I am interested in the mathematical modelling of fluid mechanical, industrial and medical problems. Active research areas include Photovoltaic devices, Surfactant systems, Tear films, Industrial mathematics and Mathematical modelling in medicine and biology.

We have had a fresh look at the old problem of the adsorption of ionic surfactant at an air-liquid interface. Standard drift/diffusion models predict too high a concentration of counter ions just below the surface, and several fudges exist to counter this. We have postulated a new model, where surfactant ions recombine in the bulk as well as near the surface, which negates the need for a fudge.

We extended this model to include the flow of non-polar lipids over the eye surface. One current goal is to couple evaporation from the eye surface to the thickness of the non-polar lipid layer.

We have also studied the salt concentration in the tear film during blinking and between blinks. Our model shows how pathological levels of salt can be locally induced in regions where the film is thinnest.

More details can be found at here.

Related publications:

The effect of polar lipids on tear film dynamics.

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