05/19/2023]
Abstract
We use numerical simulations to systematically investigate the vesicle dynamics in two-dimensional (2D) Taylor-Green vortex flow in the absence of inertial forces. Vesicles are highly deformable membranes encapsulating an incompressible fluid and they serve as numerical and experimental proxies for biological cells such as red blood cells. Vesicle dynamics has been studied in free-space or bounded shear, Poiseuille, and Taylor-Couette flows in 2D and 3D. Taylor-Green vortex are characterized with even more complicated properties than those flows such as nonuniform flow line curvature, shear gradient. We study the effects of two parameters on the vesicle dynamics: the ratio of the interior fluid viscosity to that of the exterior one and the ratio of the shear forces on the vesicle to the membrane stiffness (characterized by the capillary number). Vesicle deformability nonlinearly depends on these parameters. Although the study is in 2D, our findings contribute to the wide spectrum of intriguing vesicle dynamics: Vesicles migrate inwards and eventually rotate at the vortex center if they are sufficiently deformable. If not, then they migrate away from the vortex center and travel across the periodic arrays of vortices. The outward migration of a vesicle is a new phenomenon in Taylor-Green vortex flow and has not been observed in any other flows so far. Such cross-streamline migration of deformable particles can be utilized in several applications such as microfluidics for cell separation.
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Affiliation(s)
- Gökberk Kabacaoğlu
- Department of Mechanical Engineering, İhsan Doğramacı Bilkent University Ankara, 06800, Turkey
| | - Enkeleida Lushi
- Department of Mathematical Sciences, New Jersey Institute of Technology Newark, New Jersey 07102, USA
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3
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Xiao W, Liu K, Lowengrub J, Li S, Zhao M. Three-dimensional numerical study on wrinkling of vesicles in elongation flow based on the immersed boundary method. Phys Rev E 2023; 107:035103. [PMID: 37072945 DOI: 10.1103/physreve.107.035103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 02/15/2023] [Indexed: 04/20/2023]
Abstract
We study the wrinkling dynamics of three-dimensional vesicles in a time-dependent elongation flow by utilizing an immersed boundary method. For a quasispherical vesicle, our numerical results well match the predictions of perturbation analysis, where similar exponential relationships between wrinkles' characteristic wavelength and the flow strength are observed. Using the same parameters as in the experiments by Kantsler et al. [V. Kantsler et al., Phys. Rev. Lett. 99, 178102 (2007)0031-900710.1103/PhysRevLett.99.178102], our simulations of an elongated vesicle are in good agreement with their results. In addition, we get rich three-dimensional morphological details, which are favorable to comprehend the two-dimensional snapshots. This morphological information helps identify wrinkle patterns. We analyze the morphological evolution of wrinkles using spherical harmonics. We find discrepancies in elongated vesicle dynamics between simulations and perturbation analysis, highlighting the importance of the nonlinear effects. Finally, we investigate the unevenly distributed local surface tension, which largely determines the position of wrinkles excited on the vesicle membrane.
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Affiliation(s)
- Wang Xiao
- School of Mathematics and Statistics, Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Kai Liu
- College of Education for the Future, Beijing Normal University, Zhuhai 519087, China
| | - John Lowengrub
- Department of Mathematics, University of California Irvine, Irvine, California 92697, USA
| | - Shuwang Li
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Meng Zhao
- School of Mathematics and Statistics, Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
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4
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Kumar D, Schroeder CM. Nonlinear Transient and Steady State Stretching of Deflated Vesicles in Flow. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:13976-13984. [PMID: 34813335 DOI: 10.1021/acs.langmuir.1c01275] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Membrane-bound vesicles and organelles exhibit a wide array of nonspherical shapes at equilibrium, including biconcave and tubular morphologies. Despite recent progress, the stretching dynamics of deflated vesicles is not fully understood, particularly far from equilibrium where complex nonspherical shapes undergo large deformations in flow. Here, we directly observe the transient and steady-state nonlinear stretching dynamics of deflated vesicles in extensional flow using a Stokes trap. Automated flow control is used to observe vesicle dynamics over a wide range of flow rates, shape anisotropy, and viscosity contrast. Our results show that deflated vesicle membranes stretch into highly deformed shapes in flow above a critical capillary number Cac1. We further identify a second critical capillary number Cac2, above which vesicle stretch diverges in flow. Vesicles are robust to multiple nonlinear stretch-relax cycles, evidenced by relaxation of dumbbell-shaped vesicles containing thin lipid tethers following flow cessation. An analytical model is developed for vesicle deformation in flow, which enables comparison of nonlinear steady-state stretching results with theories for different reduced volumes. Our results show that the model captures the steady-state stretching of moderately deflated vesicles; however, it underpredicts the steady-state nonlinear stretching of highly deflated vesicles. Overall, these results provide a new understanding of the nonlinear stretching dynamics and membrane mechanics of deflated vesicles in flow.
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Affiliation(s)
- Dinesh Kumar
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Charles M Schroeder
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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5
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Yang H, Yao G, Wen D. Efficient mixing enhancement by orthogonal injection of shear-thinning fluids in a micro serpentine channel at low Reynolds numbers. Chem Eng Sci 2021. [DOI: 10.1016/j.ces.2020.116368] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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6
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Bhatia T, Robinson T, Dimova R. Membrane permeability to water measured by microfluidic trapping of giant vesicles. SOFT MATTER 2020; 16:7359-7369. [PMID: 32696791 DOI: 10.1039/d0sm00155d] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We use a microfluidic method to estimate the water permeability coefficient (p) of membranes. As model lipid membranes we employ giant unilamellar vesicles (GUVs) composed of palmitoyloleoyl phosphatidylcholine and cholesterol (10 mol%). We have developed a microfluidic device with multiple chambers to trap GUVs and allow controlled osmotic exchange. Each chamber has a ring-shaped pressure-controlled valve which upon closure allows isolation of the GUVs in a defined volume. Opening the valves leads to a rapid fluid exchange between the trapping region and the microchannel network outside, thus allowing precise control over solution concentration around the GUVs contrary to other experimental approaches for permeability measurements reported in the literature. The area and volume changes of individual vesicles are monitored with confocal microscopy. The solute concentration in the immediate vicinity of the GUVs, and thus the concentration gradient across the membrane, is independently assessed. The data are well fitted by a simple model for water permeability which assumes that the rate of change in volume of a GUV per unit area is linearly proportional to concentration difference with permeability as the proportionality constant. Experiments of GUV osmotic deflation with hypertonic solutions yield the permeability of POPC/cholesterol 9/1 membranes to be p = 15.7 ± 5.5 μm s-1. For comparison, we also show results using two other approaches, which either do not take into account local concentration changes and/or do not resolve the precise vesicle shape. We point out the errors associated with these limitations. Finally, we also demonstrate the applicability of the microfluidic device for studying the dynamics of vesicles under flow.
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Affiliation(s)
- Tripta Bhatia
- Theory & Biosystems, Max Planck Institute of Colloids and Interfaces (MPIKG), 14424 Potsdam, Germany.
| | - Tom Robinson
- Theory & Biosystems, Max Planck Institute of Colloids and Interfaces (MPIKG), 14424 Potsdam, Germany.
| | - Rumiana Dimova
- Theory & Biosystems, Max Planck Institute of Colloids and Interfaces (MPIKG), 14424 Potsdam, Germany.
