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Zhang X, Caruso C, Lam WA, Graham MD. Flow-induced segregation and dynamics of red blood cells in sickle cell disease. PHYSICAL REVIEW FLUIDS 2020; 5:053101. [PMID: 34095646 PMCID: PMC8174308 DOI: 10.1103/physrevfluids.5.053101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Blood flow in sickle cell disease (SCD) can substantially differ from normal blood flow due to significant alterations in the physical properties of the red blood cells (RBCs). Chronic complications, such as inflammation of the endothelial cells lining blood vessel walls, are associated with SCD, for reasons that are unclear. Here, detailed boundary integral simulations are performed to investigate an idealized model flow flow in SCD, a binary suspension of flexible biconcave discoidal fluid-filled capsules and stiff curved prolate capsules that represent healthy and sickle RBCs, respectively, subjected to pressure-driven flow in a planar slit. The stiff component is dilute. The key observation is that, unlike healthy RBCs that concentrate around the center of the channel and form an RBC-depleted layer (i.e. cell-free layer) next to the walls, sickle cells are largely drained from the bulk of the suspension and aggregate inside the cell-free layer, displaying strong margination. These cells are found to undergo a rigid-body-like rolling orbit near the walls. A binary suspension of flexible biconcave discoidal capsules and stiff straight (non-curved) prolate capsules is also considered for comparison, and the curvature of the stiff component is found to play a minor role in the behavior. Additionally, by considering a mixture of flexible and stiff biconcave discoids, we reveal that rigidity difference by itself is sufficient to induce the segregation behavior in a binary suspension. Furthermore, the additional shear stress on the walls induced by the presence of cells is computed for the various cases. Compared to the small fluctuations in wall shear stress for a suspension of healthy RBCs, large local peaks in wall shear stress are observed for the binary suspensions, due to the proximity of the marginated stiff cells to the walls. This effect is most marked for the straight prolate capsules. As endothelial cells are known to mechanotransduce physical forces such as aberrations in shear stress and convert them to physiological processes such as activation of inflammatory signals, these results may aid in understanding mechanisms for endothelial dysfunction associated with SCD.
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Affiliation(s)
- Xiao Zhang
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706-1691
| | - Christina Caruso
- Department of Pediatrics, Division of Pediatric Hematology/Oncology, Aflac Cancer and Blood Disorders Center of Children’s Healthcare of Atlanta, Emory University School of Medicine, Atlanta, GA 30322
| | - Wilbur A. Lam
- Department of Pediatrics, Division of Pediatric Hematology/Oncology, Aflac Cancer and Blood Disorders Center of Children’s Healthcare of Atlanta, Emory University School of Medicine, Atlanta, GA 30322
- Wallace H. Coulter Department of Biomedical Engineering, Emory University and Georgia Institute of Technology, Atlanta, GA 30332
- Winship Cancer Institute, Emory University, Atlanta, GA 30322
- Parker H. Petit Institute of Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, GA 30332
| | - Michael D. Graham
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706-1691
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Singha S, Malipeddi AR, Zurita-Gotor M, Sarkar K, Shen K, Loewenberg M, Migler KB, Blawzdziewicz J. Mechanisms of spontaneous chain formation and subsequent microstructural evolution in shear-driven strongly confined drop monolayers. SOFT MATTER 2019; 15:4873-4889. [PMID: 31165134 PMCID: PMC6914215 DOI: 10.1039/c9sm00536f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
It was experimentally demonstrated by Migler and his collaborators [Phys. Rev. Lett., 2001, 86, 1023; Langmuir, 2003, 19, 8667] that a strongly confined drop monolayer sheared between two parallel plates can spontaneously develop a flow-oriented drop-chain morphology. Here we show that the formation of the chain-like microstructure is driven by far-field Hele-Shaw quadrupolar interactions between drops, and that drop spacing within chains is controlled by the effective drop repulsion associated with the existence of confinement-induced reversing streamlines, i.e., the swapping trajectory effect. Using direct numerical simulations and an accurate quasi-2D model that incorporates quadrupolar and swapping-trajectory contributions, we analyze microstructural evolution in a monodisperse drop monolayer. Consistent with experimental observations, we find that drop spacing within individual chains is usually uniform. Further analysis shows that at low area fractions all chains have the same spacing, but at higher area fractions there is a large spacing variation from chain to chain. These findings are explained in terms of uncompressed and compressed chains. At low area fractions most chains are uncompressed (spacing equals lst, which is the stable separation of an isolated pair). At higher area fractions compressed chains (with tighter spacing) are formed in a process of chain zipping along y-shaped structural defects. We also discuss the relevance of our findings to other shear-driven systems, such as suspensions of spheres in non-Newtonian fluids.
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Affiliation(s)
- Sagnik Singha
- Department of Mechanical Engineering, Texas Tech University, Box 41021, Lubbock, TX 79409, USA.
