Measuring the impact of channel length on liquid flow through an ideal Plateau border and node system

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 10³ 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.

Horizontal imbibition of water in foams is scaled well by a simple mathematical expression that considers t^1/2 dependence and changes in volume fraction of water in foams.

A flow velocity dependence of dynamic surface tension in Plateau borders of foam

HYPOTHESIS

Liquid drainage through foams is a multiscale process, that primarily occurs through channels known as Plateau borders (PBs). Recent experimental studies of isolated PBs have observed variations in channel surface tension, γ, with liquid flow rate, Q, for systems containing soluble low molecular weight surfactant (LMWS). The current study proposes that the dynamic surface tension (DST) could be responsible for this effect, where the residence time of surfactant molecules in the PB is similar to the time required for their adsorption to the channel interface.

EXPERIMENTS

Profile geometries of isolated 'ideal' PB's were created in a bespoke experimental setup at controlled forced liquid flow rates. Average surfactant residence times, τ_Res, were calculated for solutions of Sodium dodecylsulfate (SDS), Tween 20 (T20) and Tween 80 (T80), and used to calculate corresponding average DST values in discrete regions of measured PB profiles. DST values were combined with microscale drainage theory to assess the potential physical implications on liquid flow.

FINDINGS

Significant variations in the magnitude of γ were calculated based on surfactant characteristics, where only the rapid adsorption of SDS was sufficient to produce DST values approaching equilibrium. These findings seriously question assumptions of near equilibrium surface tension in LMWS foam systems above their critical micelle concentration (CMC). Furthermore, the presence of surface tension gradients identified using this discrete approach, highlights the need to further refine the current theory to a continuous approach incorporating Marangoni effects.