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7
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Kumar D, Richter CM, Schroeder CM. Double-mode relaxation of highly deformed anisotropic vesicles. Phys Rev E 2020; 102:010605. [PMID: 32794982 DOI: 10.1103/physreve.102.010605] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Accepted: 06/17/2020] [Indexed: 06/11/2023]
Abstract
Lipid vesicles are known to undergo complex conformational transitions, but it remains challenging to systematically characterize nonequilibrium membrane dynamics in flow. Here, we report the direct observation of anisotropic vesicle relaxation from highly deformed shapes using a Stokes trap. Vesicle shape relaxation is described by two distinct characteristic timescales governed by the bending modulus and membrane tension. Interestingly, the fast double-mode timescale is found to depend on vesicle deflation or reduced volume. Experimental results are well described by a viscoelastic model of a deformed membrane. Overall, these results show that vesicle relaxation is governed by an interplay between membrane elastic moduli, surface tension, and vesicle deflation.
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Affiliation(s)
- Dinesh Kumar
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Channing M Richter
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Charles M Schroeder
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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8
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Kumar D, Richter CM, Schroeder CM. Conformational dynamics and phase behavior of lipid vesicles in a precisely controlled extensional flow. SOFT MATTER 2020; 16:337-347. [PMID: 31802095 DOI: 10.1039/c9sm02048a] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Lipid vesicles play a key role in fundamental biological processes. Despite recent progress, we lack a complete understanding of the non-equilibrium dynamics of vesicles due to challenges associated with long-time observation of shape fluctuations in strong flows. In this work, we present a flow-phase diagram for vesicle shape and conformational transitions in planar extensional flow using a Stokes trap, which enables control over the center-of-mass position of single or multiple vesicles in precisely defined flows [A. Shenoy, C. V. Rao and C. M. Schroeder, Proc. Natl. Acad. Sci. U. S. A., 2016, 113(15), 3976-3981]. In this way, we directly observe the non-equilibrium conformations of lipid vesicles as a function of reduced volume ν, capillary number Ca, and viscosity contrast λ. Our results show that vesicle dynamics in extensional flow are characterized by the emergence of three distinct shape transitions, including a tubular to symmetric dumbbell transition, a spheroid to asymmetric dumbbell transition, and quasi-spherical to ellipsoid transition. The experimental phase diagram is in good agreement with recent predictions from simulations [V. Narsimhan, A. P. Spann and E. S. Shaqfeh, J. Fluid Mech., 2014, 750, 144]. We further show that the phase boundary of vesicle shape transitions is independent of the viscosity contrast. Taken together, our results demonstrate the utility of the Stokes trap for the precise quantification of vesicle stretching dynamics in precisely defined flows.
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Affiliation(s)
- Dinesh Kumar
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
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9
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Sinha KP, Thaokar RM. A theoretical study on the dynamics of a compound vesicle in shear flow. SOFT MATTER 2019; 15:6994-7017. [PMID: 31433433 DOI: 10.1039/c9sm01102a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The dynamics of nucleate cells in shear flow is of great relevance in cancer cells and circulatory tumor cells where they determine the flow properties of blood. Buoyed by the success of giant unilamellar vesicles in explaining the dynamics of anucleate cells such as red blood cells, compound vesicles have been suggested as a simple model for nucleate cells. A compound vesicle consists of two concentric unilamellar vesicles with the inner, annular and outer regions filled with aqueous Newtonian solvents. In this work, a theoretical model is presented to study the deformation and dynamics of a compound vesicle in linear shear flow using small deformation theory and spherical harmonics with higher order approximation to the membrane forces. A coupling of viscous and membrane stresses at the membrane interface of the two vesicles results in highly nonlinear shape evolution equations for the inner and the outer vesicles which are solved numerically. The results indicate that the size of the inner vesicle (χ) does not affect the tank-treading dynamics of the outer vesicle. The inner vesicle admits a greater inclination angle than the outer vesicle. However, the transition to trembling/swinging and tumbling is significantly affected. The inner and outer vesicles exhibit identical dynamics in the parameter space defined by the nondimensional rotational (Λan) and extensional (S) strength of the general shear flow. At moderate χ, a swinging mode is observed for the inner vesicle while the outer vesicle exhibits tumbling. The inner vesicle also exhibits modification of the TU mode to IUS (intermediate tumbling swinging) mode. Moreover, synchronization of the two vesicles at higher χ and a Capillary number sensitive motion at lower χ is observed in the tumbling regime. These results are in accordance with the few experimental observations reported by Levant and Steinberg. A reduction in the inclination angle is observed with an increase in χ when the inner vesicle is replaced by a solid inclusion. Additionally, a very elaborate phase diagram is presented in the Λan-S parameter space, which could be tested in future experiments or numerical simulations.
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Affiliation(s)
- Kumari Priti Sinha
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, India.
| | - Rochish M Thaokar
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, India.
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10
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Shen Z, He Y. Migration of a red blood cell in a permeable microvessel. MEDICINE IN NOVEL TECHNOLOGY AND DEVICES 2019. [DOI: 10.1016/j.medntd.2019.100023] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022] Open
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11
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Reichel F, Mauer J, Nawaz AA, Gompper G, Guck J, Fedosov DA. High-Throughput Microfluidic Characterization of Erythrocyte Shapes and Mechanical Variability. Biophys J 2019; 117:14-24. [PMID: 31235179 DOI: 10.1016/j.bpj.2019.05.022] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Revised: 05/03/2019] [Accepted: 05/22/2019] [Indexed: 02/01/2023] Open
Abstract
The motion of red blood cells (RBCs) in microchannels is important for microvascular blood flow and biomedical applications such as blood analysis in microfluidics. The current understanding of the complexity of RBC shapes and dynamics in microchannels is mainly based on several simulation studies, but there are a few systematic experimental investigations. Here, we present a combined study that systematically characterizes RBC behavior for a wide range of flow rates and channel sizes. Even though simulations and experiments generally show good agreement, experimental observations demonstrate that there is no single well-defined RBC state for fixed flow conditions but rather a broad distribution of states. This result can be attributed to the inherent variability in RBC mechanical properties, which is confirmed by a model that takes the variation in RBC shear elasticity into account. This represents a significant step toward a quantitative connection between RBC behavior in microfluidic devices and their mechanical properties, which is essential for a high-throughput characterization of diseased cells.
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Affiliation(s)
- Felix Reichel
- Biotechnology Center, Center for Molecular and Cellular Bioengineering, Technische Universität Dresden, Dresden, Germany
| | - Johannes Mauer
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany
| | - Ahmad Ahsan Nawaz
- Biotechnology Center, Center for Molecular and Cellular Bioengineering, Technische Universität Dresden, Dresden, Germany; School of Mechanical and Manufacturing Engineering, National University of Sciences and Technology, Islamabad, Pakistan
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany
| | - Jochen Guck
- Biotechnology Center, Center for Molecular and Cellular Bioengineering, Technische Universität Dresden, Dresden, Germany; Max Planck Institute for the Science of Light, Erlangen, Germany.
| | - Dmitry A Fedosov
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany.
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12
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Pal A, Khakhar DV. Breakage of vesicles in a simple shear flow. SOFT MATTER 2019; 15:1979-1987. [PMID: 30714598 DOI: 10.1039/c8sm01501e] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The breakage of micron-size SOPC lipid vesicles in an aqueous suspension was studied in a simple shear flow over a range of shear rates (1000 s-1 to 4000 s-1). Evolution of the vesicle size distribution with time was determined using optical microscopy. The number average vesicle diameter was found to reduce continuously with time; at the highest shear rate (4000 s-1), the reduction was 38% after 6 h of shearing. The distributions indicated the existence of a critical diameter such that the number of vesicles larger than the critical diameter decreased and vesicles smaller than the critical diameter increased. The capillary number for the system (ratio of the characteristic viscous stress to the characteristic stress for stretching the lipid membrane) was two orders of magnitude lower than the values reported for breakage in an ultrasonically generated flow, indicating that vesicles do not rupture due to lysis of the membrane. Direct observation of the process in a shear cell fitted in a microscope stage revealed the mechanism of rupture. Measurements of the vesicle dimensions indicated an increase in aspect ratio with time as a result of leakage of fluid from inside vesicles. Once the aspect ratio increased above a threshold value, the vesicles elongated into long thread-like shapes, which broke into small daughter vesicles by pearling.
