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Despite decades of research on blood flow, an analogue of Navier-Stokes equations that accurately describe blood flow properties has not been established yet. The reason behind this is that the properties of blood flow seem \`a priori non universal as they depend on various factors such as global concentration of red blood cells (RBCs) and channel width. Here, we have discovered a universal law when the stress and strain rate are measured at a given local RBCs concentration. However, the local concentration must be determined in order to close the problem. We propose a non-local diffusion equation of RBCs concentration that agrees with the full simulation. The universal law is exemplified for both shear and pressure driven flows. While the theory is restricted to a simplistic geometry (straight channel) it provides a fundamental basis for future research on blood flow dynamics and could lead to the development of a new theory that accurately describes blood flow properties under various conditions, such as in complex vascular networks.

The glycocalyx is a complex layer of carbohydrate and protein molecules that surrounds the cell membrane of many types of mammalian cells. It serves several important functions, including cell adhesion and communication, and maintain cell shape and stability, especially in the case of erythrocytes. Alteration of glycocalyx composition represents a cardiovascular health threatening. For example, in diabetes mellitus glycocalyx of erythrocytes and of endothelial cells is known to be impaired, a potential source of blood occlusion in microcirculation, which may lead to blindness, and renal failure of patients. The impact of glycocalyx impairment on erythrocyte aggregation remains a largely unexplored research area. We conduct here in vitro-experiments in microfluidic devices in order to investigate erythrocytes aggregation incubated with amylase, an enzyme that partially breaks down glycocalyx molecules. It is found that incubation of erythrocytes by amylase leads to a dramatic increase of their aggregation and stability and alters the aggregates morphologies. Confocal microscopy analysis reveals a significant degradation of the glycocalyx layer, correlated with enhanced erythrocytes aggregation. An increased erythrocyte aggregation in vivo should affect oxygen and other metabolites delivery to organs and tissues. This study brings new elements about elucidation of microscopic origins of erythrocyte aggregation and their potential impact on cardiovascular pathologies.

Lift force of viscous origin is widespread across disciplines, from mechanics to biology. Here, we present the first direct measurement of the lift force acting on a particle moving in a viscous fluid along the liquid interface that separates two liquids. The force arises from the coupling between the viscous flow induced by the particle motion and the capillary deformation of the interface. The measurements show that the lift force increases as the distance between the sphere and the interface decreases, reaching saturation at small distances. The experimental results are in good agreement with the model and numerical calculation developed within the framework of the soft lubrication theory.

We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between particles and solute induces a slip flow on particle surfaces, and the solute is advected by the fluid flow and diffuses with a constant diffusivity. The fluid-structure interaction is resolved by a boundary integral method accelerated by Ewald-like decomposition. The sharp resolution of moving boundaries for solute kinetics is performed thanks to an overlapping mesh method. The framework is validated separately for the Stokes problem and the advection--diffusion problem, reaching relatively high order of accuracy. Moreover, we employ the framework to more general problems, including particles in nearly infinite domain and straight channels, and multiparticle motions., Comment: 26 pages, 13 figures