An assessment of non-Newtonian flow in laminar and turbulent mixing flow conditions


Newtonian fluids (e.g. water) exhibit a linear relationship between shear stress and shear strain rate, where the viscosity is the coefficient of proportionality between applied shear stress and velocity gradient. Fluids where this relationship does not hold are classed as non-Newtonian. In the case of non-Newtonian fluids, the viscosity is a function of the shear rate and is termed the apparent viscosity. Non-Newtonian fluids are found in both nature and industrial processes and the ways in which their behaviour differs from Newtonian fluids vary. They may exhibit shear-thinning behaviour in which the apparent viscosity decreases with increased stress (e.g. blood, ketchup), or they may be shear-thickening fluids where the apparent viscosity increases with increased stress (e.g. corn starch). Viscoplastic fluids (e.g. toothpaste, emulsions) require a yield stress before they will begin to flow.

This fully-funded PhD project provides a unique opportunity to pursue research in advanced experimental fluid mechanics. The project will study the behaviour of non-Newtonian fluids and, in particular, their behaviour in laminar, turbulent and transitional mixing flow conditions. Starting with an analysis of a yield stress fluid contained within a rotating endwall geometry, the project will use start-of-the-art simultaneous 2D3C Particle Image Velocimetry and Planar Laser Induced Fluorescence to study turbulent flow patterns to enhance our understanding of the fundamental flow physics of non-Newtonian fluids in nature and various industrial processes, including the mixing of wastewater sludge and the flow of cement slurries. There will also be the opportunity to develop numerical models of the flows identified using the University of Liverpool high performance computing resource, the parallel Linux cluster, Barkla.

This project is funded by The Faculty of Science & Engineering at The University of Liverpool and will start on 1st October 2023.

Successful candidates who meet the University of Liverpool eligibility criteria will be awarded a Faculty of Science & Engineering studentship for 3.5 years, covering UK tuition fees and an annual tax-free stipend (e.g. £17,668 p.a. for 2022-23).

The Faculty of Science & Engineering is committed to equality, diversity, widening participation and inclusion. Academic qualifications are considered alongside non-academic experience. Our recruitment process considers potential with the same weighting as past experience. Students must complete a personal statement profoma and ensure this is included in their online application.

Applicant Eligibility

Candidates will have, or be due to obtain, a Master’s Degree or equivalent from a reputable University in an appropriate field of Engineering. Exceptional candidates with a First-Class Bachelor’s Degree in an appropriate field will also be considered.

Application Process

Candidates wishing to apply should complete the University of Liverpool application form applying for a PhD in Civil Engineering and uploading: Degree Certificates & Transcripts, an up-to-date CV, a covering letter/personal statement and two academic references.


Candidates wishing to discuss the research project should contact the primary supervisor Professor John Bridgeman [], those wishing to discuss the application process should discuss this with the School Postgraduate Office [].

 How to apply


Open to UK applicants

Funding information

Funded studentship

This Scholarship is for UK [home] students only and has a financial package including: annual stipend at the UKRI rate [currently £17,668 per annum for academic year 2022-23] and student fees. Overseas students are eligible to apply if they can cover the difference in UK and Overseas tuition fees, the costs of their student visa, NHS health surcharge, travel insurance and transport to the UK, as these are excluded from the funding.