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Affiliation(s)
- Ankush Pal
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India.
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13
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Shan Y, Wang X, Ji Y, He L, Li S. Self-assembly of phospholipid molecules in solutions under shear flows: Microstructures and phase diagrams. J Chem Phys 2019; 149:244901. [PMID: 30599738 DOI: 10.1063/1.5056229] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Shear-induced microstructures and their phase diagrams were investigated for phospholipid molecules in aqueous solution by dissipative particle dynamic simulation. Self-assembled microstructures, including spherical and cylindrical micelles, spherical vesicles, lamellae, undulated lamellae, perforated lamellae, and continuous networks, were observed under various shear flows and phospholipid concentrations, where the spatial inhomogeneity and symmetry were analysed. A series of phase diagrams were constructed based on the chain lengths under various phospholipid concentrations. The phase distributions showed that the structures with spherical symmetry could be shear-induced to structures with cylindrical symmetry in the dilute solutions. In the semi-concentrated solutions, the lamellae were located in most spaces under zero shear flows, which could be shear-induced into undulated lamellae and then into cylindrical micelles. For the concentrated solutions, the strong shear flows oriented the directions of multilayer lamellae and phase transitions appeared between several cylindrical network structures. These observations on shear-induced microstructures and their distributions revealed a promising approach that could be used to design bio-microstructures based on phospholipid molecules under shear flows.
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Affiliation(s)
- Yue Shan
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
| | - Xianghong Wang
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
| | - Yongyun Ji
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
| | - Linli He
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
| | - Shiben Li
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
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14
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Gera P, Salac D. Three-dimensional multicomponent vesicles: dynamics and influence of material properties. SOFT MATTER 2018; 14:7690-7705. [PMID: 30177985 DOI: 10.1039/c8sm01087k] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In this work, the nonlinear hydrodynamics of a three-dimensional multicomponent vesicle in shear flow are explored. Using a volume- and area-conserving projection method coupled to a gradient-augmented level set and surface phase field method, the dynamics are systematically studied as a function of the membrane bending rigidity difference between the components, the speed of diffusion compared to the underlying shear flow, and the strength of the phase domain energy compared to the bending energy. Using a pre-segregated vesicle, three dynamics are observed: stationary phase, phase-treading, and a new dynamic called vertical banding. These regimes are very sensitive to the strength of the domain line energy, as the vertical banding regime is not observed when the line energy is larger than the bending energy. The findings demonstrate that a complete understanding of multicomponent vesicle dynamics requires that the full three-dimensional system be modeled, and show the complexity obtained when considering heterogeneous material properties.
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Affiliation(s)
- Prerna Gera
- Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260-4400, USA.
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15
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Mauer J, Mendez S, Lanotte L, Nicoud F, Abkarian M, Gompper G, Fedosov DA. Flow-Induced Transitions of Red Blood Cell Shapes under Shear. PHYSICAL REVIEW LETTERS 2018; 121:118103. [PMID: 30265089 DOI: 10.1103/physrevlett.121.118103] [Citation(s) in RCA: 59] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2017] [Revised: 06/29/2018] [Indexed: 05/25/2023]
Abstract
A recent study of red blood cells (RBCs) in shear flow [Lanotte et al., Proc. Natl. Acad. Sci. U.S.A. 113, 13289 (2016)PNASA60027-842410.1073/pnas.1608074113] has demonstrated that RBCs first tumble, then roll, transit to a rolling and tumbling stomatocyte, and finally attain polylobed shapes with increasing shear rate, when the viscosity contrast between cytosol and blood plasma is large enough. Using two different simulation techniques, we construct a state diagram of RBC shapes and dynamics in shear flow as a function of shear rate and viscosity contrast, which is also supported by microfluidic experiments. Furthermore, we illustrate the importance of RBC shear elasticity for its dynamics in flow and show that two different kinds of membrane buckling trigger the transition between subsequent RBC states.
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Affiliation(s)
- Johannes Mauer
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Simon Mendez
- IMAG, University of Montpellier, CNRS, Montpellier, France
| | - Luca Lanotte
- Centre de Biochimie Structurale, CNRS UMR 5048-INSERM UMR 1054, University of Montpellier, 34090 Montpellier, France
| | - Franck Nicoud
- IMAG, University of Montpellier, CNRS, Montpellier, France
| | - Manouk Abkarian
- Centre de Biochimie Structurale, CNRS UMR 5048-INSERM UMR 1054, University of Montpellier, 34090 Montpellier, France
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Dmitry A Fedosov
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
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16
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Li N, Zhang W, Jiang Z, Chen W. Spatial Cross-Correlated Diffusion of Colloids under Shear Flow. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:10537-10542. [PMID: 30117740 DOI: 10.1021/acs.langmuir.8b01803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The spatial cross-correlated diffusion of colloidal particles is often used as an essential tool to study the dynamic properties of a fluid because it directly describes the hydrodynamic interaction between two particles in a fluid. However, the experimental measurement of cross-correlated diffusion can be substantially modified by even a weak shear flow. In this work, the effect of a shear flow on spatial cross-correlated diffusion is demonstrated using experimental measurements that show a clear dependence on pair angles. An analytical solution is proposed to explain the experimental observations. A numerical simulation is performed to systemically demonstrate the influence of shear flow on spatial cross-correlated diffusion. The results of the experiment, theoretical analysis, and numerical simulation agree well with each other. Therefore, this research provides a sensitive experimental method to determine the weak shear flow in any quasi-two-dimensional fluid systems.
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Affiliation(s)
- Na Li
- State Key Laboratory of Surface Physics and Department of Physics , Fudan University , Shanghai 200438 , China
| | - Wei Zhang
- School of Physical Science and Technology , China University of Mining and Technology , Xuzhou 221116 , China
| | - Zehui Jiang
- Department of Physics , Harbin Institute of Technology , Harbin 150001 , China
| | - Wei Chen
- State Key Laboratory of Surface Physics and Department of Physics , Fudan University , Shanghai 200438 , China
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17
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Sinha KP, Thaokar RM. Effect of ac electric field on the dynamics of a vesicle under shear flow in the small deformation regime. Phys Rev E 2018; 97:032404. [PMID: 29776071 DOI: 10.1103/physreve.97.032404] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2018] [Indexed: 11/07/2022]
Abstract
Vesicles or biological cells under simultaneous shear and electric field can be encountered in dielectrophoretic devices or designs used for continuous flow electrofusion or electroporation. In this work, the dynamics of a vesicle subjected to simultaneous shear and uniform alternating current (ac) electric field is investigated in the small deformation limit. The coupled equations for vesicle orientation and shape evolution are derived theoretically, and the resulting nonlinear equations are handled numerically to generate relevant phase diagrams that demonstrate the effect of electrical parameters on the different dynamical regimes such as tank treading (TT), vacillating breathing (VB) [called trembling (TR) in this work], and tumbling (TU). It is found that while the electric Mason number (Mn), which represents the relative strength of the electrical forces to the shear forces, promotes the TT regime, the response itself is found to be sensitive to the applied frequency as well as the conductivity ratio. While higher outer conductivity promotes orientation along the flow axis, orientation along the electric field is favored when the inner conductivity is higher. Similarly a switch of orientation from the direction of the electric field to the direction of flow is possible by a mere change of frequency when the outer conductivity is higher. Interestingly, in some cases, a coupling between electric field-induced deformation and shear can result in the system admitting an intermediate TU regime while attaining the TT regime at high Mn. The results could enable designing better dielectrophoretic devices wherein the residence time as well as the dynamical states of the vesicular suspension can be controlled as per the application.
