The effect of isolated ridges and grooves on static menisci in rectangular channels

TL;DR

This paper investigates how localized geometric features like ridges and grooves on channel walls influence the shape of static liquid menisci, combining theoretical, numerical, and analytical methods to understand and control contact line behavior.

Contribution

It provides a comprehensive analysis of meniscus deformation due to wall perturbations, including explicit formulas for pressure differences and methods to engineer contact line patterns.

Findings

Local deformations depend on perturbation shape

Small changes in channel volume affect pressure difference

Explicit boundary data formulas for pressure difference

Abstract

We present theoretical and numerical results that demonstrate the sensitivity of the shape of a static meniscus in a rectangular channel to localised geometric perturbations in the form of narrow ridges and grooves imposed on the channel walls. The Young--Laplace equation is solved for a gas/liquid interface with fixed contact angle using computations, analytical arguments and semi-analytical solutions of a linearised model for small-amplitude perturbations. We find that the local deformation of the meniscus's contact line near a ridge or groove is strongly dependent on the shape of the perturbation. In particular, small-amplitude perturbations that change the channel volume induce a change in the pressure difference across the meniscus, resulting in long-range curvature of its contact line. We derive an explicit expression for this induced pressure difference directly in terms of the boundary data. We show how contact lines can be engineered to assume prescribed patterns using suitable combinations of ridges and grooves.