Motion of a spherical capsule in branched tube flow with finite inertia

Wang, Z.; Sui, Yi; Salsac, Anne‐Virginie; Barthès-Biesel, Dominique; Wang, W.

doi:10.1017/jfm.2016.603

Cited by 47 publications

(49 citation statements)

References 55 publications

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“…The numerical method is similar to the one used for capsules flowing through a circular branched channel (Wang et al 2016) and will only be outlined briefly here. The fluid flow in the whole domain is computed by means of a lattice-Boltzmann method (LBM) with a standard grid size x = y = z = 0.04l.…”

Section: Numerical Methods and Validationmentioning

confidence: 99%

“…Here k c is the bending modulus, H is the mean curvature, c 0 is the spontaneous curvature and A is the surface area. A small bending stiffness (k c = 0.0008G s l 2 ) is used to prevent the formation of wrinkles on the capsule membrane, like in our previous study (Wang et al 2016). The non-dimensional parameters of the problem are as follows.…”

Section: Problem Statementmentioning

confidence: 99%

“…At any cross-section of the parent channel perpendicular to the channel axis, one can define a separation line which divides the fluid elements that flow into the side branch from those flowing into the downstream main channel. The flow separation line is computed in cross-section S c by means of the approach of Wang et al (2016). We concentrate on the influence of side branch geometry and Reynolds number on the position of the flow separation line for q = 0.5.…”

Section: Fluid Separation Line In the Absence Of A Capsulementioning

confidence: 99%

“…Recently, Wang et al (2016) designed a three-dimensional model of the flow of a finite-sized deformable capsule in a lateral bifurcation made of cylindrical tubes having the same diameter and consisting of a straight channel with an orthogonal side branch (figure 1c) with α = π/2. They found that at low Reynolds number Re, a capsule favours the branch which receives the most flow, provided it is not too deformable.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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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.

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Section: Numerical Methods and Validationmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

Section: Fluid Separation Line In the Absence Of A Capsulementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Deformation and sorting of capsules in a T-junction

2019

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We study experimentally the motion and deformation of individual capsules transported by a constant volume-flux flow of low Reynolds number, through the T-junction of a channel with rectangular cross-section. We use millimetric ovalbumin-alginate capsules which we manufacture and characterise independently of the flow experiment. Centred capsules travel at constant velocity down the straight channel leading to the T-junction where they decelerate and expand in the spanwise direction before turning into one of the two identical daughter channels. There, non-inertial lift forces act to re-centre them and relax their shape until they reach a steady state of propagation. We find that the dynamics of fixed-size capsules within our channel geometry are governed by a capillary number Ca defined as the ratio of viscous shear forces to elastic restoring forces. We quantify the elastic forces by statically compressing the capsule to 50% of its initial diameter between parallel plates rather than by the Young's modulus of the encapsulating membrane, in order to account for different membrane thickness, pre-inflation and nonlinear elastic deformation. We show that the maximum extension in the T-junction of capsules of different stiffness collapses onto a master curve in Ca. Thus, it provides a sensitive measure of the relative stiffness of capsules at constant flow rate, particularly for softer capsules. We also find that the T-junction can sort fixed-size capsules according to their stiffness because the position in the T-junction from which capsules are entrained into the daughter channel depends uniquely on Ca. We demonstrate that a T-junction can be used as a sorting device by enhancing this initial capsule separation through a diffuser. †

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