A SLIP CONDITION-BASED ON MINIMAL ENERGY-DISSIPATION

An intrinsic difficulty arises when solving Stokes equations in Ohm su bset of R(2) when the boundary conditions on the velocity are disconti nuous: the solution is physically unacceptable since the force exerted by the fluid on the boundary is logarithmically singular. To illustra te this phenomena, we present an explicit solution in which the logari thmic singularity appears in a particularly simple form. A common meth od of avoiding the appearance of these singular forces is via an alter ation of the boundary velocity profile in the vicinity of the disconti nuity. However, there is no obvious physical criterion according to wh ich the velocity profile along the boundary should be chosen. We consi der a possible physically motivated criterion based on minimal energy dissipation. We prove the existence of a unique minimizing profile and demonstrate that the resultant velocity field does indeed exert a fin ite force along the boundary. Lastly, the minimizing profile is calcul ated numerically and the effect of free parameters is considered.