Motion of a capsule in a cylindrical tube: effect of membrane pre-stress

Abstract

We present a numerical model of the axisymmetric flow of an initially spherical capsule in a co-axial cylindrical tube. The capsule consists of a liquid droplet enclosed by a thin hyper-elastic membrane that is assumed to obey different membrane constitutive equations such as Mooney–Rivlin, Skalak et al. (1973) or Evans & Skalak (1980) laws. It is further assumed that the capsule may be subjected to some isotropic pre-stress due to initial swelling. We compute the steady flow of the capsule inside the tube as a function of the size ratio between the capsule and tube radii, the amount of pre-swelling and the membrane constitutive law. We thus determine the deformed profile geometry and specifically the onset of the curvature inversion at the back of the particle. We show that for a given size ratio, the critical flow rate at which the back curvature changes is strongly dependent on pre-inflation. The elastic tension level in the membrane as well as the additional pressure drop created by the presence of the particle are also computed. The numerical results are then compared to experimental observations of capsules with alginate membranes as they flow in small tubes (Risso. et al. 2006). It is found that the experimental capsules were probably pre-inflated by about 3% and that their membrane is best modelled by the Skalak et al. law.

Comparison between measurements of elasticity and free amino group content of ovalbumin microcapsule membranes: Discrimination of the cross-linking degree

“…The numerical model initially proposed by Quéguiner and Barthès-Biesel [19] and later improved by Diaz and Barthès-Biesel [8] and Lefebvre and Barthès-Biesel [14] is used to determine the flow of a capsule in a cylindrical channel of comparable size. The model assumptions and results are only briefly outlined; more details may be found in [14].…”

“…The problem is solved by means of a boundary integral technique, coupled to the Lagrangian tracking of the capsule interface [8,14]. The model inputs are…”

3D vesicle dynamics simulations with a linearly triangulated surface

“…In this continuous media spirit, mechanical properties of vesicles and capsules may be separated into membrane effects (in-plane elasticity) and bending. Studies on capsules generally ignore the later [21,24,[26][27][28][29][30], thanks to a thin shell hypothesis. As explained before, the situation for vesicles is somehow different, because of the prominent role of bending.…”

Transient flow of microcapsules through convergent–divergent microchannels

“…Arrows show the pore inlet and outlet Fig. 7 Damage of a d/h = 2.5 microcapsule flowing through a S1 pore (Quéguiner and Barthès-Biesel 1997;Lefebvre and Barthès-Biesel 2007). During the entrance phase, the upstream pressure and flow stream push the capsule into the tube.…”

“…The numerical models (Quéguiner and Barthès-Biesel 1997;Lefebvre and Barthès-Biesel 2007) of the flow of a capsule through cylindrical pores show that the capsule deformed profile becomes steady only after its front has reached a finite position in the tube. This entrance length depends on the size ratio and on the flow strength.…”