Brush: Dynamics of films in foam
Mar
31
Mon 4:00 PM
When Monday, March 31, 2008
Time
4:00 PM - 5:00 PM
Where Tech M416
Contact Danielle Jackson
847-491-5586
Group McCormick-Colloquia Engineering Sciences and Applied Mathematics
Applied Math Colloquium
Title: Dynamics of films in foam
Speaker: Lucien Brush, University of Washington
Abstract: The dynamics of liquid free-films separating bubbles in a foam play a critical role in the evolution of the whole foam. The lamellar free-films thin as liquid are forced into adjacent Plateau borders, which are the intersections of the films. If a rupture process is triggered then the foam coarsens. In this talk, derivation of two-dimensional thinning laws for liquid-lamellar films with Plateau borders using a matched asymptotic analysis at low capillary number is presented. The results show two different asymptotic limits having distinct thinning rates representing different foam geometries. In addition to Newtonian liquid films, generalized-Newtonian liquid films are also treated using power law and Ellis law models of the liquid viscosity. The results for the non-Newtonian liquid foams are consistent with experimental results for the draining of shear-thinning liquids in aqueous foam. Lubrication theory is also used to derive a coupled pair of partial differential equations governing the evolution of the gas-melt and the crystal-melt interfaces separating a thin melt film from its crystalline phase and from a gas. The configuration represents one that might occur in freezing foam, and is also relevant to other processes. The effects of heat transfer, alloying, gas-melt and crystal-melt surface tension, thermo capillary forces, heat of fusion, volume change and van der Waals attractions are included. Stability analysis of a static, uniform film reveals stationary and oscillatory instabilities. The effect of an imposed temperature gradient is to stabilize the film. Numerical solutions show rupture by growth of standing or traveling waves and other nonlinear effects.
Title: Dynamics of films in foam
Speaker: Lucien Brush, University of Washington
Abstract: The dynamics of liquid free-films separating bubbles in a foam play a critical role in the evolution of the whole foam. The lamellar free-films thin as liquid are forced into adjacent Plateau borders, which are the intersections of the films. If a rupture process is triggered then the foam coarsens. In this talk, derivation of two-dimensional thinning laws for liquid-lamellar films with Plateau borders using a matched asymptotic analysis at low capillary number is presented. The results show two different asymptotic limits having distinct thinning rates representing different foam geometries. In addition to Newtonian liquid films, generalized-Newtonian liquid films are also treated using power law and Ellis law models of the liquid viscosity. The results for the non-Newtonian liquid foams are consistent with experimental results for the draining of shear-thinning liquids in aqueous foam. Lubrication theory is also used to derive a coupled pair of partial differential equations governing the evolution of the gas-melt and the crystal-melt interfaces separating a thin melt film from its crystalline phase and from a gas. The configuration represents one that might occur in freezing foam, and is also relevant to other processes. The effects of heat transfer, alloying, gas-melt and crystal-melt surface tension, thermo capillary forces, heat of fusion, volume change and van der Waals attractions are included. Stability analysis of a static, uniform film reveals stationary and oscillatory instabilities. The effect of an imposed temperature gradient is to stabilize the film. Numerical solutions show rupture by growth of standing or traveling waves and other nonlinear effects.
