Stability of the flow during sedimentation in inclined channels

The conditions for wave formation and growth during sedimentation in inclined channels is investigated using a linear stability analysis in the limit of large sedimentation Grashof number with the Reynolds number remaining O(1). An asymptotic solution for long waves reveals that the critical Reynolds number is proportional to the tangent of the angle of inclination of the channel times the ratio of the thickness of the thin pure-fluid layer, which forms beneath the downward-facing surface of the channel, to the width of the channel. Hence, the critical Reynolds number is very small unless the channel is extremely long and narrow. Numerical calculations indicate, however, that the maximum amplification rates are often so small that the disturbances may be convected out of the channel before they reach an observable size. This conclusion is consistent with experiments performed in our laboratory, and the observed wave inception point and the calculated maximum amplification rates exhibit remarkably similar dependence on the angle of inclination and the suspension concentration.