Two-dimensional transient flows and stability of concentrated suspensions of clay particles and rheology.

摘要

Motivated by geophysical flows of concentrated suspensions of clay particles, such as fluid mud, molten lava, and mining slurries, boundary-layer flows of these fluids on a slope are studied theoretically and experimentally. Rheological measurements using a state-of-the-art rheometer show that the shear history of concentrated suspensions of clay particles can be divided into three regions: solid-rigid, nearly Newtonian, and shear-thinning regions. The nearly Newtonian region is very narrow in shear rate compared to the shear thinning region. The H-B model is found to be more rational than the Bingham model in a rather wide range of shear rates. A new empirical formula is proposed to estimate yield stress of mud at normal atmospheric temperature. Due to plasticity, the flow is divided into a plug layer on top of a shear layer. By using an integral method, nonlinear partial differential equations governing two-dimensional motion of a thin layer of fluid are generated in general forms with the incorporation of different rheological models. Various transient problems of discontinuous flows of non-Newtonian fluids on an incline are solved analytically by using composite matched-asymptotic perturbation methods, along with internal boundary condition - location of yield interface. These flows are both spatially and temporally unsteady, and have relatively low Reynolds number of Re≤O1/tanq and Froude number of Fr2≤Ocosq where theta is the slope angle with respect to the horizontal. The range of accuracy of the solution is quantified by physical scaling analysis. The mathematics associated with the fluid dynamics is thoroughly analyzed. The theoretical results are partly compared with laboratory experimental results, showing reasonable agreement. Laboratory experiments on subaerial and submarine transient flows are carried out, in which both quantitative measurements and qualitative observations are taken for insight of physical aspects. Long-wave instability of a fast, continuous, uniform flow down a slope is analyzed. The threshold for long-wave instability to occur is determined by the relative thickness of plug layer lambda and the dynamic parameter beta, and stable zones are established, in which yield stress and shear thinning are considered.