Droplet Dynamics

Monday 16 June 2025

Warwick Mathematics Institute, Zeeman Building, Room B3.02 (Map here)

Organiser: Peter Lewin-Jones (Mathematics Institute and Institute for Advanced Study, University of Warwick)

Contact: peter.lewin-jones (at) warwick.ac.uk

Please Register here: Registration Form

Registration Closes on 31st May.

Lunch and a coffee break will be provided for all attendees.

For those available there will also be an informal evening meal afterwards (at attendees expense), please indicate on the registration form if you are interested.

Practical Information

Travel information is available here. By public transport, the best option is a train to Coventry station and then a bus (12X) to campus. If driving, please park in the Lynchgate Car Park, which is nearest to the Mathematics Institute.

If you are staying overnight, there are various options. The on-campus conferences centres can be booked via Booking.com (Radcliffe and Scarman). If travelling by train, you may prefer to stay near Coventry Station (there are many hotels in Coventry city centre). Another option, especially if driving, is the nearby village of Kenilworth.

Abstracts

Madeleine Moore

Making a deposit: the competition between advection, diffusion and adsorption in evaporating sessile droplets

The evaporation of liquid droplets has received significant research interest due to its fundamental significance in a variety of industrial and engineering applications such as inkjet printing, microscale and colloidal patterning, DNA microarray technologies and the manufacture of Q/OLEDs. One of the key reasons for this is the familiar ‘coffee-ring’ effect that refers to the ringlike stain left behind after a solute-laden droplet evaporates on a surface and its potential use in depositing specific patterns. While deceptively simple, there is a wealth of complexity in the problem, primarily embedded in the – potentially coupled – aspects of evaporation, the associated liquid flow and particle transport. These difficulties have limited the vast majority of existing models to only treating the simplest possible cases of asymptotically-flat, circular droplets evaporating in isolation. This has dramatically limited their applicability in real-world contexts, in which these simplifications are generally broken. In this talk, we will discuss recent advances that attempt to broaden the existing theory with an eye on the ultimate goal of dynamically controlling the process to suit a specific application.

David Craig

Evaporation of Droplets on Porous Substrates

The majority of the previous work on the evaporation of particle-laden sessile droplets has focused on the situation in which the substrate is solid. However, in many applications, such as printing onto paper and fabric textiles, the substrate is porous and the imbibition of liquid into the substrate may play a significant role in the evolution, lifetime, and deposition from a particle-laden droplet. Building on recent work on droplet evaporation on a solid substrate we develop a mathematical model based on lubrication theory for the evolution of an evaporating droplet on a porous substrate. Specifically, we develop a model for the evolution of, the flow within, and the deposition from a thin, sessile droplet undergoing simultaneous evaporation and imbibition on an initially flooded porous substrate in a variety of modes, namely the constant radius (CR), constant angle (CA), stick-slide (SS), and stick-jump (SJ) modes. Motivated by the wide variety of practical applications (such as inkjet printing, DNA chip manufacturing, and disease diagnostics) which would benefit from theoretical insight into the formation of various final deposit patterns, we show that in the regime in which radial advection dominates, single contact-line ring, continuous, continuous and ring, and multiple-ring deposits are formed in the CR, CA, SS, and SJ modes, respectively. On the other hand, we show that in the regime in which both radial and axial advection dominates, the presence of imbibition suppresses the formation of a ring deposit in the CR mode.

Xitong Zhang

Contact angle hysteresis on the patterned liquid surfaces

Liquid-infused surfaces allow droplets to move more easily compared to non-infused solid surfaces by reducing the contact line pinning caused by inherent roughness of solid surfaces. Recently, we have explored infusing the solid textures with two immiscible lubricants, thereby creating patterned liquid surfaces. On such surfaces, while contact line pinning in each liquid domain is removed, we find the contact lines can still become pinned at the boundaries of the liquid patterns. Hence, here we investigate the phenomena of contact line pinning and contact angle hysteresis exhibited by a droplet on the patterned liquid surface under various conditions of lubricant liquid cloaking. In the absence of one lubricant cloaking the other, we observe a slipping-jumping-pinning loop of the contact line motion in the droplet-patterned liquid surface system. However, compared to the scenario on patterned non-infused solid surfaces, the advancing (receding) contact angles of droplets can increase (decrease) before the contact lines jump on the patterned liquid surface. When one lubricant cloaks the other outside (inside) of the droplet, these variations in advancing (receding) contact angles prior to contact line jumping are no longer observed. Such changes of behaviors are linked to the shrinking of lubricant ridge zones near the contact lines, which in turn depend on the cloaking characteristics of lubricants. These findings enhance our understanding of the underlying physics in drop-on-liquid systems, offering crucial insights for manipulating wetting behaviour and controlling droplet dynamics on patterned liquid surfaces. This research was supported by Leverhulme Trust (Research Project Grant RPG-2022-140).

