Wetting hydrodynamics

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Abstract
Bretherton's (1961) theory of the forced, steady displacement of one fluid by another in a tube or between parallel plates is generalized to account for the effects of intermolecular forces in submicroscopically thin films and of a finite driving-fluid viscosity. The theory predicts that there are two displacement regimes, depending on capillary number μU/γ. At low speed the dynamic apparent contact angle retains its static value. If the displaced fluid perfectly wets the solid an equilibrium thin-film remains ; if not, there is not a continuous thin-film. At high speed a hydrodynamically entrained film is left behind regardless of equilibrium wetting characteristics. The entrained film thickens slightly with increasing driving-fluid viscosity. These predictions accord with experiment. In addition, evidence is presented that observed discrepancies between Bretherton's theory and measured film thicknesses are caused by the presence of surface-active impurities. Finally, implications for the submicroscopic origins of seeming slip at apparent contact lines, air entrainment in coating flows, soap-film dynamics, and the generation of mixed-wettability states in porous media are discussed

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