Mathematical modelling of droplet impact on soft substrates

Lead Research Organisation: University of Oxford
Department Name: Mathematical Institute


Splashing on soft substrates is an active research topic with a wide range of applications including rainfall, pesticide application, inkjet printing, fuel combustion, forensic science and spray coating. However, recent experiments have shown that the splashing process is more complex than previously thought, so that there are many outstanding questions still remaining regarding the fundamental physical mechanisms involved in droplet splashing and how they are promoted or prohibited by substrate deformation. Finding out how to eliminate splashing is a relatively new topic, and can be useful in situations where splashing could cause hygiene or safety concerns.

Droplets splash when they impact dry, flat substrates above a critical velocity that depends on parameters such as droplet size, viscosity, and air pressure. Recent experimental results [1] have shown that substrate stiffness also affects the splashing threshold, for example, droplets on the softest substrates need over 70% more kinetic energy to splash than they do on rigid substrates. The energy losses are caused by deformations of the soft substrate during the first few microseconds of impact. There is currently no theory for the effect of substrate stiffness on the splashing threshold.

The aim of the project is to derive and analyse the impact of a liquid droplet on a range of soft substrates of practical importance, guided by extensive close collaboration with the Fluid Dynamics Laboratory in the Department of Engineering, Oxford. The objectives are to (i) use the method of matched asymptotic expansions to derive systematically reduced models for the early stages of the impact that retain all of the essential physics while remaining tractable, generalising thereby classical impact theory into new regimes; (ii) develop, test and validate state-of-the-art direct numerical simulations for the early and late stages of the impact. The reduced asymptotic models will be used to extract physical insight and both initiate and validate the numerical simulations. The numerical simulations will be used to characterise the effect of the substrate on the splashing threshold. We will begin with the simplest possible model for the substrate, namely a cantilever, before moving onto more complicated substrate rheologies including elastic, highly viscous, viscoelastic substrates and vibrating soft surfaces.

This project falls within the EPRSC Continuum Mechanics and Fluid Dynamics and Aerodynamics research areas.

[1] Howland, CJ, Antkowiak, A, Castrejón-Pita, JR; Howison, SD, Oliver, JM, Style, RW, Castrejón-Pita, AA. It's Harder to Splash on Soft Solids. Physical Review Letters 117, 184502 (2016).

Collaborators: Alfonso Castrejon-Pita, Fluid Dynamics Laboratory in the Department of Engineering, Oxford.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R513295/1 01/10/2018 30/09/2023
2100031 Studentship EP/R513295/1 01/10/2018 31/03/2022 Michael Negus