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

Abstract

A nonequilibrium thermodynamic model based on the interfacial transport phenomena (ITP) formalism was used to study deformation-relaxation behavior of water-in-water emulsions. The ITP formalism allows us to describe all water-in-water emulsions with one single theory. Phase-separated biopolymer solutions, hydrogel beads, liposomes, polymersomes, colloidosomes, and aqueous polymer microcapsules are all limiting cases of this general theory with respect to rheological behavior of the bulk phases and interfaces. Here we have studied two limiting cases of the general theory, with negligible surface rheology: phase-separated biopolymer solutions and hydrogel beads. We have determined the longest relaxation time for a small perturbation of the interfaces in these systems. Parameter maps were calculated which can be used to determine when surface tension, bending rigidity, permeability, and bulk viscoelasticity dominate the response of a droplet or gel bead. In phase-separated biopolymer solutions and dispersions of hydrogel beads six different scaling regimes can be identified for the relaxation time of a deformation. Hydrogel beads may also have a damped oscillatory response to a deformation. The results presented here provide new insight into the complex dynamics of water-in-water emulsions and also suggest new experiments that can be used to characterize the interfacial properties of these systems.

Modeling soft interface dominated systems: A comparison of phase field and Gibbs dividing surface models

“…) is the density difference of water between the two phases, evaluated at the interface, ∆P is the local Laplace pressure difference, and ∆ P is the equilibrium Laplace pressure difference [112,113]. Substituting this in (74), we find…”

“…In arriving at the latter expression we have assumed that (∂R/∂θ) 2 << 1 and (∂R/∂ϕ) 2 << 1, and hence H ≈ ∇ 2 s R(θ, ϕ, t). When combining ( 76) and ( 78) with the equation of continuity, and momentum balance for the adjoining bulk phases (16), and appropriate models for the stress deformation behavior of the bulk phases and interfaces, an expression can be derived for the longest relaxation time of a small perturbation of the interfaces in a phase separated biopolymer system [112,113].…”

“…For water-in-water emulsions with significant permeability λ p and interfacial bending rigidity k, but negligible interfacial rheology, the expression for this relaxation time is given by [112,113]…”

“…When there are polymers in the mixture which preferentially adsorb at the interfaces of the water-in-water emulsion, we may also see effects of surface rheology on the deformation relaxation process. As stated above, we then need to choose an appropriate constitutive equation for the surface extra stress tensor, and substitute this expression in the jump momentum balance [112,113]. When the surface stress deformation behavior can be described by a linear integral Maxwell model [112,113], we obtain a complex relaxation time τ * = τ ′ + iτ ′′ , where the real part τ ′ , and imaginary part τ ′′ , are given by (when the effects of viscous stresses exerted by the adjoining bulk phases are negligible) [112,113]…”

Aqueous Two-Phase Systems: simple one-step process formulation and phase diagram for characterisation

“…Many characterisation methods are based on the study of the interfacial tension between the dispersed and continuous phases 14,[19][20][21] . Theories and models have been developed to explain the deformation/relaxation behaviour of ATPS 1,22 .…”