English translation of Giesekus's famous article on flows with constant velocity gradient and the motion of particles suspended therein. Part I. Spatial flows

Abstract

Within the framework of a statistical rheology of suspensions, emulsions, and solutions, it is important to obtain an overview of the total set of flows with a constant velocity gradient. Therefore, the solutions of the differential equations of such flows are given and discussed especially with respect to the influence of the deformation and rotation parts of the velocity gradient. Subsequently, the motion of rigid particles in these flows is analyzed. Both the flow types themselves and the types of motion of the suspended particles can be divided into two broad classes. Among those with predominant deformation influence, we have hyperbolic–parabolic flows as well as a setting of the particles in fixed directions. Among those with predominant rotational influence, we have elliptical–spiral flows as well as a non-uniform orbital motion of the particles. The change from one place of motion to the other depends not only on the shape of the flow but also on the shape of the particles. Deformation becomes stronger as the form anisotropy of the particles increase.