Mathematical modelling for nano- and microscale medical challenges

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Microfluidics is a burgeoning field that refers to the behaviour, precise control, and manipulation of fluids that are geometrically constrained to a small scale (typically sub-millimetre). This is a multidisciplinary field that involves engineering, physics, chemistry, biochemistry, nanotechnology, and biotechnology. Professor Scott Tsai is the head of the Laboratory of Fields, Flows, and Interfaces (LoFFI) at Ryerson University whose efforts are focused on the development of novel nano and microfluidic technologies for medical applications. In this DPhil project, we will consider two recent discoveries in biomedical microfluidics in the LoFFI to develop mathematical models for biomedical microfluidic applications: nanobubble generation for ultrasound application and acoustic stimulation for nutrient uptake of biological cells. The research methodology will use experimental data to guide the appropriate asymptotic regimes and validate our theories. Conversely, predictions from the methodology will be used to guide future laboratory experiments. This close collaboration between mathematicians and experimentalists will be accompanied by interactions with clinicians, which will be key in advancing this research area. The mathematical models developed to describe this problem will have broader reach, enhancing mathematical understanding in complex two-phase flows. The results of this work have the potential to play a role in future targeted drug-delivery strategies, gene silencing, DNA editing technologies, intracellular imaging and gene therapies. The mathematical modelling developed to tackle this problem will also provide a more general understanding of the propagation of acoustic waves in elastic media. This DPhil project falls within the following three EPSRC research areas: Continuum Mechanics, Fluid dynamics and Aerodynamics, and Mathematical Biology.