Emulsion patterns in the wake of a liquid–liquid phase separation front

Abstract

Miscible liquids can phase separate in response to a composition change. In bulk fluids, the demixing begins on molecular-length scales, which coarsen into macroscopic phases. By contrast, confining a mixture in microfluidic droplets causes sequential phase separation bursts, which self-organize into rings of oil and water to make multilayered emulsions. The spacing in these nonequilibrium patterns is self-similar and scale-free over a range of droplet sizes. We develop a modified Cahn-Hilliard model, in which an immiscibility front with stretched exponential dynamics quantitatively predicts the spacing of the layers. In addition, a scaling law predicts the lifetime of each layer, giving rise to a stepwise release of inner droplets. Analogously, in long rectangular capillaries, a diffusive front yields large-scale oil and water stripes on the time scale of hours. The same theory relates their characteristic length scale to the speed of the front and the rate of mass transport. Control over liquid-liquid phase separation into large-scale patterns finds potential material applications in living cells, encapsulation, particulate design, and surface patterning.

Generation of High‐Order All‐Aqueous Emulsion Drops by Osmosis‐Driven Phase Separation

“…This approach facilitates infusion of multiple solutes, and waives the requirement of multiple inlets for injecting the different solutes . Compared to the previous work for ternary solutions involving organic solvents, our work demonstrates the possibility to achieve high‐order emulsion drops induced by phase separation within ATPS. Our approach is enabled by the immiscibility of the aqueous solutions which form a semipermeable interface for the two distinctive aqueous solutions.…”

“…Due to the nonequilibrium between the two phases, the polar solvent leaks out of the dispersed drop phase into the continuous phase, resulting in an increase in concentration of the ternary solution. Afterward, the ternary solution spontaneously phase‐separates into multiphase emulsions because of the finite miscibility of the mixture, giving alternating layers of oil and water phases . Despite the emergence of ternary solutions consisting of monomer, oil, polar solvent, separating agent, and/or water, to the best of our knowledge, phase‐separation‐induced formation of high‐order, oil‐free, all‐aqueous emulsion drops remains unexplored.…”

“…The characteristic relaxation time τ c is independent of the drop radius and indicates the water leakage time for our nonequilibrium all‐aqueous droplet. A recent study, which focused on the phase separation of a ternary nonequilibrium droplet consisting of diethylphthalate (DEP) oil, water, and ethanol, reveals that a stretched exponential instead of a diffusive (Epstein–Plesset theory) dynamics could well predict the temporal location of newly formed layers. In addition, the characteristic relaxation time τ c of ethanol leakage time during the phase separation of a ternary nonequilibrium droplet consisting of 12 wt% diethylphthalate (DEP) oil, 52 wt% water, and 36 wt% ethanol is 12.6 s, which is close to that of our system (14.4 s) despite the difference in the ternary systems.…”

“…A recent study, which focused on the phase separation of a ternary nonequilibrium droplet consisting of diethylphthalate (DEP) oil, water, and ethanol, reveals that a stretched exponential instead of a diffusive (Epstein–Plesset theory) dynamics could well predict the temporal location of newly formed layers. In addition, the characteristic relaxation time τ c of ethanol leakage time during the phase separation of a ternary nonequilibrium droplet consisting of 12 wt% diethylphthalate (DEP) oil, 52 wt% water, and 36 wt% ethanol is 12.6 s, which is close to that of our system (14.4 s) despite the difference in the ternary systems. Both of these results suggest that temporal location of newly formed layers during the phase‐separation of nonequilibrium all‐aqueous droplets in ATPS also follows the stretched exponential dynamics rather than the diffusive dynamics.…”

“…The diamonds (yellow), triangles (blue), squares (red), and circles (green) represent the four interfaces of a quadruple emulsion from the outmost ( d 1 ) to the innermost ( d 4 ) layers, respectively. b) The rescaled diameter, d i / d 1 ( i = 1, 2, 3, 4), of different layers as a function of complete creation time, which is well fitted with a stretched exponential function, (black curve), in which τ c = 14.4 s is considered as the characteristic relaxation time . The time zero is the same for all layers.…”