Deformation and sorting of capsules in a T-junction

Abstract

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. †

Structure and rheology of suspensions of spherical strain-hardening capsules

“…2011) and (iii) experimentally (Chang & Olbricht 1993 a , b ; de Loubens et al. 2015, 2016; Häner, Heil & Juel 2020). Under a simple shear flow, initially non-spherical capsules can exhibit several complex dynamics including the steady and oscillating tank-treading, tumbling and swinging motions (also called vacillating-breathing in the literature).…”

“…Those behaviours can be well recovered with hyperelastic constitutive laws such as the generalised Hooke, Mooney-Rivlin, neo-Hookean and Skalak laws (de Loubens et al 2015;Barthès-Biesel 2016). The deformation and dynamics of a single capsule under different flow conditions have been thoroughly investigated by many authors: (i) numerically (Navot 1998;Ramanujan & Pozrikidis 1998;Lac et al 2004;Li & Sarkar 2008;Bagchi & Kalluri 2009;Dodson & Dimitrakopoulos 2009;Farutin, Biben & Misbah 2014;Dupont et al 2016;Boedec, Leonetti & Jaeger 2017), (ii) analytically (Barthès-Biesel 1980;Barthès-Biesel & Rallison 1981;Vlahovska et al 2011) and (iii) experimentally (Chang & Olbricht 1993a,b;de Loubens et al 2015de Loubens et al , 2016Häner, Heil & Juel 2020). Under a simple shear flow, initially non-spherical capsules can exhibit several complex dynamics including the steady and oscillating tank-treading, tumbling and swinging motions (also called vacillating-breathing in the literature).…”

Sorting of capsules according to their stiffness: from principle to application

“…22 Their preparation and characterisation have been described in detail previously. 16 Briefly, we prepared spherical ovalbumin-alginate gel beads by dropwise addition of a solution in water of sodium-alginate (1% w/v), propylene glycol alginate (2% w/v) and ovalbumin (8% w/v) to a solution of calcium chloride (10% w/v). We then cross-linked their outer-shell before re-liquefying the gel core of the bead.…”

“…We selected four capsules with an average diameter D = 3.90 AE 0.03 mm and one elastic bead D bead = 3.83 mm for experimentation. 16 The capsules were from several batches manufactured under different experimental conditions in order to access different stiffness values. Hence, the capsules also had different values of inflation (1.15 r D/D bead r 1.24), membrane thickness h (0.18 r 2h/D r 0.23) and sphericity (ratio of the minimum to maximum diameter 0.88 r D min /D max r 0.93).…”

“…14,15 Moreover, sorting according to deformability was recently demonstrated experimentally in a T-junction for capsules of fixed size. 16 Moderate to high throughput experimental cell-sorting methods are also emerging on microfluidic platforms. These include the deformation of single cells through generations of tapered constrictions driven by oscillatory flow, 17 the flow through a periodic array of ridges oriented diagonally to the main stream 18 and rapid image analysis of individual cells deformed in a cross-flow with a throughput of up to 2000 cells per second.…”