Evaluation of a steady-state test of foam stability

Abstract

We have evaluated a steady-state test of foam stability, based on the steady-state height of a foam produced by a constant velocity of gas flow. This test is mentioned in the book by Bikerman [Foams, Springer, Berlin, 1973] and an elementary theory was developed for it by Verbist et al. [J. Phys. Condens. Matter 8 (1996) p. 3715]. For the study, we used an aqueous solution of the cationic surfactant dodecyl trimethylammonium bromide, C₁₂TAB, at a concentration of two times the critical micelle concentration (2 cmc). During foam generation, bubbles collapse at the top of the column which, in turn, eventually counterbalances the rate of bubble production at the bottom. The resulting balance can be described mathematically by an appropriate solution of the foam drainage equation under specified boundary conditions. Our experimental findings are in agreement with the theoretical predictions of a diverging foam height at a critical gas velocity and a finite foam height in the limit of zero velocity. We identify a critical liquid fraction below which a foam is unstable as an important parameter for characterizing foam stability. Furthermore, we deduce an effective viscosity of the liquid which flows through the foam. Currently unexplained are two experimental observations, namely sudden changes of the steady-state foam height in experiments that run over several hours and a reduction in foam height once an overflow of the foam from the containing vessel has occurred.

Keywords:

• Bikerman foam test
• drainage equation
• foams
• cationic surfactants

Acknowledgements

We thank Mark Jenkinson for initiating this work through the extensive preliminary data that he generated during his Final Year Project in 2008. We are grateful for financial support provided by COGNIS. SH and DW also acknowledge funding by the European Space Agency (MAP AO-99-108:C14914/02/NL/SH and MAP AO-99-075:C14308/00/NL/SH) and Science Foundation Ireland (08/RFP/MTR1083).

Notes

Note

1. Note that the determination of surface viscosities is subject to large errors and an established technique does not exist so far. Thus, we refer to SDS as it is a soluble surfactant with a comparable cmc (cmc (SDS) = 9 × 10⁻³ M). As SDS forms much more stable foams compared to the respective C₁₂TAB, a lower surface viscosity is expected for the latter – reliable experimental data do not exist for C₁₂TAB