Impulsive Motion in a Particle-Fluid Suspension Including Particulate Volume, Density, and Migration Effects

Abstract

Based on expansions for small and large times, velocity and particulate volume distributions are obtained from the approximate continuum representation of a suspension of uniformly distributed small spherical solid particles for flow induced by impulsive motion of an infinite flat plate. Included in the analysis are major effects of the fractional particulate volume, which is assumed to vary due to the inclusion of the particle slip-shear lift force, as well as a generalized drag interaction force. For both small and large times, the lift force results in an accumulation of particles near the wall. Motion in the horizontal direction is determined in terms of modified similarity variables for large and small times indicating an increase or decrease in the viscous boundary layer for small times depending on the fractional volume of particles, and an increase or decrease for large times depending on whether the particles are lighter or heavier than the fluid. To the zeroth order, the skin friction on the wall is shown to increase or decrease for small times depending on whether the ambient fractional particulate volume is greater or less than 1/4. For large times the friction increases for heavy particles and decreases for light particles. Finally, by using the modified Rayleigh’s method, an estimate is made for boundary-layer flow past a semi-infinite flat plate.