[School of Natural Sciences PhD Scholarships] Rheology-driven instabilities in shear-thinning fluids

About the project

About the Project Shear-thinning fluids are encountered in biological flows such as blood flow in vessels, and in industrial processes including injection moulding and channel cleaning. Their relevance extends to large-scale flows such as the flow of ice over oceans and enhanced oil recovery. Despite their widespread importance, their rheology, particularly how their effective viscosity depends on the flow configuration, remains poorly understood. The aim of this PhD project is to establish whether the behaviour of rheology-driven fluid instabilities can be used as a measure of the effective viscosity of a shear-thinning fluid. The student will conduct an experimental and theoretical investigation of the Saffman–Taylor instabilities that arise when a shear-thinning fluid displaces a highly viscous Newtonian fluid in a narrow gap, or Hele-Shaw cell, in a radial geometry. By combining laboratory experiments, image processing, and mathematical modelling, the student will establish the conditions governing the onset, evolution, and suppression of viscous fingers. They will then develop theoretical models and derive stability criteria that can be compared directly with experimental observations. The central aim will be to determine whether the onset and suppression of these instabilities can provide a practical way of inferring the effective viscosity of the shear-thinning fluid. The project is interdisciplinary, involving both experimental and theoretical components. It would be particularly well suited to a student with a background in mathematics or physics, who is interested in combining laboratory experiments with mathematical modelling. Previous laboratory experience is not essential as training will be provided. However, the student should be enthusiastic about developing skills across both experimental and theoretical aspects of the project. 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

Research areas