## NUGGET

### Deformation of Elastic Particles in Viscous Fluid Flows

Howard H. Hu and Tong Gao

**Objective:**

Develop a monolithic solver for fluid-solid interaction problems that resolves the sharp solid-fluid interface.

(a) Schematic for an elastic particle deforming in a viscous shear flow. (b) & (c) Equilibrium particle shapes at different Capillary numbers ( ) in Stokes flow regime. The velocity vectors along the fluid-solid interface indicate a tank treading motion. (d) Deformation number D and rotation angle q as functions of Ca.

Deformation and rotation of a long elastic particles in viscous shear flow . The orientation of the particle during one period of the orbit is plotted as a function of time. For a stiff particle, its orbit is very close to the classic Jeffery’s orbit for a rigid ellipsoid. However, for a soft particle, its orbit changes quite a bit from the Jeffery’s orbit, due to the compressing and stretching of the particle during the rotation.

Stability of the fluid-solid interface. It is found that the fluid-solid interface becomes unstable when the stain in the solid is beyond a critical value. The critical strain as a function of solid thickness is plotted on the right. Different linear and nonlinear elastic solid models were used.