Pacific Institute for the Mathematical Sciences - PIMS

Instabilities of a thin coating on a vertical fibre: Newtonian, shear-thinning and elastic liquids.

Surface tension would like to reduce the surface area of a cylinder of liquid by turning the cylinder into a sequence of spherical drops. In the case of a cylindrical coating on a fibre, the fibre interrupts this process. On a horizontal fibre, the coating becomes only a sequence of small bumps in the coating. On a vertical fibre, the bumps however fall and grow by leaving behind a thinner coating that the coating in front. If the initial coating is thicker than a critical value, the bumps grow indefinitely into larger and larger drops. If the initial coating is thinner than the critical value, the bumps grow into a sequence of solitary waves, all with a well defined amplitude and speed. The talk focuses on these solitary waves just below the critical value where the amplitude and speed are high, although all confined within lubrication theory. The matched asymptotic analysis is perversely difficult, requiring the full solution of the third correction before all the properties of the leading order term are fully determined. A power-law shear-thinning fluid needs only the second correction, although many more strange powers appear in the asymptotic expansion to further terms. Finally elastic liquids do not remain axisymmetric, with the coating becoming lop-sided and then dewetting on one side.

Bio: John Hinch is Professor of Fluid Mechanics in the Department of Applied Maths and Theoretical Physics at the University of Cambridge, a Fellow of Trinity College and a Fellow of the Royal Society. Professor Hinch's main research interests are: micro-hydrodynamics, colloidal dispersions, flow through porous media, polymer rheology, non-Newtonian fluid dynamics, mobile particulate systems and applications of mathematics to industrial problems.

Location: ESB 2012