Kinetics in directional drying of water that contains deformable non-volatile oil droplets

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.

Evaporation kinetics of continuous water and dispersed oil droplets

Drying of volatile oil droplets immersed in a continuous water phase was observed and analysed. Drying sample solutions were sandwiched between two glass plates and the water and oil phases were observed by confocal microscopy. In the initial stage of drying, evaporation of water was dominant and drying of the oil droplets was negligible. However, the rate of water evaporation decreased when the oil droplets were compressed. Comparison of experimental data with a diffusion model of water vapour showed that the decline in drying rates occurred earlier in the experiment than in the theoretical prediction. This implies that compression and narrowing of water paths caused the decline in the rate of water evaporation. After most water had evaporated, evaporation of the oil droplets occurred. The oil droplets did not shrink isotropically and the air-liquid interface invaded into the drying oil droplets. Cross-sectional observation by z-scanning revealed direct exposure of the oil droplets and they were pinned by the residual water phase. The water network between the oil droplets collapsed after the oil droplets had evaporated. The correlation between changes in structures and drying kinetics in both liquid phases was discussed.

Strengthening and drying rate of a drying emulsion layer

From direct observations and MRI measurements we demonstrate that during the drying of a direct (oil in water) emulsion the whole system essentially concentrates homogeneously, which leads to shrinkage, without air penetration. The structure and mechanical strength (i.e. the elastic modulus) of this concentrated bulk are not significantly different from those of an emulsion directly prepared at this higher concentration. Despite this phenomenon, the drying rate continuously and rapidly decreases as the water content decreases, in contrast with the drying of a simple granular packing. This results from a concentration gradient which develops towards the free surface of the sample where the oil droplets finally coalesce, ultimately forming an oil layer covering the sample through which the water molecules have to diffuse before evaporating. Moreover, as during the process, the liquid is transported towards the free surface where it evaporates, surfactants accumulate and tend to form a thin solid layer below the oil layer, which tends to further reduce the drying rate.

Drying kinetics of water droplets stabilized by surfactant molecules or solid particles in a thin non-volatile oil layer

We have investigated drying of water droplets stabilized by solid particles or surfactant molecules in a thin oil layer. The surfactant-stabilized droplets isotropically shrink, whereas the droplets stabilized by spherical particles severely deform during drying because of buckling of the particulate shells. However, buckling of the shells hardly affects droplet drying. The drying times for complete evaporation are almost the same for water droplets with the same initial diameter and the drying time is independent of the type of surface stabilizer (particles or surfactant). The drying kinetics of the water droplets is well described by mathematical models, in which diffusion of water molecules in the oil phase to the oil-air interface is proposed as the rate-determining process. Droplets with a diameter comparable with the thickness of the oil layer shrink faster than small droplets because of the short diffusion length from the water droplets to the oil-air interface. We also investigated drying of water droplets stabilized by plate-like mica particles. The droplets also buckled but larger shells of mica particles remained compared with those of spherical particles. In addition, a longer drying time is necessary for some droplets stabilized by mica particles. These results indicate the possible effect of the particle morphology on the buckling and drying kinetics of particle-stabilized water droplets.