On determining Navier's slip parameter at a solid boundary in flows of a Navier–Stokes fluid

Abstract

While the assumption of the “no-slip” condition at a solid boundary is unquestioningly applied to study the flow characteristics of a Navier–Stokes fluid, there was considerable debate among the early pioneers of fluid mechanics, Du Buat, Girard, Navier, Coulomb, Poisson, Prony, Stokes, and others, as to the proper condition that has to be met at a solid boundary due to a fluid, such as water flowing adjacent to the same. Contemporary usage of the no-slip boundary condition notwithstanding, in our previous study [Málek and Rajagopal, “On a methodology to determine whether the fluid slips adjacent to a solid surface,” Int. J. Non-Linear Mech. 157, 104512 (2023)], we outlined a methodology to test the validity of the assumption. In this study, we continue the investigation further by providing a scheme for determining the slip parameter that characterizes the extent of slip, if one presumes that Navier's slip boundary condition is satisfied. We find that depending on whether the volumetric flow rate is greater or less than the volumetric flow rate corresponding to the no-slip case, different scenarios present themselves regarding what transpires at the boundary.