Effects of membrane hardness and scaling analysis for capsules in planar extensional flows

Abstract

In this paper, we investigate computationally the effects of membrane hardness on the dynamics of strain-hardening capsules in planar extensional Stokes flows. As the flow rate increases, all capsules reach elongated steady-state configurations but the cross-section of the more strain-hardening capsules preserves its elliptical shape while the less strain-hardening capsules become lamellar. The capsule deformation in strong extensional flows is accompanied with very pointed edges, i.e. large edge curvatures and thus small local edge length scales, which makes the current investigation a multilength interfacial dynamics problem. Our computational results for elongated strainhardening capsules are accompanied with a scaling analysis which provides physical insight on the extensional capsule dynamics. The two distinct capsule conformations we found, i.e. the slender spindle and lamellar capsules, are shown to represent two different types of steady-state extensional dynamics. The former are stabilized mainly via the membrane's shearing resistance and the latter via its area-dilatation resistance, associated with the elongation tension normal forces and thus both types differ from bubbles which are stabilized mainly via the lateral surface-tension normal forces. Our steady-state deformation results can be used to identify the elastic properties of a real capsule, i.e. the membrane's shear and area-dilatation moduli, utilizing a single experimental technique.

Stretching of capsules in an elongation flow, a route to constitutive law

“…The relative error on the inner volume conservation is less than 0.05 %. Our simulations with the Skalak and NH models are in excellent agreement with reference results in the literature: see supplementary data 1 available at http://dx.doi.org/10.1017/jfm.2015.69 (Lac et al 2004;Dodson & Dimitrakopoulos 2009;Walter et al 2010;Dimitrakopoulos 2014).…”

“…These two models have the major and supplementary advantage of describing two kinds of mechanical responses: the strain-hardening behaviour for the Skalak model and the strain softening for the NH model. Consequently, to the best of our knowledge, simulations of the dynamics of capsules in various flows have mainly used these models: elongation flow (Lac et al 2004;Dodson & Dimitrakopoulos 2009;Walter et al 2010;Dimitrakopoulos 2014), shear flow (Ramanujan & Pozrikidis 1998;Bagchi & Kalluri 2009;Vlahovska et al 2011;Yazdani, Kalluri & Bagchi 2011;Dupont, Salsac & Barthès-Biesel 2013;Wang et al 2013), Poiseuille in a capillary (Queguiner & Barthès-Biesel 1997;Pozrikidis 2005) and with a diffuser at the outlet (Zhu et al 2014). Here, we also compute the results using a more elementary model, the generalized Hooke model.…”

Interfacial rheological properties of self-assembling biopolymer microcapsules

“…Mechanical properties of thin membrane of microcapsules are described generally by bi-dimensional non-linear viscoelastic constitutive models [20][21][22] , as for fluid interfaces 23,24 . Rheology of complex plane fluid-fluid interfaces can be characterized by specific tools that respond to small surface stresses in isolating them from bulk stresses as the double-wall ring geometry rheometer 25 .…”

“…More recently, these methods have been extended to micrometric capsules [34][35][36][37][38] . By combination with advanced numerical simulations 21,22,39 , the nonlinear elastic constitutive laws in regime of large deformation 40 and the viscosity of the membrane 41 have been determined for microcapsules made from a biopolymer (HSA) that was physically cross-linked to form a thin membrane in hydrogel. It was shown that this kind of microcapsules can sustained up to 180% of stretching without plastic deformations or break-up.…”

Dynamics of a Spherical Capsule in a Planar Hyperbolic flow: Influence of bending Resistance

“…To date all the numerical studies that solved the fluid-structure interactions between a capsule and a planar hyperbolic flow have treated the capsule wall as a two-dimensional surface devoid of bending resistance (membrane model) 7,8,9,10,11 . At low flow strength, they showed that wrinkling occurs in the central region during the transient phase and persists at steady state.…”