The occurrence of slip complicates the estimation of the viscosity in rheometric flows. Thus, special analyses and experimental protocols are needed in order to obtain reliable estimates of the viscosity and other rheological parameters. In the present work, the plane Couette flow of a Newtonian fluid is considered allowing the possibility of dynamic wall slip, i.e. slip with a slip-relaxation parameter, along the fixed plate. For comparison purposes, the analytical solution corresponding to static slip, i.e. to the Navier slip condition, is derived first. Then, the dynamic-slip solution is obtained using separation of variables as well as the one-sided Fourier transform method. Both methods give essentially the same results. The effects of the slip and slip-relaxation parameters on the solution are discussed. It is demonstrated that flow dynamics becomes slower in the presence of slip and decelerates further as the value of the slip-relaxation parameter is increased.

中文翻译：

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具有动态壁面滑移的牛顿平面库埃特流

滑移的发生使流变流动中粘度的估计复杂化。因此，需要特殊的分析和实验方案，以获得对粘度和其他流变参数的可靠估计。在目前的工作中，牛顿流体的平面 Couette 流被认为允许沿固定板动态壁滑移的可能性，即具有滑移松弛参数的滑移。为了比较，首先推导出对应于静态滑移，即纳维滑移条件的解析解。然后，使用变量分离以及单边傅立叶变换方法获得动态滑移解。两种方法给出的结果基本相同。讨论了滑移和滑移松弛参数对解的影响。