Elastic capsule deformation in general irrotational linear flows

Knowledge of the response of elastic capsules to imposed fluid flow is necessary for predicting deformation and motion of biological cells and synthetic capsules in microfluidic devices and in the microcirculation. Capsules have been studied in shear, planar extensional, and axisymmetric extensional flows. Here, the flow gradient matrix of a general irrotational linear flow is characterized by two parameters, its strain rate, defined as the maximum of the principal strain rates, and by a new term, q, the difference in the two lesser principal strain rates, scaled by the maximum principal strain rate; this characterization is valid for ellipsoids in irrotational linear flow, and it gives good results for spheres in general linear flows at low capillary numbers. We demonstrate that deformable non-spherical particles align with the principal axes of an imposed irrotational flow. Thus, it is most practical to model deformation of non-spherical particles already aligned with the flow, rather than considering each arbitrary orientation. Capsule deformation was modeled for a sphere, a prolate spheroid, and an oblate spheroid, subjected to combinations of uniaxial, biaxial, and planar extensional flows; modeling was performed using the immersed boundary method. The time response of each capsule to each flow was found, as were the steady-state deformation factor, mean strain energy, and surface area. For a given capillary number, planar flows led to more deformation than uniaxial or biaxial extensional flows. Capsule behavior in all cases was bounded by the response of capsules to uniaxial, biaxial, and planar extensional flow.