Dynamics of a nonspherical capsule in general flow

•Relevant theories are adopted to derive the governing equations in general flow.•It is the first time that the TU-SW-TU transition has been identified.•The shape dynamics of a capsule in general flow is studied in detail.

The dynamics of a capsule in general flows is studied analytically and numerically. The capsule is modeled as a liquid-filled drop enclosed by a membrane. We adapted the Keller-Skalak (KS) theory and Skotheim-Secomb model to the case of general flow, the governing equations are derived. It is found that when viscosity ratio λ=1,λ=1, the capsule dynamics in general flows is controlled by two dimensionless parameters, the ratio of vorticity to strain rate of the flow and the ratio of the elastic force to fluid stress. In the literature, the transition between swinging (SW) and tumbling (TU) is always one way (TU to SW). As far as we know, it is the first time that the TU-SW-TU transition has been identified, i.e., the transition may also transfer from SW to TU after the transition (TU to SW) occurs under some circumstances. The possible mechanism is that the rotation of the flow suppresses the deformation along the vorticity direction of the capsule. The shape dynamics of a capsule is studied in detail and the rheology of dilute capsule suspension is also investigated briefly.