Roughness on liquid-infused surfaces induced by capillary waves

TL;DR

This study uses direct numerical simulations to reveal that capillary waves on liquid-infused surfaces can induce roughness, increasing drag in turbulent flows, especially when surface tension is low or grooves are wide.

Contribution

It identifies a new failure mode of liquid-infused surfaces caused by capillary waves and provides criteria to predict surface roughness in turbulent conditions.

Findings

Capillary waves can significantly increase surface roughness and drag.

The generation of waves is explained by Miles' theory for gravity waves.

Relations are provided to predict whether a LIS will be smooth or rough.

Abstract

Liquid-infused surfaces (LIS) are a promising technique for reducing friction, fouling and icing in both laminar and turbulent flows. Previous work has demonstrated that these surfaces are susceptible to shear-driven drainage. Here, we report a different failure mode using direct numerical simulations of a turbulent channel flow with liquid-infused longitudinal grooves. When the liquid-liquid surface tension is small and/or grooves are wide, we observe traveling-wave perturbations on the interface with amplitudes larger than the viscous sublayer of the turbulent flow. These capillary waves induce a roughness effect that increases drag. The generation mechanism of these waves is explained using the theory developed by Miles for gravity waves. Energy is transferred from the turbulent flow to the LIS provided that there is a negative curvature of the mean flow at the critical layer. Given the groove width, the Weber number and an estimate of the friction Reynolds number, we provide relations to determine whether a LIS behaves as a smooth or rough surface in a turbulent flow.