[School of Natural Sciences PhD Scholarships] Passive control of Saffman-Taylor instabilities in shear-thinning fluids

About the project

About the Project Interfacial instabilities are often undesirable in industrial and geophysical flows because they can lead to inefficient displacement and complex flow patterns. Controlling these instabilities usually requires some form of external intervention. However, in radial flows involving shear-thinning fluids, the instabilities can naturally weaken and eventually disappear as the flow evolves. The aim of this PhD project is to understand the physical mechanisms responsible for this natural suppression and to determine how they might be used as a form of passive flow control. The student will investigate Saffman–Taylor instabilities arising when a shear-thinning fluid displaces a highly viscous Newtonian fluid in a radial Hele-Shaw cell. In this case, the effective viscosity of the shear-thinning fluid increases with radial distance from the source, acting to suppress viscous fingers without the need for external control. The student will combine laboratory experiments, image processing, and mathematical modelling to determine how the suppression of viscous fingers is influenced by parameters such as injection rate, fluid properties, and confinement. Particular attention will be given to the influence of wall slip and thin lubricating fluid layers, which can alter the local shear rate and therefore influence the effective viscosity. The overall goal is to design flows in which undesirable instabilities are naturally suppressed. The project is interdisciplinary, involving both experimental and theoretical aspects. It would be well suited to a student with a background in mathematics or physics. Previous laboratory experience is not essential as training will be provided, but the student should be enthusiastic about developing both experimental and theoretical skills. 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 Mathematics, Physics, Applied Mathematics or a closely related discipline OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Mathematics, Physics, Applied Mathematics or a closely related discipline. A strong interest in fluid mechanics, mathematical modelling, and experimental research is essential. This project will remain open until filled. If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026. If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

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