Film models for transport phenomena with fog formation: the classical film model

In the present analysis the classical film model (or film theory) is reviewed and extended. First, on the basis of a thorough analysis, the governing equations of diffusion, energy and momentum of a stagnant film are derived and solved. Subsequently, the well-known correction factors for the effect of suction/injection on mass, heat and momentum transfer are derived. Next, employing global balances of mass, energy and momentum, the film model is applied to channel flow. This application yields a new expression for the pressure drop and hence it is compared extensively with experimental and theoretical results of previous investigators, yielding good agreement. The onset of fog formation in a binary mixture, both in the transferring film and/or in the bulk, is explained graphically with the help of the relation between temperature and vapour mass fraction and the saturation line of the vapour.\ud \u

The modelling of coalescence processes in fluid-liquid dispersions : a review of current understanding

The review addresses current understanding of the processes of collision and coalescence in pure gas-liquid and liquid-liquid dispersions. Attention is restricted to flow-driven collisions, apart from brief reference to related gravity-driven phenomena at free-interfaces. Plane-film and full numerical solutions of drainage are compared in the immobile, partially-mobile and fully-mobile cases and related expressions developed for the coalescence probability. Finally, the perspectives and problems involved in the use of such experssions are examined, in conjunction with flow simulation codes for the mathematical modelling of particle-size evolution in dispersed flows

Fundamental problems in gas-liquid two-phase flow

Civil Engineering and Geoscience

Numerical investigation of the dynamic influence of the contact line region on the macroscopic meniscus shape

The influence of different boundary conditions applied in the contact line region on the outer meniscus shape is analysed by means of a finite-element numerical simulation of the steady movement of a liquid-gas meniscus in a capillary tube. The free-surface steady shape is obtained by solving the unsteady creeping-flow approximation of the Navier–Stokes equations starting from some initial shape. Comparisons of the outer solutions obtained using two different inner models, together with that published by Lowndes (1980), indicate the relative insensitivity of the outer solution to the type of model utilized in the contact line region

Numerical investigation of the dynamic influence of the contact line region on the macroscopic meniscus shape

The influence of different boundary conditions applied in the contact line region on the outer meniscus shape is analysed by means of a finite-element numerical simulation of the steady movement of a liquid-gas meniscus in a capillary tube. The free-surface steady shape is obtained by solving the unsteady creeping-flow approximation of the Navier–Stokes equations starting from some initial shape. Comparisons of the outer solutions obtained using two different inner models, together with that published by Lowndes (1980), indicate the relative insensitivity of the outer solution to the type of model utilized in the contact line region

The influence of surfactants on the hydrodynamics of surface wetting, I. The nondiffusing limit

The hydrodynamic model of steady wetting developed by Boenderet al.is extended to include the effect of a (nonionic) surfactant in the limiting case of negligible diffusion and low concentrations, confining attention to steady wetting between parallel plates. The approximation that the meniscus inclination becomes equal to the static contact angle at a distance from the solid of the order of a molecular dimension is extended to take account of the local surfactant concentration, making use of Young's law. A second inner boundary condition, provided by a surfactant balance at the contact line, places a restriction on the speed at which the interface is shed, leading to surfactant accumulation and partial or almost total immobilization of the interface which reduces the wetting speed. Under certain conditions, this immobilization is self-stabilizing, leading to hysteresis effects. Both these effects and the reduced wetting speed correspond with results reported in the literature