A model for unsteady state drainage of a static foam

Abstract A model for the unsteady state drainage of a standing foam has been proposed. This model accounted for (i) the liquid drainage from plateau borders due to gravity as well as the gradient of plateau border suction and (ii) the movement of the foam-liquid interface due to the accumulation of drained liquid, and assumed that the foam bed consisted of dodecahedral bubbles of the same size. The simplifying assumption of a negligible fraction of liquid in thin films, employed in the present model, was justified through the comparison of the timescales of film and plateau border drainage. Typical evolutions of a liquid holdup profile as well as a foam-liquid interface are reported for foam generated by bubbling inert gas through a liquid pool at a constant gas flow rate in the form of bubbles of the same size. The predicted equilibrium liquid holdup profile has been shown to depend only on the density difference, bubble size and surface tension but not on viscosity and surface viscosity, and compared well with experimental data. Asymptotic expression for the equilibrium disjoining pressure indicated that larger density difference, larger bubble sizes and smaller surface tensions would tend to make the standing foam less stable.