Abstract
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. 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. Our primary focus is to study the influence of the geometry of the side branch on the capsule path selection. Specifically, we consider the case where the side branch cross-section is half that of the straight channel and study various bifurcation configurations, where the branch is rectangular or square, centred or not on the straight channel axis. The capsule is initially centred on the axis of the straight channel. We impose the flow rate split ratio between the two downstream branches of the bifurcation. We summarise the results obtained for different capsule-to-channel size ratios, flow Reynolds number $Re$ (based on the parent channel size and average flow speed) and capsule mechanical deformability (as measured by the capillary number) in phase diagrams giving the critical flow rate split ratio above which the capsule flows into the side branch. A major finding is that, at 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. For $Re\leqslant 5$, this novel intriguing phenomenon primarily results from the background flow, which is strongly influenced by the side branch geometry. For higher values of $Re$, the capsule relative size and deformability also play specific roles in the path selection. The capsule trajectory does not always obey the classical Fung’s bifurcation law, which stipulates that a particle (in Fung’s case, a red blood cell) enters the bifurcation branch with the highest flow rate. We also consider the same branched channels operating under constant pressure drop conditions and show that such systems are difficult to control due to the transient additional pressure drop caused by the capsule. 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.
Highlights
Path selection of a deformable capsule suspended in an external fluid flowing through a branched microchannel is an important problem that is relevant to understand blood-related flows in the microcirculation (Popel & Johnson 2005; Secomb 2017), aerosol particle deposition in respiratory airways (Kleinstreuer & Zhang 2010) or to develop microfluidic technologies to separate or enrich suspensions (Gossett et al 2010; Tripathi et al 2015)
We present the flow patterns and pressure drops as a function of the bifurcation geometries and determine the path selection of initially spherical capsules as a function of the capsule properties, bifurcation geometry and flow Reynolds number
The results show clearly that, for a given bifurcation geometry, the flow rate is better than the velocity as the main criterion for path selection, but that the three-dimensional phenomena that occur at the bifurcation are too complex to be amenable to a simple phenomenological, one-dimensional theory
Summary
Path selection of a deformable capsule suspended in an external fluid flowing through a branched microchannel is an important problem that is relevant to understand blood-related flows in the microcirculation (Popel & Johnson 2005; Secomb 2017), aerosol particle deposition in respiratory airways (Kleinstreuer & Zhang 2010) or to develop microfluidic technologies to separate or enrich suspensions (Gossett et al 2010; Tripathi et al 2015) The aim of such studies is usually to determine the path selection of the suspended particles at a bifurcation, depending on their position in the feed channel, the flow rate split between the two branches and the bifurcation geometry. In the specific case of a centred capsule, Woolfenden & Blyth (2011) designed a low Reynolds number two-dimensional numerical model of the flow of a RBClike capsule in an asymmetric Y-bifurcation with β = 0 and different values of α They find that the capsule takes the branch with the highest flow rate, when the two branches have the same cross-section (as predicted by Fung’s model).
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