# Slow Viscous Flow of an Incompressible Suspension

*by*Gerhard Oertel,

**Serial Information**:

*Journal of the Engineering Mechanics Division*, 1965, Vol. 91, Issue 5, Pg. 145-154

**Document Type:**Journal Paper

**Abstract:**A mathematical model describes approximately the viscous creeping and incompressible flow of the fluid part of a suspension of equidistant, rigid, spherical particles, when the suspension as a whole is uniformly shortened or elongated in one direction. It is assumed that each particle is concentrically surrounded by a surface on which the flow is identical with that in a continuum. Analytic solutions are obtained for the flow, strain rate, rotation, and pressure fields and for the apparent viscosity of the suspension. The functions are plotted for the case in which the distance between the centers of neighboring particles is three times the radius of a particle. A simple approximation in exponential form is available for the viscosity of the suspension as a function of the particle concentration.

**Subject Headings:**Particles | Viscous flow | Fluid flow | Rotational flow | Viscosity | Mathematics | Mathematical models | Creep |

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