Margination Regimes and Drainage Transition in Confined Multicomponent Suspensions

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.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

Image-Based Modeling of Blood Flow and Oxygen Transfer in Feto-Placental Capillaries

“…Such effects are expected to be particularly important in small vessels and it will be vital to understand how the statistical distributions of quantities such as vascular resistance are affected by their inclusion in blood flow simulations. Non-Newtonian effects can often be incorporated into models using effective parameters or simplified equations (see [55], for example), but understanding whether such methods can be used in feto-placental capillaries of varying radius will necessitate a dedicated investigation involving simulations with discrete red blood cells.…”

Clustering of microscopic particles in constricted blood flow

“…As can be seen in figure 2 (b) the microparticles are expelled into this cell-free layer leading to a sharply peaked concentration distribution of the marginated microparticles. The origin of microparticle migration into the cell-free layer is commonly attributed to heterogeneous collisions with the RBCs [17,19,22,26,31,33,36,42].…”

Direct Tracking of Particles and Quantification of Margination in Blood Flow

“…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).…”