Fluctuations of Permeable Interfaces in Water-in-Water Emulsions

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.

Figure 1

Relaxation time ${\tau }_{(A)}$ as a function of $q_z$ for dextran (⋄), gelatin (□), and water (▵), at a fixed value of $q_x={10}^6{\mathrm{m}}^{-1}$. Filled symbols: sample 2; open symbols: sample 6.

Figure 2

Relaxation time ${\tau }_{(A)}$ as a function of $q_z$ for dextran (sample 2), at a fixed value of $q_x={10}^6{\mathrm{m}}^{-1}$. From top to bottom: ${\lambda }_p=0$, ${\lambda }_p={10}^{-5}$, ${\lambda }_p={10}^{-4}$, ${\lambda }_p=3.4\times {10}^{-3}{\mathrm{m}}^3/(\mathrm{Ns})$.

Figure 3

Relaxation time ${\tau }_{(A)}$ as a function of $q_z$ for dextran, at a fixed value of $q_x={10}^6{\mathrm{m}}^{-1}$. Filled symbols: sample 2; open symbols: sample 6. Values of $k$: 0 (▵), $100k_{B}T$ (□), and $200k_{B}T$ (⋄).