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Affiliation(s)
- Kumari Priti Sinha
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Rochish M Thaokar
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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18
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Singh SP, Gompper G, Winkler RG. Steady state sedimentation of ultrasoft colloids. J Chem Phys 2018; 148:084901. [PMID: 29495770 DOI: 10.1063/1.5001886] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The structural and dynamical properties of ultra-soft colloids-star polymers-exposed to a uniform external force field are analyzed by applying the multiparticle collision dynamics technique, a hybrid coarse-grain mesoscale simulation approach, which captures thermal fluctuations and long-range hydrodynamic interactions. In the weak-field limit, the structure of the star polymer is nearly unchanged; however, in an intermediate regime, the radius of gyration decreases, in particular transverse to the sedimentation direction. In the limit of a strong field, the radius of gyration increases with field strength. Correspondingly, the sedimentation coefficient increases with increasing field strength, passes through a maximum, and decreases again at high field strengths. The maximum value depends on the functionality of the star polymer. High field strengths lead to symmetry breaking with trailing, strongly stretched polymer arms and a compact star-polymer body. In the weak-field-linear response regime, the sedimentation coefficient follows the scaling relation of a star polymer in terms of functionality and arm length.
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Affiliation(s)
- Sunil P Singh
- Indian Institute of Science Education and Research Bhopal, Bhopal By pass Road Bhauri, Bhopal 462 066, Madhya Pradesh, India
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation and Institute of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Roland G Winkler
- Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation and Institute of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany
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19
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Hwang MY, Kim SG, Lee HS, Muller SJ. Elastic particle deformation in rectangular channel flow as a measure of particle stiffness. SOFT MATTER 2018; 14:216-227. [PMID: 29227498 DOI: 10.1039/c7sm01829k] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
In this study, we experimentally observed and characterized soft elastic particle deformation in confined flow in a microchannel with a rectangular cross-section. Hydrogel microparticles of pNIPAM were produced using two different concentrations of crosslinker. This resulted in particles with two different shear moduli of 13.3 ± 5.5 Pa and 32.5 ± 15.7 Pa and compressive moduli of 66 ± 10 Pa and 79 ± 15 Pa, respectively, as measured by capillary micromechanics. Under flow, the particle shapes transitioned from circular to egg, triangular, arrowhead, and ultimately parachute shaped with increasing shear rate. The shape changes were reversible, and deformed particles relaxed back to circular/spherical in the absence of flow. The thresholds for each shape transition were quantified using a non-dimensional radius of curvature at the tip, particle deformation, circularity, and the depth of the concave dimple at the trailing edge. Several of the observed shapes were distinct from those previously reported in the literature for vesicles and capsules; the elastic particles had a narrower leading tip and a lower circularity. Due to variations in the shear moduli between particles within a batch of particles, each flow rate corresponded to a small but finite range of capillary number (Ca) and resulted in a series of shapes. By arranging the images on a plot of Ca versus circularity, a direct correlation was developed between shape and Ca and thus between particle deformation and shear modulus. As the shape was very sensitive to differences in shear modulus, particle deformation in confined flow may allow for better differentiation of microparticle shear modulus than other methods.
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Affiliation(s)
- Margaret Y Hwang
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720, USA.
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20
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Kim Y, Lai MC, Seol Y. Numerical simulations of vesicle and bubble dynamics in two-dimensional four-roll mill flows. Phys Rev E 2017; 95:053105. [PMID: 28618515 DOI: 10.1103/physreve.95.053105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2017] [Indexed: 11/07/2022]
Abstract
We use a computational technique based on the immersed boundary method to construct a four-roll mill device with which we can generate a broad spectrum of flow types from an extensional flow to a rotational one. We put a vesicle or a bubble in the constructed four-roll mill device to investigate their interaction with the surrounding fluid. The vesicle dynamics are determined by its bending rigidity, inextensibility, and hydrodynamical force, whereas the bubble dynamics is governed by the surface tension and the hydrodynamic interaction. Depending on the type of the flow, these suspended objects go through either a tank-treading motion or a tumbling motion. We validate our numerical method by a convergence study and discuss the transition between tank-treading and tumbling motions for the vesicles and bubbles.
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Affiliation(s)
- Yongsam Kim
- Department of Mathematics, Chung-Ang University, Dongjakgu, Heukseokdong, Seoul, 156-756, Republic of Korea
| | - Ming-Chih Lai
- Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan
| | - Yunchang Seol
- National Center for Theoretical Sciences, No. 1, Sec. 4, Road. Roosevelt, National Taiwan University, Taipei 10617, Taiwan
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21
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Sachin Krishnan TV, Okamoto R, Komura S. Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid. Phys Rev E 2017; 94:062414. [PMID: 28085330 DOI: 10.1103/physreve.94.062414] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2016] [Indexed: 11/07/2022]
Abstract
We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. First we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers. Two types of instabilities are identified: a small wavelength instability and a larger wavelength instability. Considering the bulk fluid viscosity and the inter-monolayer friction as the dissipation sources, we next employ Onsager's variational principle to derive the coupled equations both for the membrane and the bulk fluid. The three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle. Most importantly, a higher fluid viscosity inside the vesicle shifts the crossover mode between the bending and the slipping to a larger value. As the vesicle parameters approach the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly. In some limiting cases, our general result reduces to the previously obtained relaxation rates.
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Affiliation(s)
- T V Sachin Krishnan
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan.,Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Ryuichi Okamoto
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - Shigeyuki Komura
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan
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22
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Plan ELCVIM, Vincenzi D. Tumbling of a Brownian particle in an extensional flow. Proc Math Phys Eng Sci 2016. [DOI: 10.1098/rspa.2016.0226] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The phenomenon of tumbling of microscopic objects is commonly associated with shear flows. We address the question of whether tumbling can also occur in stretching-dominated flows. To answer this, we study the dynamics of a semi-flexible trumbbell in a planar extensional velocity field. We show that the trumbbell undergoes a random tumbling-through-folding motion. The probability distribution of long tumbling times is exponential with a time scale exponentially increasing with the Weissenberg number.
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Liu K, Hamilton C, Allard J, Lowengrub J, Li S. Wrinkling dynamics of fluctuating vesicles in time-dependent viscous flow. SOFT MATTER 2016; 12:5663-5675. [PMID: 27136977 PMCID: PMC4927358 DOI: 10.1039/c6sm00499g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We study the fully nonlinear, nonlocal dynamics of two-dimensional vesicles in a time-dependent, incompressible viscous flow at finite temperature. We focus on a transient instability that can be observed when the direction of applied flow is suddenly reversed, which induces compressive forces on the vesicle interface, and small-scale interface perturbations known as wrinkles develop. These wrinkles are driven by regions of negative elastic tension on the membrane. Using a stochastic immersed boundary method with a biophysically motivated choice of thermal fluctuations, we investigate the wrinkling dynamics numerically. Different from deterministic wrinkling dynamics, thermal fluctuations lead to symmetry-breaking wrinkling patterns by exciting higher order modes. This leads to more rapid and more realistic wrinkling dynamics. Our results are in excellent agreement with the experimental data by Kantsler et al. [Kantsler et al., Phys. Rev. Lett., 2007, 99, 17802]. We compare the nonlinear simulation results with perturbation theory, modified to account for thermal fluctuations. The strength of the applied flow strongly influences the most unstable wavelength characterizing the wrinkles, and there are significant differences between the results from perturbation theory and the fully nonlinear simulations, which suggests that the perturbation theory misses important nonlinear interactions. Strikingly, we find that thermal fluctuations actually have the ability to attenuate variability of the characteristic wavelength of wrinkling by exciting a wider range of modes than the deterministic case, which makes the evolution less constrained and enables the most unstable wavelength to emerge more readily. We further find that thermal noise helps prevent the vesicle from rotating if it is misaligned with the direction of the applied extensional flow.
