Dr Wilson's research is mainly concerned with theoretical modelling of the flow of non-Newtonian fluids such as polymeric materials and particle suspensions. Fluids containing long polymer molecules behave very differently from ordinary (Newtonian) fluids. Under flow, the molecules become stretched and this can give rise to surprising flow behaviour, and can produce undesirable instabilities in industrial processes. Dr Wilson's current research in this area includes analytical and numerical investigation of flow instabilities in simple flows; and simulation of complex flows. She is also interested in shear-banding in entangled systems, a phenomenon in which a single fluid forms regions having quite different properties during shearing flows.

Another important class of complex fluids is suspensions of solid particles in Newtonian or non-Newtonian fluids. While the motion of single particles in Newtonian fluids is well understood, suspensions of large numbers of particles that interact through the fluid remain challenging, both analytically and numerically. Dr Wilson's current research includes investigations, using both asymptotic theory and large-scale numerical simulations, of the effect of contact between spherical particles in suspension flows.