The problem of the splitting of a suspension in bifurcating channels dividing into two branches of non equal flow rates is addressed. As observed for long, in particular in blood flow studies, the volume fraction of particles generally increases in the high flow rate branch and decreases in the other one. In the literature, this phenomenon is sometimes interpreted as the result of some attraction of the particles towards this high flow rate branch. In this paper, we focus on the existence of such an attraction through microfluidic experiments and two-dimensional simulations and show clearly that such an attraction does not occur but is, on the contrary, directed towards the low flow rate branch. Arguments for this attraction are given and a discussion on the sometimes misleading arguments found in the literature is proposed. Finally, the enrichment in particles in the high flow rate branch is shown to be mainly a consequence of the initial distribution in the inlet branch, which shows necessarily some depletion near the walls.

Abstract. This paper presents an overview of a unified framework for finite element and spectral element methods in 1D, 2D and 3D in C ++ called FEEL++. The article is divided in two parts. The first part provides a digression through the design of the library as well as the main abstractions handled by it, namely, meshes, function spaces, operators, linear and bilinear forms and an embedded variational language. In every case, the closeness between the language developed in FEEL++ and the equivalent mathematical objects is highlighted. In the second part, examples using the mortar, Schwartz (non)overlapping, three fields and two fictitious domain-like methods (the Fat Boundary Method and the Penalty Method) are presented and numerically solved in the scope of the library.

International audienceA new framework for two-fluids flow using a Finite Element/Level Set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid. This model is then enriched to deal with vesicles (which mimic red blood cells mechanical behavior) by introducing a Lagrange multiplier to constrain the inextensibility of the membrane. Moreover, high order polynomial approximation is used to increase the accuracy of the simulations. A validation of this model is finally presented on known behaviors of vesicles under flow such as ''tank treading'' and tumbling motions