Liquid drainage from high-expansion (HiEx) aqueous foams during and after filling of a container

• Analytical theory for effect of filling on induction period and drainage.
• The induction time decreases and drainage rate increases with increased fill rate.
• During filling, drainage rate is constant when foam is applied at constant rate.
• After filling, drainage rate decreases exponentially with time.
• Experiments on high-expansion foams with low water content and large bubbles.

An aqueous foam drains interstitial liquid as it fills a container after an induction period. We obtain solutions of quasi-steady and volume-averaged conservation equations containing the moving foam front to describe the induction period and the subsequent drainage, respectively. The quasi-steady theory predicts that the induction period increases with decreasing foam injection velocity. After the induction period, the theory shows a constant liquid drainage rate when the foam front propagates at a constant velocity. The space-averaged liquid fraction of the foam decreases with time and reaches a constant (pseudo-steady state) value because of the drainage. The theory shows that the liquid drainage is significant when the foam injection velocity is less than or equal to the terminal velocity of the liquid in a channel (Plateau border), which is shown to depend on foam parameters including initial liquid volume fraction and bubble diameter. At large injection velocity, the theory predicts induction time and drainage rate corresponding to free drainage from stationary foams. We also present experiments measuring liquid drained from dry foams (high-expansion foams), which are generated by forcing air through a liquid-covered metal screen at bench-scale. The experimental data show significant liquid drainage during filling in good agreement with the theoretical predictions for foams with liquid volume fraction less than 0.01. After the container is filled with the foam and the foam addition is stopped, both the theory and experiments show that the drainage rate decreases exponentially with time until equilibrium between capillarity and gravitational forces is reached and drainage ceases to occur. Thus, the theory shows striking differences in drainage behavior during and after filling in agreement with the experimental data.

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