Influence of gravity on narrow input forced drainage in 2D liquid foams

Liquid foam is a dense packing of gas bubbles in a small amount of liquid containing surfactants or other surface-active macromolecules, which is one of the highly organized materials and possesses hallmark rheological behaviour of soft matters. Forced foam drainage is the flow of constantly inputted liquid through the network of interstitial channels between bubbles under actions of gravity and capil-larity. This process involves two mechanisms: minimal viscous flow dissipation of liquid and minimal surface energy of bubbles. For constant surfactant solution, viscous dissipation usually varies with gravity. This work reports simulations of 2D forced foam drainage with narrow input in a Hele-Shaw cell under 8 different gravities, g, ranging from 9.8 to 0 ms?2. The spread of liquid both vertical due to gravity action, and horizontal due to capillary suction, is recorded over time. Positions of drainage wave fronts in both directions with time are found to be well described in the power law form, and the exponents are 0.536 5.29×10-3g and 0.479?7.27×10-3g, respectively, while the sum is close to a constant of 1.015 which is independent of gravity. For g=9.8 ms-2, the calculated exponents are in good agreement with experimental results by Hutzler et al. and Wang.

Influence of gravity on narrow input forced drainage in 2D liquid foams

Liquid foam is a dense packing of gas bubbles in a small amount of liquid containing surfactants or other surface-active macromolecules, which is one of the highly organized materials and possesses hallmark rheological behaviour of soft matters. Forced foam drainage is the flow of constantly inputted liquid through the network of interstitial channels between bubbles under actions of gravity and capillarity. This process involves two mechanisms: minimal viscous flow dissipation of liquid and minimal surface energy of bubbles. For constant surfactant solution, viscous dissipation usually varies with gravity. This work reports simulations of 2D forced foam drainage with narrow input in a Hele-Shaw cell under 8 different gravities, g, ranging from 9.8 to 0 ms⁻². The spread of liquid both vertical due to gravity action, and horizontal due to capillary suction, is recorded over time. Positions of drainage wave fronts in both directions with time are found to be well described in the power law form, and the exponents are 0.536+5.29×10⁻³ g and 0.479–7.27×10⁻³ g, respectively, while the sum is close to a constant of 1.015 which is independent of gravity. For g=9.8 ms⁻², the calculated exponents are in good agreement with experimental results by Hutzler et al. and Wang. Supported by the National Natural Science Foundation of China (Grant No. 20336040) and the Scientific Research Foundation of the State Human Resource Ministry for Returned Chinese Scholars