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Affiliation(s)
- Kai Liu
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, USA. and Department of Mathematics, University of California in Irvine, Irvine, USA
| | - Caleb Hamilton
- Department of Mathematics, University of California in Irvine, Irvine, USA
| | - Jun Allard
- Department of Mathematics, University of California in Irvine, Irvine, USA and Department of Physics, University of California in Irvine, USA
| | - John Lowengrub
- Department of Mathematics, University of California in Irvine, Irvine, USA
| | - Shuwang Li
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, USA.
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24
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Subramaniam DR, Gee DJ. Shape oscillations of elastic particles in shear flow. J Mech Behav Biomed Mater 2016; 62:534-544. [PMID: 27294284 DOI: 10.1016/j.jmbbm.2016.05.031] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Revised: 05/21/2016] [Accepted: 05/24/2016] [Indexed: 11/26/2022]
Abstract
Particle suspensions are common to biological fluid flows; for example, flow of red- and white-blood cells, and platelets. In medical technology, current and proposed methods for drug delivery use membrane-bounded liquid capsules for transport via the microcirculation. In this paper, we consider a 3D linear elastic particle inserted into a Newtonian fluid and investigate the time-dependent deformation using a numerical simulation. Specifically, a boundary element technique is used to investigate the motion and deformation of initially spherical or spheroidal particles in bounded linear shear flow. The resulting deformed shapes reveal a steady-state profile that exhibits a 'tank-treading' motion for initially spherical particles. Wall effects on particle trajectory are seen to include a modified Jeffrey׳s orbit for spheroidal inclusions with a period that varies inversely with the strength of the shear flow. Alternately, spheroidal inclusions may exhibit either a 'tumbling' or 'trembling' motion depending on the initial particle aspect ratio and the capillary number (i.e., ratio of fluid shear to elastic restoring force). We find for a capillary number of 0.1, a tumbling mode transitions to a trembling mode at an aspect ratio of 0.87 (approx.), while for a capillary number of 0.2, this transition takes place at a lower aspect ratio. These oscillatory modes are consistent with experimental observations involving similarly shaped vesicles and thus serves to validate the use of a simple elastic constitutive model to perform relevant physiological flow calculations.
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Affiliation(s)
| | - David J Gee
- Dept. of Mechanical Engineering, Gannon University, Erie, PA, USA.
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25
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Yazdani A, Li X, Em Karniadakis G. Dynamic and rheological properties of soft biological cell suspensions. RHEOLOGICA ACTA 2016; 55:433-449. [PMID: 27540271 PMCID: PMC4987001 DOI: 10.1007/s00397-015-0869-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.
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Affiliation(s)
- Alireza Yazdani
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - Xuejin Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - George Em Karniadakis
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
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26
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Dahl JB, Narsimhan V, Gouveia B, Kumar S, Shaqfeh ESG, Muller SJ. Experimental observation of the asymmetric instability of intermediate-reduced-volume vesicles in extensional flow. SOFT MATTER 2016; 12:3787-96. [PMID: 26984509 PMCID: PMC4838492 DOI: 10.1039/c5sm03004h] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Vesicles provide an attractive model system to understand the deformation of living cells in response to mechanical forces. These simple, enclosed lipid bilayer membranes are suitable for complementary theoretical, numerical, and experimental analysis. A recent study [Narsimhan, Spann, Shaqfeh, J. Fluid Mech., 2014, 750, 144] predicted that intermediate-aspect-ratio vesicles extend asymmetrically in extensional flow. Upon infinitesimal perturbation to the vesicle shape, the vesicle stretches into an asymmetric dumbbell with a cylindrical thread separating the two ends. While the symmetric stretching of high-aspect-ratio vesicles in extensional flow has been observed and characterized [Kantsler, Segre, Steinberg, Phys. Rev. Lett., 2008, 101, 048101] as well as recapitulated in numerical simulations by Narsimhan et al., experimental observation of the asymmetric stretching has not been reported. In this work, we present results from microfluidic cross-slot experiments observing this instability, along with careful characterization of the flow field, vesicle shape, and vesicle bending modulus. The onset of this shape transition depends on two non-dimensional parameters: reduced volume (a measure of vesicle asphericity) and capillary number (ratio of viscous to bending forces). We observed that every intermediate-reduced-volume vesicle that extends forms a dumbbell shape that is indeed asymmetric. For the subset of the intermediate-reduced-volume regime we could capture experimentally, we present an experimental phase diagram for asymmetric vesicle stretching that is consistent with the predictions of Narsimhan et al.
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Affiliation(s)
- Joanna B Dahl
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, CA 94720-1460, USA.
| | - Vivek Narsimhan
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Bernardo Gouveia
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, CA 94720-1460, USA.
| | - Sanjay Kumar
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, CA 94720-1460, USA. and Department of Bioengineering, University of California, Berkeley, Berkeley, CA 94720-1762, USA
| | - Eric S G Shaqfeh
- Department of Chemical Engineering, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA and Institute of Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Susan J Muller
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, CA 94720-1460, USA.
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28
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Varshney A, Afik E, Kaplan Y, Steinberg V. Oscillatory elastic instabilities in an extensional viscoelastic flow. SOFT MATTER 2016; 12:2186-2191. [PMID: 26758020 DOI: 10.1039/c5sm02415c] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Dilute polymer solutions are known to exhibit purely elastic instabilities even when the fluid inertia is negligible. Here we report the quantitative evidence of two consecutive oscillatory elastic instabilities in an elongation flow of a dilute polymer solution as realized in a T-junction geometry with a long recirculating cavity. The main result reported here is the observation and characterization of the first transition as a forward Hopf bifurcation resulted in a uniformly oscillating state due to breaking of time translational invariance. This unexpected finding is in contrast with previous experiments and numerical simulations performed in similar ranges of the Wi and Re numbers, where the forward fork-bifurcation into a steady asymmetric flow due to the broken spatial inversion symmetry was reported. We discuss the plausible discrepancy between our findings and previous studies that could be attributed to the long recirculating cavity, where the length of the recirculating cavity plays a crucial role in the breaking of time translational invariance instead of the spatial inversion. The second transition is manifested via time aperiodic transverse fluctuations of the interface between the dyed and undyed fluid streams at the channel junction and advected downstream by the mean flow. Both instabilities are characterized by fluid discharge-rate and simultaneous imaging of the interface between the dyed and undyed fluid streams in the outflow channel.
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Affiliation(s)
- Atul Varshney
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel 76100.
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29
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Barrett JW, Garcke H, Nürnberg R. Numerical computations of the dynamics of fluidic membranes and vesicles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052704. [PMID: 26651720 DOI: 10.1103/physreve.92.052704] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2015] [Indexed: 06/05/2023]
Abstract
Vesicles and many biological membranes are made of two monolayers of lipid molecules and form closed lipid bilayers. The dynamical behavior of vesicles is very complex and a variety of forms and shapes appear. Lipid bilayers can be considered as a surface fluid and hence the governing equations for the evolution include the surface (Navier-)Stokes equations, which in particular take the membrane viscosity into account. The evolution is driven by forces stemming from the curvature elasticity of the membrane. In addition, the surface fluid equations are coupled to bulk (Navier-)Stokes equations. We introduce a parametric finite-element method to solve this complex free boundary problem and present the first three-dimensional numerical computations based on the full (Navier-)Stokes system for several different scenarios. For example, the effects of the membrane viscosity, spontaneous curvature, and area difference elasticity (ADE) are studied. In particular, it turns out, that even in the case of no viscosity contrast between the bulk fluids, the tank treading to tumbling transition can be obtained by increasing the membrane viscosity. Besides the classical tank treading and tumbling motions, another mode (called the transition mode in this paper, but originally called the vacillating-breathing mode and subsequently also called trembling, transition, and swinging mode) separating these classical modes appears and is studied by us numerically. We also study how features of equilibrium shapes in the ADE and spontaneous curvature models, like budding behavior or starfish forms, behave in a shear flow.
