Scaling law for the kinetics of water imbibition in polydisperse foams

We investigated the kinetics of water imbibition in polydisperse foams. We used a Hele-Shaw cell, and horizontal imbibition was observed for a timescale of up to 10(3) s in which the gravity effect was negligible. While several papers have reported kinetics for imbibition in foams, imbibition kinetics in polydisperse foams and its variations in longer timescales are not well understood. The tip position of imbibition was proportional to the square root of time in the initial stage of imbibition, but it showed plateauing in the late stage of imbibition. We evaluated the proportional constant A in the initial stage of imbibition as a kinetic constant for the time-dependent increase in the tip position, which showed a clear dependency on the initial and final water volume fractions in the foams. Conversely, the mean initial radius of the curvature and the channel length in the Plateau borders did not show any clear correlations with A, although both valuables are frequently used in modeling for liquid imbibition in foams. On the basis of the t(1/2) dependence, the correlation of A with the water volume fraction and the increase in the water volume fraction during imbibition, we proposed a simple equation to describe the tip position over the entire period of imbibition. We used them to scale all of the experimental data, which showed good agreement with the theoretical line. This clearly showed that the water volume fraction in the foams during imbibition was the key factor to quantitatively describe the rate of water imbibition. Features in the kinetics of imbibition were discussed.