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Cox and Weaire  rightly emphasize that our solution of the drainage equation for the “Eiffel Tower” geometry does not treat the boundary conditions. There should be a no- flow condition at the top, and, after leakage begins, the liquid fraction should be pegged to εc ≈ 0.36 at the bottom. They then show how approximating the no-flow conditions at the top can improve agreement with numerical solution. But as argued in , we maintain that the neglect of capillarity coming from boundary conditions at the bottom dominates, and that this cannot explain our measurements. At short times, capillarity can delay the onset of leakage, and at long times it can counter gravity and retain liquid in the foam indefinitely; in either case, leakage is slower than our approximate solution, contrary to experiment. Therefore, we speculated that the discrepancy arose from neglect of coarsening, whereby the average bubble size increases via gas diffusion from smaller to larger bubbles. This is an important puzzle because, while the drainage equation successfully predicts forced-drainage experiments, it fails dramatically for free-drainage experiments
Saint-Jalmes, A., & Durian, D. J. (2001). Reply to Comment by S. J. Cox and D. Weaire on "Free Drainage of Aqueous Foams: Container Shape Effects on Capillarity and Vertical Gradients". Europhysics Letters, 55 (3), 447-448. http://dx.doi.org/10.1209/epl/i2001-00435-1
Date Posted:11 October 2017
This document has been peer reviewed.