On the Navier-slip boundary condition for computations of impinging droplets

TL;DR

This paper proposes a mesh-dependent relation for the slip number in Navier-slip boundary conditions to improve the accuracy of impinging droplet simulations, validated against experiments and theory.

Contribution

It introduces a new slip relation based on Reynolds, Weber numbers, and mesh size, enhancing computational predictions of droplet wetting behavior.

Findings

Relative error less than 10% on hydrophilic surfaces

Validation against experimental wetting diameters

Agreement with theoretical maximum wetting diameters

Abstract

A mesh-dependent relation for the slip number in the Navier-slip with friction boundary condition for computations of impinging droplets with sharp interface methods is proposed. The relation is obtained as a function of Reynolds number, Weber number and the mesh size. The proposed relation is validated for several test cases by comparing the numerically obtained wetting diameter with the experimental results. Further, the computationally obtained maximum wetting diameter using the proposed slip relation is verified with the theoretical predictions. The relative error between the computationally obtained maximum wetting diameter and the theoretical predictions is less than 10 % for impinging droplet on a hydrophilic surface, and the error increases in the case of hydrophobic surface.