Path selection of a spherical capsule in a microfluidic branched channel: towards the design of an enrichment device

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.

Abnormal morphology biases haematocrit distribution in tumour vasculature and contributes to heterogeneity in tissue oxygenation

“…For δ = 4d, the new HS model predicts haematocrits within 5% relative error of the values calculated from RBC simulations ( Table 2). Given the uncertainty in determining discharge haematocrit in the RBC simulations and given that the new model neglects effects due to asymmetric streamline splitting [38], we conclude that our new model provides a good, leading-order approximation to the effects of CFL disruption on HS. Finally, we compare the CFL evolution dynamics calculated from the RBC simulations (for θ = 0 and θ = π) with those predicted from the proposed evolution of X 0,f and X 0,u ((S.21) and (S.22)).…”

“…Interestingly, we observe small but statistically significant asymmetries in the haematocrit split in bifurcation 1 in the extended double-t geometry (19.2% vs 20.8%, p < 0.001, Figure 3a) and cross geometry (19.7% vs 20.4%, p = 0.035, Figure 3c), which consistently favour the side branch. We attribute this secondary effect to an asymmetrical streamline split in the chosen geometry as investigated in [38].…”

Emergent cell-free layer asymmetry and biased haematocrit partition in a biomimetic vascular network of successive bifurcations

“…The first examines the relative motion of individual RBCs (or their biomimetic counterpart, vesicles or capsules) against the background flow in different bifurcation geometries (e.g. [29,31,32,30,35,36,79]), typically aimed at microfluidic design optimisation for cell sorting or enrichment. The second approach focuses on quantifying the split of RBC fluxes or discharge haematocrits within a flowing RBC suspension at bifurcations (e.g.…”

“…Several underlying effects have been proposed, such as the vessel obstruction effect [29], the unbalanced shear-force effect [30], the branching angle effect [31], and the low-flow attraction effect [32]. Recently, threedimensional (3D) computer simulations considering more realistic cell-wall interactions [24,33,34,35,36,37,38] emerged to overcome the inherent limitations of 2D models.…”

Deformation and sorting of capsules in a T-junction

“…Their results have been confirmed and extended by recent experimental studies (Vesperini et al 2017;Häner 2017). To our knowledge, sorting according to stiffness in branched geometries is limited to the numerical studies by Wang et al (2016Wang et al ( , 2018 and Villone et al (2017) cited above. In the current paper, we explore the sorting capabilities of the T-junction for capsules of fixed size.…”