Effect of bending rigidity and interfacial permeability on the dynamical behavior of water-in-water emulsions

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.