From Passive Motion of Capsules to Active Motion of Cells

Abstract

In the past three decades, there has been great progress in the mathematical modeling and computational methods for fluid mechanics of suspensions of micron-scale particles. In medical or biological applications, the particles can be very deformable, self propelled or both. Research on mathematical and computational methods for the modelling of suspensions of such particles is currently very active. In this review paper, we introduce some of the concepts that are used to analyse suspensions of either passive deformable particles or active locomotive particles. To simplify matters, we consider simple model particles that are initially spherical. In one case, the particle is a liquid droplet enclosed by a thin deformable membrane (a ‘capsule’) and is deformed by hydrodynamic forces. In the other case, the particle remains spherical but propels itself by means of a velocity wave on its surface. Athough the basic equations for locomotive spherical cells and for capsules are similar, the resulting suspension characteristics are quite different owing to the different boundary conditions on the surface of the particles.