Mathematical modelling of thin viscous flows with biological surfactants

Project description

Surfactants are substances that decrease the surface tension at a liquid interface, enabling the fluid to wet and spread more easily. Mathematical modelling of surfactant-laden flow is an active research topic in fluid mechanics, often combining lubrication theory with a conservation law for the interfacial surfactant concentration. An emerging field of research is to harness surfactants in biological applications. For example, in wound healing biological surfactants can dislodge biofilms and aid wound cleaning, leading to improved wound care [1]. The interplay between fluid flow, surfactants, and cells in biological applications provides a rich source of new problems in applied mathematics. In this project, the PhD candidate will explore mathematical models for biological surfactants using a combination of continuum mechanics, asymptotic analysis, and numerical computation. The project will be supervised by Dr Edward Green (U. Adelaide), an expert in continuum mechanical models of biological tissue, and Dr Anna Kalogirou (U. Nottingham), a fluid mechanist with expertise in multi-layer flows, including surfactant-laden flows. Expected outcomes include new mathematical theory for thin biological fluid flows, with potential application in biofilm removal and wound care.

This project is offered as part of the Adelaide–Nottingham Alliance. The successful candidate will spend approximately half of their PhD at Nottingham and the other half as Adelaide (Australia).

Project co-supervisors:

• Dr Edward Green (School of Computer and Mathematical Sciences, The University of Adelaide)

• Dr Alex Tam (UniSA STEM, The University of South Australia)