Abstract

Zekang Cheng – Finite element method for multiphase flow with thermocapillarity

Tim Beeson-Jones – Minimising Viscous Fingering Using Variational Calculus

When oil is displaced by water in a Hele-Shaw cell or porous medium, it is well known that the interface is unstable if the water is less viscous than the oil. Polymers may be added to the displacing fluid to reduce these adverse viscosity gradients. We show how gelling introduces a time dependency to the most unstable Saffman-Taylor wavelength in a rectilinear geometry, and how this in turn permits the calculation of an optimal flow rate to minimise the largest amplitude in the system. Dias & Miranda (2012) showed how to apply the Euler-Lagrange equation to a non-gelling axisymmetric flow. We also explore their findings and resolve an apparent disparity with other prior work.