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Affiliation(s)
- John W Barrett
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Harald Garcke
- Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
| | - Robert Nürnberg
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
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30
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Selective flow-induced vesicle rupture to sort by membrane mechanical properties. Sci Rep 2015; 5:13163. [PMID: 26302783 PMCID: PMC4548244 DOI: 10.1038/srep13163] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2015] [Accepted: 07/10/2015] [Indexed: 01/01/2023] Open
Abstract
Vesicle and cell rupture caused by large viscous stresses in ultrasonication is central to biomedical and bioprocessing applications. The flow-induced opening of lipid membranes can be exploited to deliver drugs into cells, or to recover products from cells, provided that it can be obtained in a controlled fashion. Here we demonstrate that differences in lipid membrane and vesicle properties can enable selective flow-induced vesicle break-up. We obtained vesicle populations with different membrane properties by using different lipids (SOPC, DOPC, or POPC) and lipid:cholesterol mixtures (SOPC:chol and DOPC:chol). We subjected vesicles to large deformations in the acoustic microstreaming flow generated by ultrasound-driven microbubbles. By simultaneously deforming vesicles with different properties in the same flow, we determined the conditions in which rupture is selective with respect to the membrane stretching elasticity. We also investigated the effect of vesicle radius and excess area on the threshold for rupture, and identified conditions for robust selectivity based solely on the mechanical properties of the membrane. Our work should enable new sorting mechanisms based on the difference in membrane composition and mechanical properties between different vesicles, capsules, or cells.
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31
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Kolahdouz EM, Salac D. Dynamics of three-dimensional vesicles in dc electric fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012302. [PMID: 26274157 DOI: 10.1103/physreve.92.012302] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2015] [Indexed: 06/04/2023]
Abstract
A numerical and systematic parameter study of three-dimensional vesicle electrohydrodynamics is presented to investigate the effects of varying electric field strength and different fluid and membrane properties. The dynamics of vesicles in the presence of dc electric fields is considered, in both the presence and absence of linear shear flow. For suspended vesicles it is shown that the conductivity ratio and viscosity ratio between the interior and exterior fluids, as well as the vesicle membrane capacitance, substantially affect the minimum electric field strength required to induce a full prolate-oblate-prolate transition. In addition, there exists a critical electric field strength above which a vesicle will no longer tumble when exposed to linear shear flow.
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Affiliation(s)
- Ebrahim M Kolahdouz
- Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, New York 14226, USA
| | - David Salac
- Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, New York 14226, USA
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32
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Niu X, Pan TW, Glowinski R. The dynamics of inextensible capsules in shear flow under the effect of the natural state. Biomech Model Mechanobiol 2014; 14:865-76. [DOI: 10.1007/s10237-014-0641-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Accepted: 12/09/2014] [Indexed: 11/29/2022]
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Aland S, Egerer S, Lowengrub J, Voigt A. Diffuse interface models of locally inextensible vesicles in a viscous fluid. JOURNAL OF COMPUTATIONAL PHYSICS 2014; 277:32-47. [PMID: 25246712 PMCID: PMC4169042 DOI: 10.1016/j.jcp.2014.08.016] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid with inertial forces. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. We introduce a new equation for the local Lagrange multiplier whose solution essentially provides a harmonic extension of the multiplier off the interface while maintaining the local inextensibility constraint near the interface. We also develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. Asymptotic analysis is presented that shows that our new system converges to a relaxed version of the inextensible sharp interface model. This is also verified numerically. To solve the equations, we use an adaptive finite element method with implicit coupling between the Navier-Stokes and the diffuse interface inextensibility equations. Numerical simulations of a single vesicle in a shear flow at different Reynolds numbers demonstrate that errors in enforcing local inextensibility may accumulate and lead to large differences in the dynamics in the tumbling regime and smaller differences in the inclination angle of vesicles in the tank-treading regime. The local relaxation algorithm is shown to prevent the accumulation of stretching and compression errors very effectively. Simulations of two vesicles in an extensional flow show that local inextensibility plays an important role when vesicles are in close proximity by inhibiting fluid drainage in the near contact region.
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Affiliation(s)
- Sebastian Aland
- Institut für wissenschaftliches Rechnen, TU Dresden, 01062 Dresden, Germany
| | - Sabine Egerer
- Institut für wissenschaftliches Rechnen, TU Dresden, 01062 Dresden, Germany
| | - John Lowengrub
- Department of Mathematics, and Department of Biomedical Engineering, UC Irvine, Irvine, CA 92697, USA
| | - Axel Voigt
- Institut für wissenschaftliches Rechnen, TU Dresden, 01062 Dresden, Germany
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35
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Guedda M, Benlahsen M, Misbah C. Rheological properties of a vesicle suspension. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052302. [PMID: 25493791 DOI: 10.1103/physreve.90.052302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2014] [Indexed: 06/04/2023]
Abstract
The rheological behavior of a dilute suspension of vesicles in linear shear flow at a finite concentration is analytically examined. In the quasispherical limit, two coupled nonlinear equations that describe the vesicle orientation in the flow and its shape evolution were derived [Phys. Rev. Lett. 96, 028104 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.028104] and serve here as a starting point. Of special interest is to provide, for the first time, an exact analytical prediction of the time-dependent effective viscosity η_{eff} and normal stress differences N_{1} and N_{2}. Our results shed light on the effect of the viscosity ratio λ (defined as the inner over the outer fluid viscosities) as the main controlling parameter. It is shown that η_{eff},N_{1}, and N_{2} either tend to a steady state or describe a periodic time-dependent rheological response, previously reported numerically and experimentally. In particular, the shear viscosity minimum and the cusp singularities of η_{eff},N_{1}, and N_{2} at the tumbling threshold are brought to light. We also report on rheology properties for an arbitrary linear flow. We were able to obtain a constitutive law in a closed form relating the stress tensor to the strain rate tensor. It is found that the resulting constitutive markedly contrasts with classical laws known for other complex fluids, such as emulsions, capsule suspensions, and dilute polymer solutions (Oldroyd B model). We highlight the main differences between our law and classical laws.
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Affiliation(s)
- M Guedda
- LAMFA, CNRS UMR 7352, Département de Mathématiques, Université de Picardie Jules Verne, Amiens F-80039, France
| | - M Benlahsen
- LPMC, Département de Physique, Université de Picardie Jules Verne, Amiens F-80039, France
| | - C Misbah
- Université de Grenoble/CNRS Laboratoire Interdisciplinaire de Physique (LIPhy), UMR 5588, Grenoble F-38041, France
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36
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Lázaro GR, Hernández-Machado A, Pagonabarraga I. Rheology of red blood cells under flow in highly confined microchannels: I. effect of elasticity. SOFT MATTER 2014; 10:7195-206. [PMID: 25105872 DOI: 10.1039/c4sm00894d] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
We analyze the rheology of dilute red blood cell suspensions in pressure driven flows at low Reynolds number, in terms of the morphologies and elasticity of the cells. We focus on narrow channels of width similar to the cell diameter, when the interactions with the walls dominate the cell dynamics. The suspension presents a shear-thinning behaviour, with a Newtonian-behaviour at low shear rates, an intermediate region of strong decay of the suspension viscosity, and an asymptotic regime at high shear rates in which the effective viscosity converges to that of the solvent. We identify the relevant aspects of cell elasticity that contribute to the rheological response of blood at high confinement. In a second paper, we will explore the focusing of red blood cells while flowing at high shear rates and how this effect is controlled by the geometry of the channel.
