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Abstract-
The boundary condition relating the macroscopic jump in the
tangential velocity across a permeable interface to the shear
rate prevailing on either side of the interface is discussed.
The computation of the velocity jump hinges on the
realization that a shear flow on one side of the interface
induces a slip velocity on that side and a streaming drift
velocity on the other side. The direction and magnitude of
the slip and drift velocities depend on the interface
constitution, solid fraction, and Reynolds number. Numerical
computations are performed for model three- and
two-dimensional interfaces consisting of a periodic array of
spheroidal particles and cylinders, and the slip and drift
velocity coefficients are evaluated by asymptotic and
numerical methods. The results show that, in some cases, a
shear flow in one direction above the array induces a drift
velocity in the opposite direction beneath the array. To
study the effect of the fluid inertia, the Navier-Stokes
equation is solved numerically using a finite-difference
method on an orthogonal grid generated by conformal mapping.
The results reveal that inertial effects promote the
magnitude of the slip and drift velocity, and illustrate the
streamline pattern near the interface.
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