Tensorial hydrodynamic slip

TL;DR

This paper introduces a tensorial generalization of the Navier slip boundary condition to better model flows over anisotropic textured surfaces, enabling more accurate analysis of complex surface effects.

Contribution

It presents a tensorial slip boundary condition derived from microstructural theories, allowing for the analysis of anisotropic surface effects in fluid flows.

Findings

Exact solutions for shear and pressure-driven flows over textured surfaces.

Demonstration of how rotating textures affects slip via matrix algebra.

Potential for extracting local slip tensors from experimental measurements.

Abstract

We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or simply postulated as an constitutive relation, subject to certain general constraints on the interfacial mobility. The power of the tensor formalism is to capture complicated effects of surface anisotropy, while preserving a simple fluid domain. This is demonstrated by exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures. From such solutions, the effects of rotating a texture follow from simple matrix algebra. Our results may be useful to extracting local slip tensors from global measurements, such as the permeability of a textured channel or the force required to move a patterned surface, in experiments or simulations.