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Affiliation(s)
- Guillermo R Lázaro
- Departament d'Estructura i Constituents de la Materia, Universitat de Barcelona, Av. Diagonal 647, E08028 Barcelona, Spain.
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37
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Abreu D, Levant M, Steinberg V, Seifert U. Fluid vesicles in flow. Adv Colloid Interface Sci 2014; 208:129-41. [PMID: 24630339 DOI: 10.1016/j.cis.2014.02.004] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2013] [Revised: 02/05/2014] [Accepted: 02/05/2014] [Indexed: 12/20/2022]
Abstract
We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.
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38
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Geislinger TM, Franke T. Hydrodynamic lift of vesicles and red blood cells in flow--from Fåhræus & Lindqvist to microfluidic cell sorting. Adv Colloid Interface Sci 2014; 208:161-76. [PMID: 24674656 DOI: 10.1016/j.cis.2014.03.002] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2014] [Revised: 02/28/2014] [Accepted: 03/02/2014] [Indexed: 12/31/2022]
Abstract
Hydrodynamic lift forces acting on cells and particles in fluid flow receive ongoing attention from medicine, mathematics, physics and engineering. The early findings of Fåhræus & Lindqvist on the viscosity change of blood with the diameter of capillaries motivated extensive studies both experimentally and theoretically to illuminate the underlying physics. We review this historical development that led to the discovery of the inertial and non-inertial lift forces and elucidate the origins of these forces that are still not entirely clear. Exploiting microfluidic techniques induced a tremendous amount of new insights especially into the more complex interactions between the flow field and deformable objects like vesicles or red blood cells. We trace the way from the investigation of single cell dynamics to the recent developments of microfluidic techniques for particle and cell sorting using hydrodynamic forces. Such continuous and label-free on-chip cell sorting devices promise to revolutionize medical analyses for personalized point-of-care diagnosis. We present the state-of-the-art of different hydrodynamic lift-based techniques and discuss their advantages and limitations.
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39
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Levant M, Steinberg V. Complex dynamics of compound vesicles in linear flow. PHYSICAL REVIEW LETTERS 2014; 112:138106. [PMID: 24745463 DOI: 10.1103/physrevlett.112.138106] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2013] [Indexed: 06/03/2023]
Abstract
We report first experimental observations of dynamics of compound vesicles in linear flow realized in a microfluidic four-roll mill. We show that while a compound vesicle undergoes the same main tank-treading, trembling (TR), and tumbling regimes, its dynamics are far richer and more complex than that of unilamellar vesicles. A new swinging motion of the inner vesicle is found in TR in accord with simulations. The inner and outer vesicles can exist simultaneously in different dynamical regimes and can undergo either synchronized or unsynchronized motions depending on the filling factor. A compound vesicle can be used as a physical model to study white blood cell dynamics in flow similar to a unilamellar vesicle used successfully to model anucleate cells.
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Affiliation(s)
- Michael Levant
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Victor Steinberg
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
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40
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Computational Analysis of Dynamic Interaction of Two Red Blood Cells in a Capillary. Cell Biochem Biophys 2014; 69:673-80. [DOI: 10.1007/s12013-014-9852-4] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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41
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Krüger T, Gross M, Raabe D, Varnik F. Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells. SOFT MATTER 2013; 9:9008-15. [PMID: 25353617 DOI: 10.1039/c3sm51645h] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Via computer simulations, we provide evidence that the shear rate induced red blood cell tumbling-to-tank-treading transition also occurs at quite high volume fractions, where collective effects are important. The transition takes place as the ratio of effective suspension stress to the characteristic cell membrane stress exceeds a certain value and does not explicitly depend on volume fraction or cell deformability. This value coincides with that for a transition from an orientationally less ordered to a highly ordered phase. The average cell deformation does not show any signature of transition, but rather follows a simple scaling law independent of volume fraction.
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Affiliation(s)
- Timm Krüger
- Centre for Computational Science, University College London, 20 Gordon Street, London WC1H 0AJ, UK
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42
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Honerkamp-Smith AR, Woodhouse FG, Kantsler V, Goldstein RE. Membrane viscosity determined from shear-driven flow in giant vesicles. PHYSICAL REVIEW LETTERS 2013; 111:038103. [PMID: 23909365 DOI: 10.1103/physrevlett.111.038103] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2013] [Indexed: 05/26/2023]
Abstract
The viscosity of lipid bilayer membranes plays an important role in determining the diffusion constant of embedded proteins and the dynamics of membrane deformations, yet it has historically proven very difficult to measure. Here we introduce a new method based on quantification of the large-scale circulation patterns induced inside vesicles adhered to a solid surface and subjected to simple shear flow in a microfluidic device. Particle image velocimetry based on spinning disk confocal imaging of tracer particles inside and outside of the vesicle and tracking of phase-separated membrane domains are used to reconstruct the full three-dimensional flow pattern induced by the shear. These measurements show excellent agreement with the predictions of a recent theoretical analysis, and allow direct determination of the membrane viscosity.
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Affiliation(s)
- Aurelia R Honerkamp-Smith
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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43
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Slow sedimentation and deformability of charged lipid vesicles. PLoS One 2013; 8:e68309. [PMID: 23874582 PMCID: PMC3708946 DOI: 10.1371/journal.pone.0068309] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2013] [Accepted: 05/28/2013] [Indexed: 11/19/2022] Open
Abstract
The study of vesicles in suspension is important to understand the complicated dynamics exhibited by cells in in vivo and in vitro. We developed a computer simulation based on the boundary-integral method to model the three dimensional gravity-driven sedimentation of charged vesicles towards a flat surface. The membrane mechanical behavior was modeled using the Helfrich Hamiltonian and near incompressibility of the membrane was enforced via a model which accounts for the thermal fluctuations of the membrane. The simulations were verified and compared to experimental data obtained using suspended vesicles labelled with a fluorescent probe, which allows visualization using fluorescence microscopy and confers the membrane with a negative surface charge. The electrostatic interaction between the vesicle and the surface was modeled using the linear Derjaguin approximation for a low ionic concentration solution. The sedimentation rate as a function of the distance of the vesicle to the surface was determined both experimentally and from the computer simulations. The gap between the vesicle and the surface, as well as the shape of the vesicle at equilibrium were also studied. It was determined that inclusion of the electrostatic interaction is fundamental to accurately predict the sedimentation rate as the vesicle approaches the surface and the size of the gap at equilibrium, we also observed that the presence of charge in the membrane increases its rigidity.
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44
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Abreu D, Seifert U. Noisy nonlinear dynamics of vesicles in flow. PHYSICAL REVIEW LETTERS 2013; 110:238103. [PMID: 25167533 DOI: 10.1103/physrevlett.110.238103] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2013] [Indexed: 05/28/2023]
Abstract
We present a model for the dynamics of fluid vesicles in linear flow which consistently includes thermal fluctuations and nonlinear coupling between different modes. At the transition between tank treading and tumbling, we predict a trembling motion which is at odds with the known deterministic motions and for which thermal noise is strongly amplified. In particular, highly asymmetric shapes are observed even though the deterministic flow only allows for axisymmetric ones. Our results explain quantitatively recent experimental observations [Levant and Steinberg, Phys. Rev. Lett. 109, 268103 (2012)].
