Linear shear flow past a hemispherical droplet adhering to a solid surface

TL;DR

This study provides an exact solution for three-dimensional shear flow over a hemispherical droplet on a solid surface, analyzing effects of viscosity ratio, surface deformations, and forces involved.

Contribution

It generalizes previous solutions by incorporating viscosity ratio effects and surface deformations in shear flow over hemispherical droplets.

Findings

Derived exact solutions for shear flow over hemispherical droplets

Analyzed the impact of viscosity ratio on forces and torque

Examined surface deformations at small Capillary numbers

Abstract

This paper investigates the properties of a three dimensional shear flow overpassing a hemispherical droplet resting on a plane wall. The exact solution is computed as a function of the viscosity ratio between the droplet and the surrounding fluid and generalizes the solution for the hemispherical no-slip bump given in an earlier paper by Price (1985). Several expressions including the torque and the force acting on the drop will be considered as well as the importance of the deformations on the surface for small Capillary numbers.