Nathan Coombs

Vapour-mediated impact of hydrogel spheres: The elastic Leidenfrost effect

The Leidenfrost effect, whereby an object near a hot surface evaporates quickly enough to lift itself up and hover, is commonly associated with liquid drops. There are, however, known instances of this effect for stiff sublimable solids (e.g. dry ice) and hydrogels. In this talk I will consider the latter of these cases and discuss experimental findings for Leidenfrost-levitated hydrogel spheres, giving particular attention to the interfacial oscillations that lead to energy injection. Building on existing models of liquid drops, this talk explores a computational framework which couples the elasticity equations of the hydrogel to lower dimensional lubrication equations for the vapour, thus balancing accuracy and computational efficiency. Findings from our simulations are shown to be consistent with experiments at a qualitative level.

Time permitting, insights from linear stability analysis will also be discussed.

Vatsal Sanjay

Impacting spheres: from viscous drops to elastic beads

The impact of spherical objects on surfaces represents a fundamental problem in contact mechanics, spanning from liquid drops governed by Wagner impact theory to elastic beads described by Hertz contact theory. This talk presents a unified framework for understanding impact phenomena across this spectrum, drawing from extensive numerical simulations and theoretical analysis. This unified perspective reveals that both liquid drops and elastic beads share fundamental impact characteristics: initial kinetic energy conversion, force peak generation through momentum change, spreading/deformation phases governed by material properties, and energy recovery during rebound.

Glen McHale

Surfaces Slippery to Liquids
Frictional forces resisting droplet motion often appear to be separate to surface wettability and liquid adhesion. Here I will show how equilibrium surface wettability, representing normal adhesion, combines with hysteresis, representing surface heterogeneity, to produce static and kinetic contact line friction. I will show how an Amontons’-like liquid-on-solid law provides a unified view for the design of superhydrophobic, liquid-infused and liquid-like surfaces slippery to liquids. I will show how a contact line coefficient of friction, defined as the ratio of the frictional to normal component of surface tension forces, can be related to the Kawasaki-Furmidge equation. I will present experimental data from tilt angle experiments on liquid-like surfaces with low and high mobility for water droplets showing measurements are consistent with the predicted shape factor k=pi/4. Finally, I will show how strong, but dilute, defects introduce pinning into near-perfect slippery surfaces.

Acknowledgements. Many collaborators contributed to this work, which was part-funded by the UK Engineering and Physical Sciences Research Council (EPSRC) and the Leverhulme Trust.

Marc Pradas

Exploiting bifurcations for droplet control on smooth surfaces

The shape and stability of a droplet in contact with a solid surface are influenced by the surface’s chemical composition, topography, and, crucially, the droplet’s size. As its size changes—typically through evaporation or condensation—droplets on smooth patterned surfaces can undergo sudden changes in shape and position. These abrupt transitions, known as snaps, are induced by the surface pattern and arise from fold and pitchfork bifurcations, which respectively drive symmetric and asymmetric motions. However, determining which type of snap is likely to occur remains an open fundamental question, with implications for the rational design of surfaces to control droplet behaviour.

Here, we combine theoretical analysis with diffuse-interface simulations to investigate the dynamics of droplet snaps and their dependence on the system’s physical properties. Our results reveal that asymmetric patterns induce imperfect pitchfork bifurcations, which can be exploited to direct droplet motion. Additionally, we show that the likelihood of symmetric or asymmetric snaps depends on the separation between fold and pitchfork bifurcation points and how this separation evolves as droplets grow or shrink. These findings can inform strategies for controlling droplets using smooth surface patterns and have broader relevance in systems where competing bifurcations dictate stability, such as snap-through instabilities in elastic media.