Modeling the motion of capsules in flow

This review presents the mechanical behavior of a capsule under the influence of viscous deforming forces due to a flowing fluid. We focus on artificial capsules that are initially spherical with an internal liquid core and that are enclosed by a very thin hyperelastic membrane with different constitutive laws. The recent modeling strategies are outlined together with their respective advantages and limitations. We then consider the motion and deformation of a single initially spherical capsule freely suspended in a simple shear or plane hyperbolic flow and discuss the effect of the membrane constitutive law, of initial pre-stress and of membrane buckling under compression. We then consider the flow of spherical capsules in small pores and show how it can be used to evaluate the mechanical properties of the membrane.