Two-dimensional Stokes flow with suction and small surface tension by Cummings, L, Howison, S

“…This solution is analysed in the limit of small surface tension. An apparent 'stability paradox' (where two equivalent flow geometries are found, one of which is 'stable' and the other unstable) is resolved by allowing the coefficients to take complex values.…”

ON THE CLASSIFICATION OF SOLUTIONS TO THE ZERO-SURFACE-TENSION MODEL FOR HELE-SHAW FREE-BOUNDARY FLOWS by Hohlov, Y, Howison, S

“…We discuss the classification of solutions to the zero-surface-tension model for Hele-Shaw flows in bounded and unbounded regions with suction and injection. …”

Two-dimensional Stokes and Hele-Shaw flows with free surfaces by Cummings, L, Howison, S, King, JR

“…We also discuss blow-up of zero-surface-tension Stokes flows, and consider a class of weak solutions, valid beyond blow-up, which are obtained as the zero-surface-tension limit of flows with positive surface tension.…”

IRREGULAR MORPHOLOGIES IN UNSTABLE HELE-SHAW FREE-BOUNDARY PROBLEMS by Lacey, A, Howison, S, Ockendon, J, Wilmott, P

“…A model is presented that is intended to describe the evolution of the ill-posed Hele-Shaw suction free-boundary problem at times after that at which 'blow-up' would occur in the absence of surface-tension effects. For small surface tension, it is proposed that the free-boundary morphology consists of thin 'cracks', whose shape and thickness are predicted when appropriate initial data are prescribed. …”

HELE-SHAW FREE-BOUNDARY PROBLEMS WITH SUCTION by Howison, S, Lacey, A, Ockendon, J

“…In the absence of surface tension, the solution of most Hele-Shaw free-boundary problems with suction becomes singular at finite time, say t = t *, when the free boundary develops a cusp. …”

A mathematical model for drying paint layers by Howison, S, Moriarty, J, Ockendon, J, Terrill, E, Wilson, S

“…The effects of variable surface tension, viscosity, solvent diffusivity and solvent evaporation rate are all included in the model. …”

FINGERING IN HELE-SHAW CELLS by Howison, S

“…The results are valid when surface-tension effects in the plane of the cell are negligible. …”

Conserved quantities in Stokes flow with free surfaces by Cummings, L, Howison, S, King, JR

“…We derive an infinite set of invariants for two-dimensional Stokes flow with a free surface, driven by a point sink, in the case that surface tension effects are negligible. The complex variable methods used are closely related to those used for certain Hele-Shaw flows, which likewise have infinitely many conserved quantities. © 1997 American Institute of Physics.…”

A MODEL FOR NONSMOOTH FREE BOUNDARIES IN HELE-SHAW FLOWS by Hohlov, Y, Howison, S, Huntingford, C, Ockendon, J, Lacey, A

“…A special case of the Stefan model for the evolution of zero surface tension Hele-Shaw free-boundary problems is presented. …”

Free and moving boundary problems in hydrodynamics. by Howison, S

“…These solutions break down in finite time. Examines surface tension effects and proposes a numerical method for ill posed Hele Shaw flow. …”