[School of Natural Sciences PhD Scholarships] Feedback control to optimize and explore viscous fingering

About the project

About the Project Active feedback control - where control inputs are chosen in response to real time observations - is a very powerful tool to alter the dynamics of a system. It can suppress or enhance instability, select particular patterns, or drive systems towards new configurations. The aim of this project is to explore the limitations and potential of feedback control in interfacial fluid mechanics to (i) select and control dynamics, (ii) explore new dynamical regimes, and (iii) gain insight into underlying physical mechanisms. The initial setup will involve radial viscous fingering, where the injection of a less viscous fluid (air) into a more viscous region readily leads to instability and pattern formation. This setup is accessible in laboratory experiments, and can be modelled using lubrication theory. In the simplest theoretical case, with this idealised model, small displacement from a circular bubble and feedback control delivered by same-fluid injection and suction, the resulting linear control problem has an elegant analytic solution. The project will build from this point to explore robustness of control to nonlinear effects, errors in model assumptions, changes in the model structure, and effectiveness in practical experiments with Newtonian or shear thinning fluid. As the project progresses, there is scope to investigate broader, more abstract questions, such as how control allows us to probe and characterise new systems and to build physical insight in situations where an appropriate model structure is not known. This PhD project will involve a range of scientific skills, including fluid mechanics, linear stability, control theory, nonlinear dynamics, experimental fluid mechanics and numerical methods. Training in each of these areas can be provided as needed, but students should be interested in how different areas and approaches combine. This project is expected to start in September 2027. Before you apply: We strongly recommend that you contact the supervisors for this project before you apply. How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships . If you don’t already have an applicant account, please follow the instructions here . When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications . Please note late or incomplete applications will not be considered. Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status. We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder. Eligibility : The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in Applied Mathematics, Physics, or Engineering OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Applied Mathematics, Physics, or Engineering. This project will remain open until filled. If your application is submitted by 1 st November 2026, you can expect a decision by 18 th December 2026. If your application is submitted by 15 th January 2027, you can expect a decision by 30 th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

Research areas