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

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.

Looking for future biological control agents: the comparative function of the deutosternal groove in mesostigmatid mites

“…Indeed the particular arrangement of small amplitude subcapitular ridges and grooves appears to be a designed element to manipulate the shape of fluid menisci over long ranges (see Johnstone et al. 2022 ). In the postulated mechanism herein, the transverse denticulated ridges, in turn, ensure that the liquid film between the longitudinal edges remains macroscopically stable, thereby creating a continuous basal ‘slippery track’ when little volume is present.…”