I am an applied mathematician working on problems that arise in fluid dynamics.
I am interested in systems involving immiscible fluids that are characterised
by the presence of spatiotemporally evolving sharp interfaces.
To obtain a quantitative description of the dynamics we need to determine
moving interfaces as part of the solution. Such problems are of much practical importance but
are notoriously difficult mathematically
for several reasons:
- The Navier-Stokes (or Stokes or Euler) equations need to be solved in changing domains.
- In certain applications we may need to also solve for the temperature or electrostatic fields.
- Several nonlinear boundary conditions need to be specified at the unknown interface(s). These are
The solutions may not exist for all times. In fact we can encounter singularities in finite time
accompanied by topological transitions. A simple example is the breakup of
I use a combination of modelling, analysis and computations to gain a
of the underlying nonlinear mechanisms in multi-fluid flows at
- Continuity of velocities (for viscous flows).
- Continuity of normal and tangential stresses. The geometry of the interface enters here
when surface tension is present.
- A kinematic boundary condition.
- Conservation equations for physical scalar quantities on the interface, e.g. surfactants, charges etc.