Air blade runner: controlling liquid films with high-precision gas jets
This is a fully-funded 4-year PhD position based in the HetSys Centre for Doctoral Training at the University of Warwick.
Project outline
We will develop new mathematical models and control methods for falling liquid films. Why falling liquid films? They form a beautiful theoretical setting with applications in microchip manufacturing and smart printing.
How will we do it? Using precise jets that blow air into the fluid from above, improving on recent work on control that injects or removes fluid from below these films, which is less practical.
This project will involve model development and validation, numerical simulation, and control development under model uncertainty and noisy observations of the system. It offers very interesting development directions which we look forward to exploring together.
Supervisors
Primary: Dr Susana Gomes (Maths)
Dr Radu Cimpeanu (Maths)
- Develop accurate models for interfacial flows involving forcing from air jets (this includes modelling the air flow caused by the air jets and its influence on the stresses affecting the fluid-air interface).
- Compare the interfacial evolution tracked by the model with the outputs of direct numerical simulations of the Navier-Stokes equations. Use this comparison to quantify model uncertainty.
- Derive controls that are appropriate for this problem, and that are robust to model uncertainties and noise in observations.
- Ultimately create a pipeline for this type of system, from modelling to simulation and control, which is transferable to other (similar) contexts.
- Development of new mathematical models and appropriate controls for these.
- Design of controls under uncertainty for highly nonlinear problems.
- Software development (e.g. GitHub repository with tutorials, examples, etc.) to facilitate knowledge transfer.
- Development of transferable research skills as part of a friendly cross-generational research group.
- Publication in appropriate journals (namely in fluid dynamics, scientific computing, and control theory, Journal of Open Source Software).
- Presentation at conferences and workshops (e.g. British Applied Mathematics Colloquium, SIAM Conference in Control and its Applications, International Congress on Industrial and Applied Mathematics, American Physical Society Division of Fluid Dynamics).
- Mathematical modelling
- Scientific computing (efficient numerical simulation of partial differential equations (PDEs), numerical linear algebra associated with PDE discretisation, including the solution to control problems)
- Optimal control, and feedback control theory
- Software reproducibility
- Working within an interdisciplinary project, communicating with colleagues from other disciplines and outside of academia
- Communication and presentation skills
These skills position you for careers in AI research, computational materials science, national laboratories, tech industry or academic research. The HetSys training provides a foundation for these skills through dedicated courses and cohort activities.
We require at least a II(i) honours degree at BSc or an integrated masters degree (e.g. MPhys, MChem, MSci, MEng etc.) in a physical sciences, mathematics or engineering discipline. We do not accept applications from existing PhD holders.
If you are an overseas candidate please check here that you hold the equivalent grades before applying.
For postgraduate study in HetSys, the term “overseas” or “international” student refers to anyone who does not qualify for UK home fee status. This includes applicants from the European Union (EU), European Economic Area (EEA), and Switzerland, unless they hold settled or pre-settled status under the UK’s EU Settlement Scheme.
If you are a European applicant without UK residency or immigration status that qualifies you for home fees, you will be classified as an overseas student.