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Sinha K, Graham MD. Shape-mediated margination and demargination in flowing multicomponent suspensions of deformable capsules. SOFT MATTER 2016; 12:1683-1700. [PMID: 26679746 DOI: 10.1039/c5sm02196k] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present detailed simulations and theory for flow-induced segregation in suspensions of deformable fluid-filled capsules with different shapes during simple shear flow in a planar slit. This system is an idealized model for transport for blood cells and/or drug carriers in the microcirculation or in microfluidic devices. For the simulations, an accelerated implementation of the boundary integral method was employed. We studied the binary mixtures of spherical and ellipsoidal capsules, varying the aspect ratio κ of the ellipsoid while keeping constant either (a) equatorial radius or (b) volume. Effects of a variety of parameters was studied, including κ, volume fraction and number fraction of the spherical capsules in the mixture. In suspensions where the ellipsoids have the same equatorial radius as the spheres, capsules with lower κ marginate. In suspension where the ellipsoids have the same volume as the spheres, ellipsoidal (both oblate and prolate) capsules are seen to demarginate in a mixture of primarily spherical capsules. To understand these results, a mechanistic framework based on the competition between wall-induced migration and shear-induced collisions is presented. A simplified drift-diffusion theory based on this framework shows excellent qualitative agreement with simulation results.
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Affiliation(s)
- Kushal Sinha
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706-1691, USA.
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Fornari W, Brandt L, Chaudhuri P, Lopez CU, Mitra D, Picano F. Rheology of Confined Non-Brownian Suspensions. PHYSICAL REVIEW LETTERS 2016; 116:018301. [PMID: 26799045 DOI: 10.1103/physrevlett.116.018301] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2015] [Indexed: 06/05/2023]
Abstract
We study the rheology of confined suspensions of neutrally buoyant rigid monodisperse spheres in plane-Couette flow using direct numerical simulations. We find that if the width of the channel is a (small) integer multiple of the sphere diameter, the spheres self-organize into two-dimensional layers that slide on each other and the effective viscosity of the suspension is significantly reduced. Each two-dimensional layer is found to be structurally liquidlike but its dynamics is frozen in time.
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Affiliation(s)
- Walter Fornari
- Linné Flow Centre and SeRC, KTH Mechanics, SE-100 44 Stockholm, Sweden
| | - Luca Brandt
- Linné Flow Centre and SeRC, KTH Mechanics, SE-100 44 Stockholm, Sweden
| | - Pinaki Chaudhuri
- Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
| | - Cyan Umbert Lopez
- Linné Flow Centre and SeRC, KTH Mechanics, SE-100 44 Stockholm, Sweden
| | - Dhrubaditya Mitra
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
| | - Francesco Picano
- Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131 Padova, Italy
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Sonn-Segev A, Bławzdziewicz J, Wajnryb E, Ekiel-Jeżewska ML, Diamant H, Roichman Y. Structure and dynamics of a layer of sedimented particles. J Chem Phys 2015; 143:074704. [DOI: 10.1063/1.4928644] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Adar Sonn-Segev
- Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Jerzy Bławzdziewicz
- Department of Mechanical Engineering, Texas Tech University, 7th and Boston, Lubbock, Texas 79409, USA
| | - Eligiusz Wajnryb
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, Warsaw 02-106, Poland
| | - Maria L. Ekiel-Jeżewska
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, Warsaw 02-106, Poland
| | - Haim Diamant
- Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Yael Roichman
- Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
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Henríquez Rivera RG, Sinha K, Graham MD. Margination regimes and drainage transition in confined multicomponent suspensions. PHYSICAL REVIEW LETTERS 2015; 114:188101. [PMID: 26001019 DOI: 10.1103/physrevlett.114.188101] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2015] [Indexed: 06/04/2023]
Abstract
A mechanistic theory is developed to describe segregation in confined multicomponent suspensions such as blood. It incorporates the two key phenomena arising in these systems at low Reynolds number: hydrodynamic pair collisions and wall-induced migration. In simple shear flow, several regimes of segregation arise, depending on the value of a "margination parameter" M. Most importantly, there is a critical value of M below which a sharp "drainage transition" occurs: one component is completely depleted from the bulk flow to the vicinity of the walls. Direct simulations also exhibit this transition as the size or flexibility ratio of the components changes.
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Affiliation(s)
- Rafael G Henríquez Rivera
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706-1691, USA
| | - Kushal Sinha
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706-1691, USA
| | - Michael D Graham
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706-1691, USA
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7
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Ghosh S, Mugele F, Duits MHG. Effects of shear and walls on the diffusion of colloids in microchannels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052305. [PMID: 26066175 DOI: 10.1103/physreve.91.052305] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2015] [Indexed: 06/04/2023]
Abstract
Colloidal suspensions flowing through microchannels were studied for the effects of both the shear flow and the proximity of walls on the particles' self-diffusion. Use of hydrostatic pressure to pump micron-sized silica spheres dispersed in water-glycerol mixture through poly(dimethylsiloxane) channels with a cross section of 30×24μm(2), allowed variation in the local Peclet number (Pe) from 0.01 to 50. To obtain the diffusion coefficients, image-time series from a confocal scanning laser microscope were analyzed with a method that, after finding particle trajectories, subtracts the instantaneous advective displacements and subsequently measures the slopes of the mean squared displacement in the flow (x) and shear (y) directions. For dilute suspensions, the thus obtained diffusion coefficients (D(x) and D(y)) are close to the free diffusion coefficient at all shear rates. In concentrated suspensions, a clear increase with the Peclet number (for Pe > 10) is found, that is stronger for D(x) than for D(y). This effect of shear-induced collisions is counteracted by the contribution of walls, which cause a strong local reduction in D(x) and D(y).
