## Numerical Simulation of Channel Poiseuille Flow of Solid-Liquid Mixtures

*H.H. Hu*

ABSTRACT A generalized Galerkin finite element technique which incorporates
both the fluid and particle equations of motion into a single variational
equation is developed to simulate the motion of a large number of solid
particles in a flowing liquid. In this method the hydrodynamic forces and
moments acting on the solid particles are eliminated in the formulation, so
they need not be computed explicitly. Using the developed numerical procedure,
we study the Poiseuille flow of solid-liquid mixtures in a vertical channel.
The computation is performed within a unit cell which is periodic in the
direction along the channel. The gravity is directed along the channel walls,
and a pressure gradient is applied against the gravity and drives the flow. The
effects of the appliedpressure gradient, the particle Reynolds number, and the
fraction of the solid loading on the flow pattern of the solid-liquid mixture
are studied. It was found that when the applied pressure gradient is large
enough to overcome the gravity, the particles migrate away from the channel
walls and there is a clear liquid layer next to the walls which lubricates the
flow. As the particle Reynolds number is increased, particles interact more
strongly and large clusters of particles are formed in the flow.

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*Last updated October 16, 2000*