Capsule deformation and orientation in general linear flows

We considered the response of spherical and non-spherical capsules to general flows. (A capsule is an elastic membrane enclosing a fluid, immersed in fluid.) First, we established that nonspherical capsules align with the imposed irrotational linear flow; this means that initial orientation does not affect steady-state capsule deformation, so this steady-state deformation can be determined entirely by the capillary number and the type of flow. The type of flow is characterized by $r$: $r=0$ for axisymmetric flows, and $r=1$ for planar flows; intermediate values of $r$ are combinations of planar and axisymmetric flow. By varying the capillary number and $r$, all irrotational linear Stokes flows can be generated. For the same capillary number, planar flows lead to more deformation than uniaxial or biaxial extensional flows. Deformation varies monotonically with $r$, so one can determine bounds on capsule deformation in general flow by only looking at uniaxial, biaxial, and planar flow. These results are applicable to spheres in all linear flows and to ellipsoids in irrotational linear flow.