Interfacial shear-stress effects on transient capillary wedge flow

Abstract

The effects on the transient capillary flow in a wedge due to the interfacial shear-stress distribution S along the flow direction z is studied theoretically. With the assumptions of a slender liquid column and negligible gravitational and inertia effects, the problem is reduced to finding the axial velocity distribution at any cross section. The propagation of the liquid column h(z,t) and the tip location l(t) are then solved with the aid of the continuity equation. When the half-wedge angle α, the contact angle θ, and the shear-stress distribution on the free surface S are constant, analytic solutions exist. Otherwise, numerical simulation has to be applied. The results indicate that when S(z) is acting in the flow direction, the flow is strengthened and the liquid column propagates faster. When S(z) is opposing the flow direction, reverse flow may exist near the free surface and the propagation speed of the liquid column is reduced. Moreover, for a capillary flow in a wedge with constant α, θ, and S, both the analytic solutions and the numerical simulation predict that l(t)∝t3/5 for the constant-flow-rate stage and l(t)∝t1/2 for the constant-height flow stage. When S is a function of the flow direction z, the above functional relationship between l and t becomes no longer valid; it varies as the liquid column propagates along the wedge.