The effect of Thompson and Troian’s nonlinear slip condition on Couette flows between concentric rotating cylinders

In this work, a detailed study of the effect of the Thompson and Troian’s nonlinear slip condition on the flow behaviour of a Newtonian incompressible fluid between two concentric rotating cylinders (Couette flow) is considered. In Thompson and Troian’s nonlinear condition, the slip length on the Navier slip condition is considered to be a function of the tangential shear rate at the solid surface instead of being a constant. The resulting formulation presents an apparent singularity on the slip length when a critical shear rate is approached. By considering this type of nonlinear slip condition, it is possible to predict complex characteristics of the flow field not previously reported in the literature, and to show the effect of nonlinear slip on the inverted velocity profiles previously observed in the linear slip case. Particular attention is given to the behaviour of the flow field near the critical shear rate. In such a limit, it is found that the flow field tends to slip flow with a finite slip length. Consequently, previous critique on the singular behaviour of Thompson and Troian’s nonlinear model is not valid in the present case.