Impact of Fluids of Different Densities

The impact of two bodies of liquid, such as droplets, is a phenomenon that occurs 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 length scales. For example, in 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 laboratory experiments. It is here that mathematical modelling can excel. In many applications, it is the early stages of the impact that capture the critical physical phenomena, such as the formation of splash or spray and the subsequent breakup 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. 94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021

BSc in Mathematics or cognate discipline

The standard University IELTS English language requirement is 6.5 overall with 6.0 in each individual element (reading, writing, listening and speaking).

International students: £23,100

UK students: £5,238

UK/Home: £5,238

International: £23,100

October 2026, February 2027, July 2027, October 2027

31 July 2027

• Loughborough, United Kingdom