Abstract
We computationally study the transient motion of an initially spherical capsule flowing through a right-angled tube bifurcation, composed of tubes having the same diameter. The capsule motion and deformation is simulated using a three-dimensional immersed-boundary lattice Boltzmann method. The capsule is modelled as a liquid droplet enclosed by a hyperelastic membrane following the Skalak’s law (Skalak et al., Biophys. J., vol. 13(3), 1973, pp. 245–264). The fluids inside and outside the capsule are assumed to have identical viscosity and density. We mainly focus on path selection of the capsule at the bifurcation as a function of the parameters of the problem: the flow split ratio, the background flow Reynolds number $Re$, the capsule-to-tube size ratio $a/R$ and the capillary number $Ca$, which compares the viscous fluid force acting on the capsule to the membrane elastic force. For fixed physical properties of the capsule and of the tube flow, the ratio $Ca/Re$ is constant. Two size ratios are considered: $a/R=0.2$ and 0.4. At low $Re$, the capsule favours the branch which receives most flow. Inertia significantly affects the background flow in the branched tube. As a consequence, at equal flow split, a capsule tends to flow straight into the main branch as $Re$ is increased. Under significant inertial effects, the capsule can flow into the downstream main tube even when it receives much less flow than the side branch. Increasing $Ca$ promotes cross-stream migration of the capsule towards the side branch. The results are summarized in a phase diagram, showing the critical flow split ratio for which the capsule flows into the side branch as a function of size ratio, $Re$ and $Ca/Re$. We also provide a simplified model of the path selection of a slightly deformed capsule and explore its limits of validity. We finally discuss the experimental feasibility of the flow system and its applicability to capsule sorting.
Highlights
A capsule is a liquid droplet enclosed by a thin membrane which can resist shear deformation
Capsules are suspended in a fluid and flow through a complicated network of tubes or channels: this is the case for red blood cells (RBCs) in the human circulation or for artificial capsules flowing through microfluidic devices
This flow configuration is interesting as it leads to non-symmetric flow conditions between the two branches, contrary to the classical T-junction that is equivalent in terms of geometry and has received great attention
Summary
A capsule is a liquid droplet enclosed by a thin membrane which can resist shear deformation. A good understanding of this problem is needed to elucidate some intriguing phenomena in human circulation It will benefit the design and optimization of microfluidic devices using branched channels, for instance to sort capsules or biological cells depending on their properties. Fenton, Carr & Cokelet (1985) considered blood flow in a microfabricated branched tube with a diameter of 100 μm for both branches and investigated the effect of cell deformability on the partitioning of RBCs at the bifurcation. The same group found that the cell enrichment in the higher flow rate branch is increased by the cell deformability (Barber et al 2008) They studied the effect of cell interaction and found that it leads to a more uniform cell partitioning compared with dilute suspensions, in which cell interaction is negligible (Barber, Restrepo & Secomb 2011). Their 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
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