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Affiliation(s)
- S Ghosh
- Physics of Complex Fluids Group, Department of Science and Technology, MESA+ Institute, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands
| | - F Mugele
- Physics of Complex Fluids Group, Department of Science and Technology, MESA+ Institute, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands
| | - M H G Duits
- Physics of Complex Fluids Group, Department of Science and Technology, MESA+ Institute, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands
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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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Lin NYC, McCoy JH, Cheng X, Leahy B, Israelachvili JN, Cohen I. A multi-axis confocal rheoscope for studying shear flow of structured fluids. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2014; 85:033905. [PMID: 24689598 DOI: 10.1063/1.4868688] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We present a new design for a confocal rheoscope that enables uniform uniaxial or biaxial shear. The design consists of two precisely positioned parallel plates with a gap that can be adjusted down to 2 ±0.1 μm, allowing for the exploration of confinement effects. By using our shear cell in conjunction with a biaxial force measurement device and a high-speed confocal microscope, we are able to measure the real-time biaxial stress while simultaneously imaging the material three-dimensional structure. We illustrate the importance of the instrument capabilities by discussing the applications of this instrument in current and future research topics in colloidal suspensions.
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Affiliation(s)
- Neil Y C Lin
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Jonathan H McCoy
- Department of Physics and Astronomy, Colby College, Waterville, Maine 04901, USA
| | - Xiang Cheng
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Brian Leahy
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Jacob N Israelachvili
- Department of Chemical Engineering, and Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Itai Cohen
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
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10
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Katz JI. Mean-field model of layering instability in shearing suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:021003. [PMID: 25353411 DOI: 10.1103/physreve.89.021003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2013] [Indexed: 06/04/2023]
Abstract
Concentrated suspensions may shear thin when the suspended particles form planar sheets that slide over one another with less friction than if the particles are randomly distributed. In a naive model the suspension is described by a mean effective viscosity and particles that collide with each other redistribute the mean density in the shearing direction. This leads to a diffusion equation for the particle density. If the viscosity in the unthinned state is a steeply increasing function of particle density the effective diffusion coefficient is negative and the diffusion equation, meaningful only on scales larger than the particle separation, is ill posed. This singularity corresponds to the formation of planar sheets of particles and defines a critical particle density for the onset of shear thinning.
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Affiliation(s)
- J I Katz
- Department of Physics and McDonnell Center for the Space Sciences, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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11
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Relation between ordering and shear thinning in colloidal suspensions. Proc Natl Acad Sci U S A 2013; 110:3771-6. [PMID: 23431185 DOI: 10.1073/pnas.1301055110] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Colloidal suspensions exhibit shear thinning and shear thickening. The most common interpretation of these phenomena identifies layering of the fluid perpendicular to the shear gradient as the driver for the observed behavior. However, studies of the particle configurations associated with shear thinning and thickening cast doubt on that conclusion and leave unsettled whether these nonequilibrium phenomena are caused primarily by correlated particle motions or by changes in particle packing structure. We report the results of stokesian dynamics simulations of suspensions of hard spheres that illuminate the relation among the suspension viscosity, shear rate, and particle configuration. Using a recently introduced sampling technique for nonequilibrium systems, we show that shear thinning can be decoupled from layering, thereby eliminating layering as the driver for shear thinning. In contrast, we find that there is a strong correlation between shear thinning and a two-particle measure of the shear stress. Our results are consistent with a recent experimental study.
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Blawzdziewicz J, Wajnryb E. The swapping-trajectory effect: lattice evolution and buckling transition in wall-bounded hydrodynamic crystals. ACTA ACUST UNITED AC 2012. [DOI: 10.1088/1742-6596/392/1/012008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Kumar A, Graham MD. Mechanism of margination in confined flows of blood and other multicomponent suspensions. PHYSICAL REVIEW LETTERS 2012; 109:108102. [PMID: 23005332 DOI: 10.1103/physrevlett.109.108102] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2012] [Indexed: 05/19/2023]
Abstract
Flowing blood displays a phenomenon called margination, in which leukocytes and platelets are preferentially found near blood vessel walls, while erythrocytes are depleted from these regions. Here margination is investigated using direct hydrodynamic simulations of a binary suspension of stiff (s) and floppy (f) capsules, as well as a stochastic model that incorporates the key particle transport mechanisms in suspensions-wall-induced hydrodynamic migration and shear-induced pair collisions. The stochastic model allows the relative importance of these two mechanisms to be directly evaluated and thereby indicates that margination, at least in the dilute case, is largely due to the differential dynamics of homogeneous (e.g. s-s) and heterogeneous (s-f) collisions.
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Affiliation(s)
- Amit Kumar
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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