Motion of Small Particles in Skew Shape Suspended in a Viscous Liquid

Abstract

The resistance experienced by a curved and elongated small particle is studied by the method of velocity perturbations. The fundamental equations determining the perturbations are derived from the equations of Oseen. The particle is curved in such a way that the axis of the particle is formed by an arc of circle. The opening angle may vary to exhibit various shapes from a straight ellipsoid to a closed ring. Results illustrate the circumstances under which manifests the cooperation between the different parts of the particle. Apart from this pure hydrodynamical interest, the problem has applications to long chain molecules in solution and to suspensions of swimming organisms. It demonstrates the effect of skew shape by taking for the chain molecule a model in the form of a variable-curved ellipsoid instead of a sphere or a cluster of spherical symmetry, as the coordination of the chain links, even in the case of free rotation, leads initially to configurations of variable skewness generally obscured under the averaging processes by current theories.