Impact of fluids of different densities (Ref: MA/MM-SF1/2026)

About the Project

The impact of two bodies of liquid, such as droplets, is a phenomenon occurring widely in nature and in engineering applications, from waves breaking onto layers of marine biological matter to streams of different inks in additive manufacturing. Impacts are notoriously complicated problems to study, with rapid topological changes occurring over disparate lengthscales. For example, for wave impact, the size of the wavefront may be orders of magnitude larger than the spray thrown up post-impact. Impacts may therefore be challenging to capture using direct numerical simulations or in the laboratory.

It is here the mathematical modelling can excel. In many applications, it is the early of stages of the impact that captures the critical relevant physical phenomena, such as the formation of splash or spray and the subsequent break up of the splash into smaller satellite droplets. In this project, we will seek to extend existing models of liquid-liquid impact to scenarios in which the density of the fluids is allowed to change. We will build upon inviscid Wagner theory for impact dynamics by accounting for such density differences and including the effects of viscosity and surface tension in the fluids where necessary.

The successful applicant will need to have experience in fluid dynamics and mathematical modelling, while knowledge of asymptotic methods and complex variable methods will be highly beneficial.

Name of primary supervisor/CDT lead:
Madeleine Moore m.r.moore@lboro.ac.uk
https://www.lboro.ac.uk/departments/maths/staff/madeleine-moore/

Entry requirements:

• Essential: BSc in Mathematics or cognate discipline with a significant mathematical component (e.g. Physics)
• Desired: MSc in Mathematics or cognate discipline with a significant mathematical component (e.g. Mathematical Modelling or Physics)

English language requirements:
Applicants must meet the minimum English language requirements. Further details are available on the International website (http://www.lboro.ac.uk/international/applicants/english/).

Bench fees required: No

Closing date of advert: 31st July 2027

Start date: October 2026, February 2027, July 2027, October 2027

Full-time/part-time availability: Full-time 3 years

Fee band: 2025/26 Band RA (UK £5,006, International £22,360)

How to apply:
All applications should be made online. Under programme name, select Mathematical Sciences. Please quote the advertised reference number: MA/MM-SF1/2026 in your application.
To avoid delays in processing your application, please ensure that you submit a CV and the minimum supporting documents.
The following selection criteria will be used by academic schools to help them make a decision on your application. Please note that this criteria is used for both funded and self-funded projects.
Please note, applications for this project are considered on an ongoing basis once submitted and the project may be withdrawn prior to the application deadline, if a suitable candidate is chosen for the project

Project search terms:
applied mathematics, fluid mechanics, asymptotic analysis