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Levant M, Steinberg V. Intermediate regime and a phase diagram of red blood cell dynamics in a linear flow. Phys Rev E 2017; 94:062412. [PMID: 28085369 DOI: 10.1103/physreve.94.062412] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2016] [Indexed: 11/07/2022]
Abstract
In this paper we investigate the in vitro dynamics of a single rabbit red blood cell (RBC) in a planar linear flow as a function of a shear stress σ and the dynamic viscosity of outer fluid η_{o}. A linear flow is a generalization of previous studies dynamics of soft objects including RBC in shear flow and is realized in the experiment in a microfluidic four-roll mill device. We verify that the RBC stable orientation dynamics is found in the experiment being the in-shear-plane orientation and the RBC dynamics is characterized by observed three RBC dynamical states, namely tumbling (TU), intermediate (INT), and swinging (SW) [or tank-treading (TT)] on a single RBC. The main results of these studies are the following. (i) We completely characterize the RBC dynamical states and reconstruct their phase diagram in the case of the RBC in-shear-plane orientation in a planar linear flow and find it in a good agreement with that obtained in early experiments in a shear flow for human RBCs. (ii) The value of the critical shear stress σ_{c} of the TU-TT(SW) transition surprisingly coincides with that found in early experiments in spite of a significant difference in the degree of RBC shape deformations in both the SW and INT states. (iii) We describe the INT regime, which is stationary, characterized by strong RBC shape deformations and observed in a wide range of the shear stresses. We argue that our observations cast doubts on the main claim of the recent numerical simulations that the only RBC spheroidal stress-free shape is capable to explain the early experimental data. Finally, we suggest that the amplitude dependence of both θ and the shape deformation parameter D on σ can be used as the quantitative criterion to determine the RBC stress-free shape.
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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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Abstract
Isolated microfluidic stagnation points – formed within microfluidic interfaces – have come a long way as a tool for characterizing materials, manipulating micro particles, and generating confined flows and localized chemistries.
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Affiliation(s)
- Ayoola T. Brimmo
- Division of Engineering
- New York University Abu Dhabi
- Abu Dhabi
- UAE
- Tandon School of Engineering
| | - Mohammad A. Qasaimeh
- Division of Engineering
- New York University Abu Dhabi
- Abu Dhabi
- UAE
- Tandon School of Engineering
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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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Kaoui B, Jonk RJW, Harting J. Interplay between microdynamics and macrorheology in vesicle suspensions. SOFT MATTER 2014; 10:4735-4742. [PMID: 24851823 DOI: 10.1039/c4sm00563e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The microscopic dynamics of objects suspended in a fluid determines the macroscopic rheology of a suspension. For example, as shown by Danker and Misbah [Phys. Rev. Lett., 2007, 98, 088104], the viscosity of a dilute suspension of fluid-filled vesicles is a non-monotonic function of the viscosity contrast (the ratio between the viscosities of the internal encapsulated and the external suspending fluids) and exhibits a minimum at the critical point of the tank-treading-to-tumbling transition. By performing numerical simulations, we recover this effect and demonstrate that it persists for a wide range of vesicle parameters such as the concentration, membrane deformability, or swelling degree. We also explain why other numerical and experimental studies lead to contradicting results. Furthermore, our simulations show that this effect even persists in non-dilute and confined suspensions, but that it becomes less pronounced at higher concentrations and for more swollen vesicles. For dense suspensions and for spherical (circular in 2D) vesicles, the intrinsic viscosity tends to depend weakly on the viscosity contrast.
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Affiliation(s)
- Badr Kaoui
- Theoretical Physics I, University of Bayreuth, Universitätsstrasse 30, D-95447 Bayreuth, Germany.
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Gross M, Krüger T, Varnik F. Rheology of dense suspensions of elastic capsules: normal stresses, yield stress, jamming and confinement effects. SOFT MATTER 2014; 10:4360-72. [PMID: 24796957 DOI: 10.1039/c4sm00081a] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
We study the shearing rheology of dense suspensions of elastic capsules, taking aggregation-free red blood cells as a physiologically relevant example. Particles are non-Brownian and interact only via hydrodynamics and short-range repulsive forces. An analysis of the different stress mechanisms in the suspension shows that the viscosity is governed by the shear elasticity of the capsules, whereas the repulsive forces are subdominant. Evidence for a dynamic yield stress above a critical volume fraction is provided and related to the elastic properties of the capsules. The shear stress is found to follow a critical jamming scenario and is rather insensitive to the tumbling-to-tank-treading transition. The particle pressure and normal stress differences display some sensitivity to the dynamical state of the cells and exhibit a characteristic scaling, following the behavior of a single particle, in the tank-treading regime. The behavior of the viscosity in the fluid phase is rationalized in terms of effective medium models. Furthermore, the role of confinement effects, which increase the overall magnitude and enhance the shear-thinning of the viscosity, is discussed.
