Rebecca Hill

Rebecca is a Mathematics graduate who recently completed her PhD in Mechanical Engineering, investigating how hydrodynamic instabilities are influenced by non Newtonian fluids and solid particle suspensions. She is currently an Interim Lecturer in the Department of Mechanical and Aerospace Engineering.

What did you study?

At school I studied Maths, Further Maths and Physics. I always enjoyed maths and science, so it felt like the most natural thing to do was to choose the subjects that I found interesting (it also helped that they were the subjects I tended to be best at).

I completed an MMath in Mathematics in 2021, specialising in applied mathematics, before moving into Mechanical Engineering for my PhD (2021-2025). My PhD research focused on hydrodynamic instabilities in complex fluids, including non-Newtonian fluids and solid particle suspensions, and how these instabilities affect mixing and fluid-solid transport.

I have always been interested in the mathematics behind physical problems, particularly understanding why systems behave the way they do. Moving into Mechanical Engineering gave me the opportunity to apply that mathematical perspective to real physical problems, while also gaining a better understanding of how the mathematics translates into physical behaviour. 

What inspired you to choose and study your degree subject?

For a long time, I was torn between maths and physics, or some combination of the two. Ultimately, it was a single piece of advice that swayed me towards maths: "if you enjoy it even when it is challenging or frustrating, then that is probably the path you should follow."

At university, I was mostly drawn to applied mathematics. I became particularly interested in how mathematical ideas could be used to understand physical systems, which eventually led me into Mechanical Engineering. My research now sits somewhere between mathematics, fluid mechanics and engineering, where I mainly use theory and computational methods to investigate complex fluid behaviour. 

What has been your most exciting project?

My PhD research is definitely my most exciting project so far.

I investigated how hydrodynamic instabilities are influenced by non-Newtonian fluids and particle suspensions, and what those changes mean for processes such as mixing and fluid-solid transport. Most of my work was theoretical and computational, using mathematical and numerical models as tools to investigate how changing fluid properties affects flow behaviour.

One of the things I enjoyed most was that the research rarely followed a completely predictable path. A single result can shift the direction of a project entirely, revealing questions you hadn’t anticipated. That constant need to think differently, question assumptions and adapt to new problems is what makes research so exciting.

What are your top tips?

Embrace the interdisciplinary nature of research and learn the “languages” of other disciplines. Mathematicians, engineers, physicists, chemists and biologists all approach problems differently, and understanding those perspectives makes collaboration far more effective. Some of the most interesting discoveries can happen at the intersections between disciplines, so being open-minded and willing to learn from different perspectives is incredibly valuable.

I would also say: don't be afraid of not knowing something. Research is, by definition, about working on things where you do not already know the answer. Being comfortable with asking questions and learning as you go is much more important than knowing everything from the beginning.

Do you have any advice to share?

"You should not undersell or underestimate yourself... you are far more capable than you believe." – D.J.C., 2021.

"We all know that you are capable - you just need to learn to see it too." - S.A.R., 2026. 

It's easy to focus on the things you don't know yet, the things you could have done better, or the people who seem to be further ahead, and forget how much you are actually capable of achieving. Having people who remind you of that makes a huge difference.

So, don't underestimate the value of community and good mentors, because you cannot do everything by yourself, no matter how hard you might try. Having people around you who are willing to answer questions, offer advice, encourage you when things are difficult, and recognise your achievements is invaluable.

And finally, don't feel that you have to have your entire career planned from the beginning. My own path from Mathematics into Mechanical Engineering was not something I had planned when I started university. Following the things I found interesting led me somewhere I hadn't expected, and that turned out to be the best thing.

Why are you passionate about your subject?

I love that I can constantly ask questions and then try to find answers. What I enjoy most about research is that there is always something new to understand. A problem that initially seems straightforward can turn out to have a much more complicated explanation, or a result can raise a question that you had never considered before.

I also enjoy the combination of mathematical ideas with physical problems. You can start with an equation or a mathematical argument and ultimately use it to understand something happening in a real physical system.

View Rebecca's LinkedIn profile.