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Longitudinal and transversal flow over a cavity containing a second immiscible fluid
An analytical solution for the flow field of a shear flow over a rectangular
cavity containing a second immiscible fluid is derived. While flow of a
single-phase fluid over a cavity is a standard case investigated in fluid
dynamics, flow over a cavity which is filled with a second immiscible fluid,
has received little attention. The flow filed inside the cavity is considered
to define a boundary condition for the outer flow which takes the form of a
Navier slip condition with locally varying slip length. The slip-length
function is determined from the related problem of lid-driven cavity flow.
Based on the Stokes equations and complex analysis it is then possible to
derive a closed analytical expression for the flow field over the cavity for
both the transversal and the longitudinal case. The result is a comparatively
simple function, which displays the dependence of the flow field on the cavity
geometry and the medium filling the cavity. The analytically computed flow
field agrees well with results obtained from a numerical solution of the
Navier-Stokes equations. The studies presented in this article are of
considerable practical relevance, for example for the flow over
superhydrophobic surfaces.Comment: http://journals.cambridge.or
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