Coarse-grained theory to predict the concentration distribution of red blood cells in wall-bounded Couette flow at zero Reynolds number

Narsimhan, Vivek; Zhao, Hong; Shaqfeh, Eric S. G.

doi:10.1063/1.4810808

Cited by 38 publications

(42 citation statements)

References 62 publications

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“…2 shows φ p normalized by its mean volume fractionφ p . In the unconfined limit C → ∞, l d → η p /φ pc , confirming the φ −1 dependence found earlier in scaling analyses [23,25,28]. More generally, Eq.…”

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confidence: 75%

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Margination Regimes and Drainage Transition in Confined Multicomponent Suspensions

2015

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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.Introduction. Flow-induced segregation is ubiquitous in multicomponent suspensions and granular materials, including systems as disparate as hard macroscopic particles in air [1], polydisperse droplet suspensions [2], foams [3], and blood. During blood flow, the focus of the present work, both the leukocytes and platelets segregate near the vessel walls, a phenomenon known as margination, while the red blood cells (RBCs) tend to be depleted in the near-wall region, forming a so-called cell-free or depletion layer [4]. Engineering the margination process has been proposed for microfluidic cell separations in blood (e.g. [5]) as well as for enhanced drug delivery to the vasculature [6].Direct simulations of flowing multicomponent suspensions -models of blood -can capture margination phenomena [7][8][9][10][11][12][13][14][15][16], but developing a fundamental understanding of underlying mechanisms and parameterdependence from simulations is difficult. It is thus important to have a simple yet mechanistic mathematical model, ideally one with closed form solutions that reveal parameter-dependence, that can distill out the essential phenomena that drive segregation and capture the key effects and transitions. We present such a model here.Theory. We consider a dilute suspension containing N s types of deformable particles with total volume fraction φ undergoing flow in a slit bounded by no-slip walls at y = 0 and y = 2H and unbounded in x and z. Quantities referring to a specific component α in the mixture will have subscript α: for example n α is the number density of component α. We consider here only simple shear (plane Couette) flow and, consistent with the diluteness assumption, take the shear rateγ to be independent of the local number densities and thus independent of position. In a dilute suspension of particles, where φ ≪ 1, the particle-particle interactions can be treated as a sequence of uncorrelated pair collisions [17][18][19]. For the moment, we neglect molecular diffusion of the particles. This issue is further addressed below. Since the particles are deformable, they migrate away from the wall during flow with velocity v αm (y) [20,21]. The evolution of the particle number density distributions can be idealized by a kinetic master equation that captures the migration

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confidence: 75%

“…Since the particles are deformable, they migrate away from the wall during flow with velocity v αm (y) [20,21]. The evolution of the particle number density distributions can be idealized by a kinetic master equation that captures the migration and collision effects ( [16,19,22,23]). Assuming uniform particle distributions in x and z, this equation is…”

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confidence: 99%

Margination Regimes and Drainage Transition in Confined Multicomponent Suspensions

2015

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“…Couette flow simulations were used as control cases, to confirm that the specific results obtained around the pillar are related only to the flow geometry. In the Couette flow, capsules simply interact by switching positions, as observed in computations of two interacting vesicles or capsules (37) in the presence of a wall. The specific phenomenon shown in the article of capsules exploring regions very close to the pillar wall is thus the result of a combination between geometrical characteristics of the corner and multibody effects.…”

Section: Role Of the Flow Geometrymentioning

confidence: 96%

Microfluidic Study of Enhanced Deposition of Sickle Cells at Acute Corners

Loiseau

Massiera

Mendez

et al. 2015

Biophysical Journal

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Sickle cell anemia is a blood disorder, known to affect the microcirculation and is characterized by painful vaso-occlusive crises in deep tissues. During the last three decades, many scenarios based on the enhanced adhesive properties of the membrane of sickle red blood cells have been proposed, all related to a final decrease in vessels lumen by cells accumulation on the vascular walls. Up to now, none of these scenarios considered the possible role played by the geometry of the flow on deposition. The question of the exact locations of occlusive events at the microcirculatory scale remains open. Here, using microfluidic devices where both geometry and oxygen levels can be controlled, we show that the flow of a suspension of sickle red blood cells around an acute corner of a triangular pillar or of a bifurcation, leads to the enhanced deposition and aggregation of cells. Thanks to our devices, we follow the growth of these aggregates in time and show that their length does not depend on oxygenation levels; instead, we find that their morphology changes dramatically to filamentous structures when using autologous plasma as a suspending fluid. We finally discuss the possible role played by such aggregates in vaso-occlusive events.

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“…It follows that once a stiff particle reaches the near-wall CFL, it tends to remain there (34,35). This phenomenon in combination with the CFL, which arises from lift forces, is thought to be responsible for the margination of particles in blood flow (32). Further, the migration velocities and collision tendencies of particles have been linked with margination behavior (36).…”

Section: Introductionmentioning

confidence: 99%

Direct Tracking of Particles and Quantification of Margination in Blood Flow

Carboni

Bognet

Bouchillon

et al. 2016

Biophysical Journal

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Margination refers to the migration of particles toward blood vessel walls during blood flow. Understanding the mechanisms that lead to margination will aid in tailoring the attributes of drug-carrying particles for effective drug delivery. Most previous studies evaluated the margination propensity of these particles via an adhesion mechanism, i.e., by measuring the number of particles that adhered to the channel wall. Although particle adhesion and margination are related, adhesion also depends on other factors. In this study, we quantified the margination propensity of particles of varying diameters (0.53, 0.84, and 2.11 mm) and apparent wall shear rates (30, 61, and 121 s À1 ) by directly tracking fluorescent particles flowing through a microfluidic channel. The margination parameter, M, is defined as the total number of particles found within the cell-free layers normalized by the total number of particles that passed through the channel. In this study, an M-value of 0.2 indicated no margination, which was observed for all particle sizes in water. In the case of blood, larger particles were found to have higher M-values and thus marginated more effectively than smaller particles. The corresponding M-values at the device outlet were 0.203, 0.223, and 0.285 for 0.53-, 0.84-, and 2.11-mm particles, respectively. At the inlet, the M-values for all particle sizes in blood were <0.2, suggesting that non-fully-developed flow and constriction may lead to demargination. For particle velocities transverse to the flow direction (v y ), all particle sizes showed a larger standard deviation of v y as well as a higher effective diffusivity when the particles were suspended in blood relative to water. These higher values are attributed to collisions between the blood cells and particles, further supporting recent simulation results. In terms of flow rates, for a given particle size, the higher the flow rate, the higher the M-value.

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Coarse-grained theory to predict the concentration distribution of red blood cells in wall-bounded Couette flow at zero Reynolds number

Cited by 38 publications

References 62 publications

Margination Regimes and Drainage Transition in Confined Multicomponent Suspensions

Margination Regimes and Drainage Transition in Confined Multicomponent Suspensions

Microfluidic Study of Enhanced Deposition of Sickle Cells at Acute Corners

Direct Tracking of Particles and Quantification of Margination in Blood Flow

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