Flow-Induced Deformation of a Capsule in Unbounded Stokes Flow

Abstract

Dynamics of deformable capsules in fluid flow is great interest in chemical engineering, bioengineering, and food industry. To investigate the motion and deformation of a capsule, both the fluid mechanics of the internal and external liquids and the solid mechanics of the membrane must be solved precisely. To express the elastic behaviours of the solid membrane, two different kinds of modelling are commonly used. One is a continuum constitutive law and the other is a discrete spring network model. This study first examines the correlations between the mechanical properties of the discrete spring network model and those of continuum constitutive laws. We also derive the relationships between the spring constant and continuum properties, such as Young modulus, Poisson ratio, area dilation modulus, and shear elastic modulus. Next, we investigate the motion and deformation of a capsule in simple shear flow. Especially, we analyze the dynamics of a non-spherical capsule in shear. In the absence of inertia effect of fluid motions, a boundary element method is used to compute the internal and external Stokes flow. The results show that the orientation of a non-spherical capsule is variant under time reversal, though that of a rigid particle is invariant. Interestingly, the alignment of a non-spherical capsule over a long time duration shows a transition depending on the shear rate.