Laminar flow of fine sediment-water mixtures

Flows of sediment-water mixture (suspensions) are common superficial proces ses in nature. To investigate the possibility of predicting the behaviour o f such flows, we study the free surface flow of a clay-water suspension dow n a slope, which may represent a simple realistic model for the flow of som e concentrated sediment-water mixture in a natural environment. The hydrody namic lubrication equations governing the flow are derived from the full Na vier-Stokes equations, including an appropriate tensorial expression for th e constitutive equation of the suspension (a Herschel-Bulkley fluid with a hysteresis in the yield strength). Results have been obtained for the free surface and length of an unsteady, laminar, isothermal flow of the suspensi on. The theory is in good agreement with laboratory experiments with fine c lay suspensions.