Effect of Bending Rigidity and Interfacial Permeability on the Dynamical Behavior of Water-in-Water Emulsions

Abstract

Phase separation in aqueous biopolymer mixtures results in the formation of an interface, separating two aqueous bulk phases. The properties of that interface are key parameters to understand and predict phenomena, such as the phase-separation process and deformation of droplets in a flow field. In these processes, the structures and sizes of the morphologies depend on the balance between viscous and interfacial forces. Normally, one assumes that the interfacial tension is the only important parameter regarding the interfacial forces. However, we will show that in these water-in-water emulsions, bending rigidity and interfacial permeability also play an important role. Spinning drop experiments show that at long time scales the interface is permeable to both dissolved biopolymers and water. From droplet relaxation experiments, we could conclude that, for shorter time scales, water is the only ingredient that can diffuse through the interface. Due to this permeability, these methods cannot be used to calculate the interfacial tension accurately, without taking into account the permeability of the interface. Including the permeability, we give a full description for the relaxation time of deformed droplets. From this description, the interfacial tension and the permeability of the interface can be deduced simultaneously. We also incorporate the permeability and the bending rigidity into the description of the kinetics of phase separation. From this theoretical description, we predict four different regimes to occur in the phase-separation process depending on the size of the domains. For the scaling of the domain size with time, we find an exponent of (1)/(4) for bending- and permeability-dominated coarsening, an exponent of (1)/(3) for bending-dominated coarsening, an exponent of (1)/(2) for interfacial tension- and permeability-dominated coarsening, and an exponent of 1 for interfacial tension-dominated coarsening. The crossover between the different regimes depends on two different critical radii, R(c), equal to (2k/gamma)(1/2) and R(lambda), equal to etalambda(eff). Taking values for the interfacial properties, we find these critical radii to be larger than a micrometer, indicating that both bending rigidity and permeability are of importance during phase separation.

Fluctuations of Permeable Interfaces in Water-in-Water Emulsions

“…Sample 6 is almost insensitive to the value of the bending rigidity. In this system relaxation is clearly dominated by permeability and surface tension, and we find A L 2 x = p 0 , also in agreement with [5]. This analysis shows conclusively that mass transfer has an important effect on the dynamic behavior of water-inwater emulsions, like phase-separated (bio)polymer solutions, liposomes, polymersomes, or coloidosomes.…”

“…3 we have plotted the relaxation time for dextran, for both systems, and values of the bending rigidity of 0, 100, and 200k B T. We see that A in system 2 (close to the critical point) is very sensitive to variations in k. The relaxation in this system is dominated by the permeability and bending rigidity, and we find that A scales as ÿ1 A p kq 4 x . With q x 1=L x , where L x is the wavelength of the perturbations, we find A L 4 x = p k , a scaling that is in agreement with the scaling found for rigidity and permeability dominated coarsening during phase separation in [5]. Sample 6 is almost insensitive to the value of the bending rigidity.…”

“…This relaxation time is an important parameter, since it is also describes the relaxation of small mechanical perturbations of the interface during production, processing and application of these systems. The calculations of the relaxation time confirm the scaling regimes found earlier in [5]. Although the primary focus of this Letter will be on phase-separated biopolymer solutions, the results of this analysis are also applicable to phase-separated aqueous polymer-colloid systems, liposomes, polymersomes, or colloidosomes.…”

“…In these systems water and dissolved molecules can transfer easily from one aqueous bulk phase to the other. This high permeability of the interface has a significant effect on the stressdeformation and deformation-relaxation behavior of, for example, droplets in phase-separated biopolymer solutions [4,5].That mass transfer can have an appreciable effect on the dynamic behavior of a deformed droplet was also shown in recent interfacial tension measurements of biopolymer solutions, using the spinning drop method [6]. Droplets deformed by spinning the capillary, slowly dissolved, and the rate of dissolution increased with increasing spinning rate, or increasing deformation of the droplets.…”

“…In these systems water and dissolved molecules can transfer easily from one aqueous bulk phase to the other. This high permeability of the interface has a significant effect on the stressdeformation and deformation-relaxation behavior of, for example, droplets in phase-separated biopolymer solutions [4,5].…”