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Rivulet flow and stability Liang, Margaret Hongxia

Abstract

Two dimensional, steady-state rivulet flow down an inclined plane, and combined rivulet/air flow i n a circular pipe are studied. Both asymptotic analysis and numerical methods are used to solve the Navier-Stoke equations for rivulet flow down an inclined plane. Asymptotic approximation, which is valid only for rivulet of large cross-sectional aspect ratios, is substantiated by exact numerical solutions up to specified error tolerance. Standard shooting techniques are used to solve ODE for rivulet shape and finite element methods are used to approximate the flow velocity. The stability of the rivulet flow is also studied based on energy criterion. We find that pure gravity driven rivulets are subject to break up and pure shear driven rivulets are stable in that sense. For the combined air/rivulet flow, the relationship between pressure gradients and fluxes is investigated using the annulus rivulet and circular arc rivulet models. The annulus rivulet model is solved analytically, and the circular arc rivulet is computed using FEMLAB . It is found that pressure gradient needed to drive the rivulet flow is much more sensitive to change in channel size than to change in contact angle. Finally, linear stability analysis of the combined air/rivulet flow in a rectangular domain is formulated.

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