# Multiphase unsteady Stokes flow over grooved surfaces: an analytical study

## TL;DR

This paper presents an analytical study of multiphase unsteady Stokes flow over grooved surfaces, deriving solutions and validating them with numerical simulations, focusing on flow response and shear stress under oscillatory conditions.

## Contribution

It introduces analytical expressions for multiphase unsteady Stokes flow over grooved textures, including effects of oscillation frequency and interface position, validated by numerical simulations.

## Key findings

- Analytical solutions match numerical simulations well.
- Flow transfer function depends on oscillation frequency and interface location.
- Effective slip length and shear stress are characterized for grooved surfaces.

## Abstract

This paper studies multiphase flow within grooved textures exposed to external unsteadiness. We derive analytical expressions for multiphase unsteady Stokes flow driven by oscillating streamwise/spanwise velocity in the presence of periodic grooves. Good agreement is obtained between the analytical solution and direct numerical simulations performed using the volume of fluid method. The effects of oscillation frequency, Reynolds number, and the multiphase interface location on the transfer function between the input signal external to the groove and output near the interface, are examined. The effective slip length and the shear stress over the grooved plane are described.