Vladimir Zubkov

3. Stability of Lubrication flows, drag-out problem in liquid film theory. PhD project.

drag-out problem

Under the supervision of Prof Eugene Benilov (University of Limerick), I considered an infinite plate being withdrawn from an infinite pool of viscous liquid. The problem has infinitely many steady solutions, all of which are stable – but only one of these is realized in practice. This particular steady solution can only be singled out by matching it to a self-similar solution describing the non-steady upper part of the drag-out film. We used various methods to solve the problem, in particular numerical calculations of the Stokes equations and, when applicable, the lubrication approximation was utilised to obtain the thin film asymptotic solution and also to characterise its stability.


E.S. Benilov, S.J. Chapman, J.B. McLeod, J.R. Ockendon and V.S. Zubkov, 2010, On liquid films on an inclined plate, J. Fluid Mech., vol. 663, pp. 53-69.

E.S. Benilov and V.S. Zubkov, 2008, On the drag-out problem in liquid film theory, J. FluidMech. (2008), vol. 617, pp. 283-299.