ON THE ROLE OF MECHANICAL INTERACTIONS IN THE STEADY-STATE GRAVITY FLOW OF A 2-CONSTITUENT MIXTURE DOWN AN INCLINED PLANE

In this work, we investigate the isothermal gravity-driven Stokes how of a mixture of two constant true density viscous fluids which are ove rlain by a (single-constituent) constant density viscous fluid down an inclined-plane. The continuum thermody namical theory for such a syst em implies that, in the simplest case, the constituents of such a mixt ure interact mechanically with each other because of (1) friction or d rag between the constituents, and (2) the non-uniform (volume) distrib ution of constituents, in the mixture. The former interaction is propo rtional to the relative velocity of the two constituents, and the latt er to the gradient of the volume fraction. The coefficient of the volu me fraction gradient in this latter interaction has the dimensions of pressure, and is usually interpreted as the fluid pressure p in the ca se of a fluid-solid mixture. More generally, however, this pressure re presents that maintaining saturation in the mixture. In this work, we formulate a model for a saturated mixture in which this coefficient ta kes a slightly more general form, i.e. delta p, where delta is a dimen sionless constant varying between 0 and 1. In particular, in the conte xt of the thin-layer approximation, analytical solutions of the lowest -order non-dimensionalized constituent momentum balances, under the us ual assumption delta = 1, yield only pure constituent-1 or pure consti tuent-2 'mixtures'. On the other hand, numerical solution of these mom entum balances for delta not equal 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 qualita tive agreement with observations on the variation of sediment in these bodies with depth for delta greater than or equal to 0.95, i.e. in th is case the sediment remains concentrated at the bottom of the layer.