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Affiliation(s)
- Markus Gross
- Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, Universitätsstr. 150, 44780 Bochum, Germany.
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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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Minetti C, Podgorski T, Coupier G, Dubois F. Fully automated digital holographic processing for monitoring the dynamics of a vesicle suspension under shear flow. BIOMEDICAL OPTICS EXPRESS 2014; 5:1554-68. [PMID: 24877015 PMCID: PMC4026899 DOI: 10.1364/boe.5.001554] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2014] [Revised: 04/10/2014] [Accepted: 04/11/2014] [Indexed: 05/16/2023]
Abstract
We investigate the dynamics of a vesicle suspension under shear flow between plates using DHM with a spatially reduced coherent source. Holograms are grabbed at a frequency of 24 frames/sec. The distribution of the vesicle suspension is obtained after numerical processing of the digital holograms sequence resulting in a 4D distribution. Obtaining this distribution is not straightforward and requires special processing to automate the analysis. We present an original method that fully automates the analysis and provides distributions that are further analyzed to extract physical properties of the fluid. Details of the numerical implementation, as well as sample experimental results are presented.
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Affiliation(s)
- Christophe Minetti
- Service de Chimie-Physique EP, Université libre de Bruxelles, 50 Avenue F. Roosevelt, CP16/62, B-1050 Brussels, Belgium
| | - Thomas Podgorski
- Laboratoire Interdisciplinaire de Physique, CNRS-UMR 5588, Université Grenoble I, B.P. 87, 38402 Saint Martin d’Hères Cedex, France
| | - Gwennou Coupier
- Laboratoire Interdisciplinaire de Physique, CNRS-UMR 5588, Université Grenoble I, B.P. 87, 38402 Saint Martin d’Hères Cedex, France
| | - Frank Dubois
- Service de Chimie-Physique EP, Université libre de Bruxelles, 50 Avenue F. Roosevelt, CP16/62, B-1050 Brussels, Belgium
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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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Thiébaud M, Misbah C. Rheology of a vesicle suspension with finite concentration: a numerical study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062707. [PMID: 24483486 DOI: 10.1103/physreve.88.062707] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2013] [Revised: 10/14/2013] [Indexed: 06/03/2023]
Abstract
Vesicles, closed membranes made of a bilayer of phospholipids, are considered as a biomimetic system for the mechanics of red blood cells. The understanding of their dynamics under flow and their rheology is expected to help the understanding of the behavior of blood flow. We conduct numerical simulations of a suspension of vesicles in two dimensions at a finite concentration in a shear flow imposed by countertranslating rigid bounding walls by using an appropriate Green's function. We study the dynamics of vesicles, their spatial configurations, and their rheology, namely, the effective viscosity η(eff). A key parameter is the viscosity contrast λ (the ratio between the viscosity of the encapsulated fluid over that of the suspending fluid). For small enough λ, vesicles are known to exhibit tank treading (TT), while at higher λ they exhibit tumbling (TB). We find that η(eff) decreases in the TT regime, passes a minimum at a critical λ=λ(c), and increases in the TB regime. This result confirms previous theoretical and numerical works performed in the extremely dilute regime, pointing to the robustness of the picture even in the presence of hydrodynamic interactions. Our results agree also with very recent numerical simulations performed in three dimensions both in the dilute and more concentrated regime. This points to the fact that dimensionality does not alter the qualitative features of η(eff). However, they disagree with recent simulations in two dimensions. We provide arguments about the possible sources of this disagreement.
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Affiliation(s)
- Marine Thiébaud
- Laboratoire Interdisciplinaire de Physique/UMR5588, Université Grenoble I/CNRS, Grenoble F-38041, France
| | - Chaouqi Misbah
- Laboratoire Interdisciplinaire de Physique/UMR5588, Université Grenoble I/CNRS, Grenoble F-38041, France
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Omori T, Ishikawa T, Imai Y, Yamaguchi T. Membrane tension of red blood cells pairwisely interacting in simple shear flow. J Biomech 2013; 46:548-53. [DOI: 10.1016/j.jbiomech.2012.09.017] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2012] [Revised: 09/18/2012] [Accepted: 09/24/2012] [Indexed: 10/27/2022]
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Li, X, Vlahovska PM, Karniadakis GE. Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease. SOFT MATTER 2013; 9:28-37. [PMID: 23230450 PMCID: PMC3516861 DOI: 10.1039/c2sm26891d] [Citation(s) in RCA: 64] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
We review recent advances in multiscale modeling of the mechanics of healthy and diseased red blood cells (RBCs), and blood flow in the microcirculation. We cover the traditional continuum-based methods but also particle-based methods used to model both the RBCs and the blood plasma. We highlight examples of successful simulations of blood flow including malaria and sickle cell anemia.
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Affiliation(s)
- Xuejin Li,
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
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