## Abstract

In this work, we investigate the isothermal gravity-driven Stokes flow of a mixture of two constant true density viscous fluids which are overlain by a (single-constituent) constant density viscous fluid down an inclined plane. The continuum thermodynamical theory for such a system implies that, in the simplest case, the constituents of such a mixture interact mechanically with each other because of (1) friction or drag between the constituents, and (2) the non-uniform (volume) distribution of constituents, in the mixture. The former interaction is proportional to the relative velocity of the two constituents, and the latter to the gradient of the volume fraction. The coefficient of the volume fraction gradient in this latter interaction has the dimensions of pressure, and is usually interpreted as the fluid pressure p in the case of a fluid-solid mixture. More generally, however, this pressure represents that maintaining saturation in the mixture. In this work, we formulate a model for a saturated mixture in which this coefficient takes a slightly more general form, i.e. δp, where δ is a dimensionless constant varying between 0 and 1. In particular, in the context of the thin-layer approximation, analytical solutions of the lowest-order non-dimensionalized constituent momentum balances, under the usual assumption δ=1, yield only pure constituent-1 or pure constituent-2 ‘mixtures’. On the other hand, numerical solution of these momentum balances for δ = 1 yield non-trivial volume fraction variations with depth in the layer, and hence represent true mixture solutions. Applying this model to the case of a sediment-ice mixture, such as that found in a glacier or ice sheet, one obtains good qualitative agreement with observations on the variation of sediment in these bodies with depth for δ > 0.95, i.e. in this case the sediment remains concentrated at the bottom of the layer.

## Footnotes

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- Received February 17, 1995.
- Accepted June 27, 1995.

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