Droplets With Dynamic Size On Smooth Surfaces

Droplets interacting with solid surfaces are found in a wide variety of daily life experiences and natural phenomena. Their study serves as a canonical example of a wetting phenomenon which, despite its simplicity, has been shown to be a remarkably complicated problem. Many theoretical efforts over the last few years have focused their attention on understanding how the properties of the solid surface affect the dynamics of the droplet, with particular emphasis on droplet control and manipulation, which is important for a wide range of technological applications, including the rapidly growing fields of nano- and micro-fluidics.

Quite often the volume of the droplets is subject to external, time-dependent variations - a situation that we refer to as droplets with dynamic size. This occurs, for example, when there is mass exchange through the droplet interface (evaporation/condensation phenomena), or when droplets sit on porous materials so that liquid is absorbed through the pores.

When the volume of a droplet increases or decreases, it is widely accepted that microscopic defects on the surface (either chemical or topographical) induce pinning effects, which block the translational motion of the contact line, i.e. the line where the liquid/gas interface meets the solid surface. As a consequence, droplets exhibit what is known as stick-slip motion, which has crucial effects on, e.g., the way droplets evaporate, but has been proved to be notoriously difficult to predict, and more importantly control. Precisely because of this, the use of smooth, pinning-free surfaces with controllable macroscopic properties/topographies has become a major need in the design of many microfluidic/wetting systems. However, a quantitative understanding of the interplay between the volume changes in droplets and smooth variations on the surface, and how this affects both the dynamics and the shape of the droplet, still elude us.

This project will explore the fundamental interplay between a time-dependent variation of the droplet volume and simple smooth variations on solid surfaces. Using a balanced combination of analytical and computational techniques, we aim to investigate under which conditions a droplet may naturally exhibit lateral motion as its volume changes in time, and to exploit this in applications on droplet control, such as directed motion. We will also investigate whether simple configurations like periodic variations are able to induce complex dynamics, such as random walks and collective phenomena in a multi-droplet system.

The ultimate goal of the proposed research is the systematic and predictive theoretical and computational analysis of the dynamics of droplets with dynamic size on surfaces that have controllable and experimentally amenable properties. As a consequence, the outputs of this project can be used to recommend new design rules, geometries, and operational protocols for improved droplet control and manipulation in technological applications that rely on cooling/heating processes and/or porous-based micro-devices.

The ultimate goal of the proposed research is the understanding of how solid surfaces can be designed to control and manipulate droplets with dynamic size. This a key aspect in many rapidly developing technologies in the UK's biomedical, printing, and computer hardware industries, to name but a few. The systematic use of state-of-the-art theoretical and computational techniques, as proposed here, can generate valuable insight into many aspects of these systems, and particularly how they can be integrated into a wide variety of functional materials and microfluidic processes at different scales.

To stimulate interaction with industry, the PI will organise a multi-disciplinary workshop at the Open University, in Milton Keynes. This will provide a valuable platform for leading experts from academia and industry to identify promising inter-disciplinary collaborations. One of the aims of this event will be to discuss how the ideas developed in this project, along with other recent advances in the area, can be carried through to implementation in specific industrial applications. In addition to the workshop, the results of this project will be disseminated at several international conferences and through the PI's national and international collaborators.

The UK is currently world-leading in the areas of interfacial fluid mechanics, multiphase flow, and microfluidics. These communities will benefit from the training of one PDRA with an inter-disciplinary outlook that combines analytical and computational skills in fluid mechanics and statistical physics. The PDRA will also benefit from training in scientific writing, networking through attendance to conferences, project management, and public engagement. This project will further establish the UK's reputation in these areas and strengthen links with other research groups, both nationally and internationally.

The problem of droplets with a time-dependent volume interacting with solid surfaces can be used to illustrate how mathematical methods are applied to understand a variety of physical concepts, such as capillarity and wetting, stability, mass transfer, and fluid flow. To make the results of this research accessible to as wide an audience as possible and to inspire others to carry out mathematical research, the PI will promote aspects of the research programme by means of dissemination to non-academics and the general public, including: (i) Teaching-based dissemination, i.e. via incorporating research highlights into module content that is related to the proposed research, (ii) Giving public presentations to students of all levels; and (iii) Social media/outreach activities, where this research will also be featured, such as e.g. the new initiatives #HiddenMaths and #MeetUsMonday at the Open University.