Hydrodynamic pairing of soft particles in a confined flow

Abstract

The mechanism of hydrodynamics-induced pairing of soft particles, namely closed bilayer membranes (vesicles, a model system for red blood cells) and drops, is studied numerically with a special attention paid to the role of the confinement (the particles are within two rigid walls). This study unveils the complexity of the pairing mechanism due to hydrodynamic interactions. We find both for vesicles and for drops that two particles attract each other and form a stable pair at weak confinement if their initial separation is below a certain value. If the initial separation is beyond that distance, the particles repel each other and adopt a longer stable interdistance. This means that for the same confinement we have (at least) two stable branches. To which branch a pair of particles relaxes with time depends only on the initial configuration. An unstable branch is found between these two stable branches. At a critical confinement the stable branch corresponding to the shortest interdistance merges with the unstable branch in the form of a saddle-node bifurcation. At this critical confinement we have a finite jump from a solution corresponding to the continuation of the unbounded case to a solution which is induced by the presence of walls. The results are summarized in a phase diagram, which proves to be of a complex nature. The fact that both vesicles and drops have the same qualitative phase diagram points to the existence of a universal behavior, highlighting the fact that with regard to pairing the details of mechanical properties of the deformable particles are unimportant. This offers an interesting perspective for simple analytical modeling.

Vortical flow structures induced by red blood cells in capillaries

“…If two cells come close to each other, however, they can form a stable cluster due to their hydrodynamic interaction. [19][20][21][22][23][24][25][26] A significant amount of the liquid between the cells seems to be "encapsulated" and does not mix anymore with the liquid outside of the cluster. Similarly, to the tracer trajectories of single cells, we observed hairpin loops and vortices for tracers moving in the plane of observation and straight lines for tracers moving orthogonal to it (Figure 3A (Multimedia view)), as a consequence of our optical projection.…”

“…In addition, some works reported on observations of clusters of two or more RBCs formed without any molecular interactions that can be induced by the plasma molecules (often referred to as rouleaux formation) but kept together with a certain distance of a few microns in-between the cells by hydrodynamic interactions. [19][20][21][22][23][24][25][26] While there is good agreement between numerical simulations and experiments regarding the actual shape of RBCs, less attention has been paid to resolve the flow field of the surrounding plasma experimentally. While in the absence of RBCs, the flow would be a simple parabolic Poiseuille profile, the presence of RBCs strongly disturbs the flow.…”

A pair of particles in inertial microfluidics: effect of shape, softness, and position

“…In their subsequent work 61 they extended the understanding of a particle pair to study the behavior of particle trains 62 in inertial microfluidics. At low Reynolds numbers, Lac et al 63 and Aouane et al 64 investigated the interaction of two soft capsules in shear and Poiseuille flows, respectively. The inertial counterparts of these two problems were also studied.…”

Shear thinning and shear thickening of a confined suspension of vesicles

“…where K is a constant characterizing the streamline. Knowing v x and v y from the boundary integral equation (as described for example in [38]), we obtain ψ by calculating the integral (13) numerically. Taking a specific desired initial position (x 0 ,y 0 ) fixes a given value of K. The streamlines are obtained by linking the points which have the same given value of stream function K. In Fig.…”