Thanks to the extensive

In the dilute limit, the problem has, however, not been thoroughly studied experimentally, possibly due to the difficulty of manipulating individual cells. The problem has mostly been studied in recent years using two-dimensional numerical models [9, 10]. The results showed that, at equal flow rate between the two downstream channels, the capsule tends to flow into the side branch in particular when the capsule is highly deformable. But to what extent the results obtained from previous two-dimensional simulations can be applied to three-dimensional flows remains unclear.

The objective of the present study is to conduct a systematic and in-depth three-dimensional numerical study of a deformable capsule in a branched tube and to determine the influence of inertia. Contrary to many biological systems, for which neglecting inertia is a good assumption, capsules are not necessarily small in size and the flow speed can be fast in some applications [11].

In the present work, we computationally study the motion of an initially spherical capsule flowing through a straight channel with an orthogonal lateral branch, using a three-dimensional immersed- boundary lattice Boltzmann method [12, 13]. Our primary focus is to study the influence of the geometry of the side branch on the capsule path selection. The capsule is enclosed by a strain-hardening membrane and contains an internal fluid of the same viscosity as the fluid in which it is suspended. It is initially centered on the axis of the feed channel. We impose the flow rate split ratio between the two downstream branches of the bifurcation. We analyze the reference cases wherein the side channel has the same cross- section as the main branch, and then compare the results to other geometries, in which the side branch has a half cross-sectional area as compared to the main branch. We consider different capsule-to-channel size ratio, flow Reynolds number (Re) and ratio of capillary to Reynolds numbers, and summarize the results in phase diagrams indicating the critical flow split ratio above which the capsule flows into the side branch.

The capsule trajectory does not always obey the classical Fung's bifurcation law. For Re ≤ 5 and equal flow rate split between the two downstream branches, the capsule will enter a branch which is narrow in the spanwise direction, but will not enter a branch which is narrow in the flow direction. We show that this novel phenomenon results primarily from the background flow which is strongly influenced by the side branch cross-section geometry. For higher values of Re, the capsule relative size and deformability also play a specific role in the path selection: increasing the capillary number generally promotes cross-stream migration of the capsule towards the side branch. The present results obtained for dilute systems open new perspectives on the design of microfluidic systems with optimal channel geometries and flow conditions to enrich cell and particle suspensions. KW - Microcapsule; bifurcated microchannel; fluid-structure interactions; lattice-Boltzmann; finite elements DO - 10.32604/mcb.2019.07148