Foam drainage with twin inputs in two dimensions

Forced foam drainage is the flow of constantly input liquid through the network of interstitial channels between bubbles in foam under actions of gravity and capillarity. When two streams of liquid are input with twin narrow nozzles separated with a distance, they usually merge into a singular drainage wave to propagate in foams. This work reports results of behaviours of the merged drainage wave. We find that (1) along the vertical direction beneath one nozzle, the liquid spreading is well described by power law with exponents greater than that of individual drainage. (2) Along the vertical direction down the center of the two nozzles, we find the spreading speed is nearly constant for a fixed separation. As the separation distance increases six times, the speed increases only about 14%. This result would benefit designing of micro-mixers and micro-reactors, based on foam-like channels, for liquid/liquid systems widely used in pharmaceutical industry.