Decay of standing foams: drainage, coalescence and collapse

摘要: Abstract A summary of recent theoretical work on the decay foams is presented. In a series papers, we have proposed models for drainage, coalescence and collapse with time. Each our papers dealt different aspect foam involved several assumptions. The fundamental equations, assumptions results obtained are discussed in detail presented within unified framework. Film drainage modeled using Reynolds equation flow between parallel circular disks film rupture assumed to occur when thickness falls below certain critical which corresponds maximum disjoining pressure. Fluid Plateau border channels Hagen-Poiseuille type ducts triangular cross-section. be composed pentagonal dodecahedral bubbles global conservation equations liquid, gas surfactant solved obtain information about state decaying as function Homogeneous produced by mixing bubbling (pneumatic foams) considered. It shown that draining eventually arrives at mechanical equilibrium opposing forces due gravity Plateau-border suction gradient balance each other. properties this can predicted from salt concentration foaming solution, density liquid bubble radius. For homogeneous foams, it possible conditions under there no foam. There three scenarios equilibrium: separation single phase (separation continuous or dispersed via collapse), both phases (drainage occurs) (neither nor occurs). behavior depends dimensionless group measure relative magnitudes gravitational capillary forces. generalized diagram used determine behavior. pneumatic effects various system parameters such superficial velocity, size concentrations rate evolution fraction profile discussed. steady height attained occurs during generation also evaluated. Bubble non-uniformity sizes films constitute faces polyhedral bubbles. This leads film-drainage rates hence thicknesses any volume element Smaller drain faster earlier, causing containing them coalesce. distribution foam, being larger regions where greater has occurred. formation very stable Newton black high explained.