On the Deformation of an Elastic Particle Falling in a Viscous Fluid

Abstract

The steady motion of a flexible solid particle in a quienscent unbounded viscous fluid is investigated theoretically. It is assumed that the particle is a homogeneous, isotropic elastic body obeying Hooke's law and that the undeformed particle is spherical in shape. It is further assumed that the motion of fluid obeys the Stokes equation. It is shown that for small values of the parameter α=η U 0 / G R 0 , where η is the shear viscosity of fluid, G the shear modulus of the particle and U 0 the terminal settling velocity of a rigid particle whose radius is R 0 , the particle deforms into a prolate spheroid and the deviation from a sphere is in proportion to α 2 . The effect of the deformation on the terminal settling velocity of the particle is also included in the analysis.