Saffman-Taylor Instabilities in Shear-Thinning Fluids - Ashleigh Hutchinson скачать в хорошем качестве

Saffman-Taylor Instabilities in Shear-Thinning Fluids - Ashleigh Hutchinson

LIFD Symposium | Ashleigh Hutchinson | 12th June 2025 Abstract: In this talk, we consider a simple mathematical model of the radial injection of a shear-thinning fluid, initially occupying a circular region of some initial injection radius,  which displaces a viscous Newtonian fluid within a Hele-Shaw cell. For Newtonian fluids, Saffman-Taylor instabilities are known to develop when the displacing fluid is less viscous than the displaced fluid. However, when the displacing fluid is shear-thinning, its viscosity depends on radial distance from the source. Using a linear stability analysis, we show that there exists a critical radius where for injection radii larger than this critical value, the flow remains stable. In addition, we derive a series of critical radii for each mode corresponding to a sinusoidal perturbation of the fluid-fluid interface. The theoretical results are compared to a set of Hele-Shaw laboratory experiments in which a shear-thinning fluid called Xanthan gum is injected radially into a small gap between two plates, displacing a viscous Newtonian silicone oil. This comparison shows significant discrepancies between theory and experiment, and we delve into this problem further to locate the missing physics. Bio: Dr Ashleigh Jane Hutchinson is a Lecturer in Applied Mathematics at the University of Manchester, UK. In 2016 she earned her PhD from the University of the Witwatersrand, Johannesburg, South Africa. In 2021, she was awarded a prestigious Newton International Fellowship, allowing her to conduct research at Cambridge University, UK. Her research is primarily focused on fluid mechanics, particularly problems involving low-Reynolds number flows and non-Newtonian fluids, which have a variety of applications in both nature and industry. Dr Hutchinson’s approach to solving complex problems is multidisciplinary, combining theoretical modelling, laboratory experiments and numerical simulations. In addition to fluid dynamics, she has a keen interest in other areas of applied mathematics, including population dynamics, energy conservation, and mining. For more information on LIFD, please visit our website: https://fluids.leeds.ac.uk/ Sign up to the LIFD mailing list: https://leeds.onlinesurveys.ac.uk/lif...