Fluctuations of Permeable Interfaces in Water-in-Water Emulsions

Abstract

The fluctuations of highly permeable interfaces, encountered in phase-separated biopolymer solutions, liposomes, polymersomes, or colloidosomes, are investigated. An expression for the power spectrum of the height correlation function is derived for a multicomponent system, incorporating the effects of mass transfer across the interface, using nonequilibrium thermodynamics. We also derive an expression for the relaxation time of the height correlation function, and calculate the relaxation time for a phase-separated gelatin-dextran-water system. Comparing our expression with the expression for an impermeable interface shows that mass transfer has a significant impact on the relaxation time of the interface. DOI: 10.1103/PhysRevLett.98.066105 PACS numbers: 68.35.Ja, 68.05.ÿn Water-in-water emulsions, such as phase-separated (bio)polymer solutions, liposomes, polymersomes, or colloidosomes, can be used for encapsulation and texturing applications in pharmaceutical, food, or cosmetic products. The interfaces in these emulsions have properties that differ significantly from those found in oil-water or water-air systems, stabilized by a simple surfactant. The interfacial tension in water-in-water emulsions is often extremely low. For example, in phase-separated biopolymer solutions the surface tension is of the order of 10 ÿ6 N=m [1]. The bending rigidity of interfaces in these systems can be significant, as high as 500 kT [2]. As a result, the bending rigidity can have an appreciable effect on the dynamic behavior of these systems [3].Another important property of the interfaces in water-inwater emulsions is their permeability. 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 previous work we used scaling analysis to study the effects of permeability and bending rigidity on the dynamic behavior of phase-separated biopolymer solutions [4 -6]. In systems with a composition close to the critical point, we observed that the relaxation time of the system scales as L 4 = p k , with L a characteristic length scale of the system, p the permeability of the interface, and k the bending rigidity. In systems with a composition far from the critical point, relaxation is dominated by surface tension and permeability, andHere we will use a more formal approach, using nonequilibrium thermodynamics to derive expressions for the power spectrum of the height correlation function and the relaxa...

Dynamics of Encapsulation and Controlled Release Systems Based on Water-in-Water Emulsions: Negligible Surface Rheology

“…A common procedure to determine the relaxation time is to expand R (θ,φ, t ) and the velocity and pressure fields in spherical harmonics. To facilitate comparison of our results with previous results obtained for flat interfaces in a phase-separated biopolymer solution, , we will not use an expansion in spherical harmonics, but instead Fourier transform the set of equations. As a result, we will obtain a continuous spectrum of relaxation times, rather than a discrete one, and need to introduce a realistic cutoff to obtain an expression for the longest relaxation time.…”

“…If we denote the amplitude of the perturbation by δ R 0 , then q r ∼ 1/δ R 0 . Substituting this in (), we find τ ( A ) B L = 1 λ p + ϕ ( A ) ( 1 ) + ϕ ( A ) ( 2 ) 2 R 0 4 2 γ 0 R 0 2 + k ϕ ( A ) ( i ) = ρ ̅ ( A ) ( i ) δ R 0 Δ ρ ̅ ( A ) κ ( i ) Equation 28 not only gives us the relaxation time but can also be used to calculate the decay of the correlation function of the fluctuations of the interface. ...…”

“…This is valid when k ( A ) (δρ ( A ) (1) − δρ ( A ) (2) ) ≪ λ p Δ̅ρ ( A ) (Δ P − Δ P̅ ), where k ( A ) = D ( A ) / l is the mass transfer coefficient for species A , D ( A ) is the diffusion coefficient of species A , and l is the thickness of the interface. Accounting for ordinary diffusion will introduce a second characteristic time that scales as τ od ∼ 1/( q 2 D ( A ) ) and is independent of the deformation of the droplet. , It will not affect the expression for the longest relaxation times τ BL and τ HL calculated in the next sections.…”

Dynamics of thermally driven capillary waves for two-dimensional droplets

“…29 In other recent work, Madsen et al 30 measured the dispersion relation of capillary waves on a liquid surface near the transition in water-glycerol solutions using x-ray photon correlation spectroscopy and were able to observe both propagating and overdamped capillary waves. With advancements in experimental techniques such as fluorescence microscopy and imaging, researchers also started to study thermally driven capillary waves in biological systems, such as phase separated biopolymer solutions, 31 and quasi-two-dimensional systems such as lipid bilayer membranes and monolayers at the airwater interface. [32][33][34] In this paper, we use the linearized Navier-Stokes equation for an incompressible fluid to obtain a quantitative description of the interfacial roughness of a binary droplet system.…”

Internal relaxation time in immersed particulate materials

“…However, the presence of asperities on rough surfaces has been shown to strongly affect lubrication, and this topic is still an active field of research [22,23,24,25]. Between bubbles or droplets, the flow of liquid is even more complex, as the surfaces are soft and can stretch [26,27], they can be permeable [28] and exhibit some repulsive electrostatic interactions leading to disjoncting pressure [29] as well as adhesion [2,30,31]. This paper presents a numerical investigation on the dynamics of the solid-liquid transition in a model immersed particulate material.…”