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

Eleanor C Johnstone,Andrew L Hazel,Oliver E Jensen

doi:10.1017/jfm.2022.26

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.

Highlights

The behaviour of fluids when the dominant force is surface tension underpins many fundamental physical and industrially valuable processes, including microfluidics and inkjet printing (Yang, Yang & Hong 2005; He et al 2017; Calver et al 2020); directional transport of liquids in biological processes (Prakash, Quéré & Bush 2008; Zheng et al 2010; Ju et al 2012; Comanns et al 2015; Xu & Jensen 2017; Bhushan 2019); engineering applications such as water harvesting (Brown & Bhushan 2016; Xu et al 2016; Li et al 2017); and the behaviour of fluids in low-gravity situations (Passerone 2011)
We present results for the displacement of the static meniscus and the contact line induced by Gaussian perturbations (3.2)
In the channel-volume-preserving case, the response of the meniscus and contact line is localised around the perturbations in the y direction, whereas in the channel-volume-changing case, the perturbations induce a larger-amplitude response that is felt across the entire depth and width of the channel

Summary

Introduction

The behaviour of fluids when the dominant force is surface tension underpins many fundamental physical and industrially valuable processes, including microfluidics and inkjet printing (Yang, Yang & Hong 2005; He et al 2017; Calver et al 2020); directional transport of liquids in biological processes (Prakash, Quéré & Bush 2008; Zheng et al 2010; Ju et al 2012; Comanns et al 2015; Xu & Jensen 2017; Bhushan 2019); engineering applications such as water harvesting (Brown & Bhushan 2016; Xu et al 2016; Li et al 2017); and the behaviour of fluids in low-gravity situations (Passerone 2011). The behaviour that we study here is that of a very simple static system, which forms the ‘basic state’ for many of these dynamical problems. We seek to quantify and describe the sensitivity of menisci in confined channels to imperfections in geometry. Understanding such sensitivity is important in the industrial and biological processes described above, where natural or manufactured surfaces are in general not perfectly smooth. Stroock & Ajdari (2004) provide a general discussion of the role of channel geometry in controlling fluids in microchannels. Anna (2016) and Ajaev & Homsy (2006) give a more general discussion of the modelling and applications of drops and bubbles in microchannels and confined channels

Methods

Results

Conclusion