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Affiliation(s)
- David Abreu
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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45
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Levant M, Steinberg V. Amplification of thermal noise by vesicle dynamics. PHYSICAL REVIEW LETTERS 2012; 109:268103. [PMID: 23368624 DOI: 10.1103/physrevlett.109.268103] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2012] [Indexed: 06/01/2023]
Abstract
A novel noise amplification mechanism resulting from the interaction of thermal fluctuations and nonlinear vesicle dynamics is reported. It is observed in a time-dependent vesicle state called trembling (TR). High spatial resolution and very long time series of TR compared to the vesicle period allow us to quantitatively analyze the generation and amplification of spatial and temporal modes of the vesicle shape perturbations. During a compression part of each TR cycle, a vesicle finds itself on the edge of the wrinkling instability, where thermally excited spatial modes are amplified.
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Affiliation(s)
- Michael Levant
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, Israel
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46
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Kim Y, Lai MC. Numerical study of viscosity and inertial effects on tank-treading and tumbling motions of vesicles under shear flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:066321. [PMID: 23368052 DOI: 10.1103/physreve.86.066321] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2011] [Revised: 09/27/2012] [Indexed: 06/01/2023]
Abstract
An inextensible vesicle under shear flow experiences a tank-treading motion on its membrane if the viscosity contrast between the interior and exterior fluids is small. Above a critical threshold of viscosity contrast, the vesicle undergoes a tumbling bifurcation. In this paper, we extend our previous work [Kim and Lai, J. Comput. Phys. 229, 4840 (2010)] to the case of different viscosity and investigate the transition between the tank-treading and tumbling motions in detail. The present numerical results are in a good agreement with other numerical and theoretical studies qualitatively. In addition, we study the inertial effect on this transition and find that the inertial effect might inhibit the tumbling motion in favor of the tank-treading motion, which is observed recently in the literature. The critical viscosity contrast for the transition to the tumbling motion usually increases as the reduced area increases in the Stokes regime. However, we surprisingly observe that the critical viscosity contrast decreases as the reduced area increases to some point in the flow of slightly higher Reynolds number. Our numerical result also shows that the inertial effect has stronger inhibition to tumbling motion when the reduced area is small.
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Affiliation(s)
- Yongsam Kim
- Department of Mathematics, Chung-Ang University, Dongjakgu Heukseokdong, Seoul 156-756, Korea.
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47
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Guedda M, Abaidi M, Benlahsen M, Misbah C. Dynamic modes of quasispherical vesicles: exact analytical solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:051915. [PMID: 23214822 DOI: 10.1103/physreve.86.051915] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2012] [Revised: 10/18/2012] [Indexed: 06/01/2023]
Abstract
In this paper we introduce a simple mathematical analysis to reexamine vesicle dynamics in the quasispherical limit (small deformation) under a shear flow. In this context, a recent paper [Misbah, Phys. Rev. Lett. 96, 028104 (2006)] revealed a dynamic referred to as the vacillating-breathing (VB) mode where the vesicle main axis oscillates about the flow direction and the shape undergoes a breathinglike motion, as well as the tank-treading and tumbling (TB) regimes. Our goal here is to identify these three modes by obtaining explicit analytical expressions of the vesicle inclination angle and the shape deformation. In particular, the VB regime is put in evidence and the transition dynamics is discussed. Not surprisingly, our finding confirms the Keller-Skalak solutions (for rigid particles) and shows that the VB and TB modes coexist, and whether one prevails over the other depends on the initial conditions. An interesting additional element in the discussion is the prediction of the TB and VB modes as functions of a control parameter Γ, which can be identified as a TB-VB parameter.
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Affiliation(s)
- M Guedda
- Université de Picardie Jules Verne, LAMFA CNRS UMR 7352, Amiens F-80039, France.
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48
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Holme MN, Fedotenko IA, Abegg D, Althaus J, Babel L, Favarger F, Reiter R, Tanasescu R, Zaffalon PL, Ziegler A, Müller B, Saxer T, Zumbuehl A. Shear-stress sensitive lenticular vesicles for targeted drug delivery. NATURE NANOTECHNOLOGY 2012; 7:536-43. [PMID: 22683843 DOI: 10.1038/nnano.2012.84] [Citation(s) in RCA: 193] [Impact Index Per Article: 16.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2012] [Accepted: 04/30/2012] [Indexed: 05/20/2023]
Abstract
Atherosclerosis results in the narrowing of arterial blood vessels and this causes significant changes in the endogenous shear stress between healthy and constricted arteries. Nanocontainers that can release drugs locally with such rheological changes can be very useful. Here, we show that vesicles made from an artificial 1,3-diaminophospholipid are stable under static conditions but release their contents at elevated shear stress. These vesicles have a lenticular morphology, which potentially leads to instabilities along their equator. Using a model cardiovascular system based on polymer tubes and an external pump to represent shear stress in healthy and constricted vessels of the heart, we show that drugs preferentially release from the vesicles in constricted vessels that have high shear stress.
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Affiliation(s)
- Margaret N Holme
- University of Geneva, Department of Organic Chemistry, Quai Ernest-Ansermet 30, 1211 Geneva, Switzerland
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49
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Abreu D, Seifert U. Effect of thermal noise on vesicles and capsules in shear flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:010902. [PMID: 23005361 DOI: 10.1103/physreve.86.010902] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2012] [Indexed: 06/01/2023]
Abstract
We add thermal noise consistently to reduced models of undeformable vesicles and capsules in shear flow and derive analytically the corresponding stochastic equations of motion. We calculate the steady-state probability distribution function and construct the corresponding phase diagrams for the different dynamical regimes. For fluid vesicles, we predict that at small shear rates thermal fluctuations induce a tumbling motion for any viscosity contrast. For elastic capsules, due to thermal mixing, an intermittent regime appears in regions where deterministic models predict only pure tank treading or tumbling.
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Affiliation(s)
- David Abreu
- II Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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50
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Yazdani A, Bagchi P. Three-dimensional numerical simulation of vesicle dynamics using a front-tracking method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:056308. [PMID: 23004863 DOI: 10.1103/physreve.85.056308] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2011] [Indexed: 06/01/2023]
Abstract
Three-dimensional numerical simulation using the front-tracking method is presented on the dynamics of a vesicle in a linear shear flow. The focus here is to elucidate the parametric dependence and the self-similarity of the vesicle dynamics, quantification of vesicle deformation, and the analysis of shape dynamics. A detailed comparison of the numerical results is made with various theoretical models and experiments. It is found that the applicability of the theoretical models is limited despite some general agreement with the simulations and experiments. The deviations between the perturbative results and the simulation results occur even in the absence of thermal noise. Specifically, we find that the vesicle dynamics does not follow a self-similar behavior in a two-parameter phase space, as proposed in a theoretical model. Rather, the dynamics is governed by three controlling parameters, namely, the excess area, viscosity ratio, and dimensionless shear rate. Additionally, we find that a linear scaling of the tank-treading angle, as proposed in the theoretical model, is possible only for nearly spherical vesicles. The breakdown of the scaling occurs at higher values of the excess area even in the absence of thermal noise. We find that the vesicle deformation saturates at large shear rates, and the asymptotic deformation matches well with a theoretical prediction for nearly spherical vesicles. The dependence of the critical viscosity ratio associated with the onset of unsteady dynamics on the vesicle excess area is in excellent agreement with the experimental observation. We show that near the transition between the tank-treading and tumbling dynamics, both the vacillating-breathing-like motion characterized by a smooth ellipsoidal shape and the trembling-like motion characterized by a highly deformed shape are possible. For the trembling-like motion, the shape is highly three-dimensional with concavities and lobes, and the vesicle deforms more in the vorticity direction than in the shear plane. A Fourier spectral analysis of the vesicle shape shows the presence of the odd harmonics and higher order modes beyond fourth order.
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Affiliation(s)
- Alireza Yazdani
- Department of Mechanical & Aerospace Engineering, Rutgers University, the State University of New Jersey, Piscataway, 08854, USA
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