A silicone-oil-in-water emulsion has interfacial tension

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Non-equilibrium statistical mechanics and stochastic thermodynamics

Soft Matter at the Thermal Scale, Ch Spinodal decomposition and coarsening

Problem

A silicone-oil-in-water emulsion has interfacial tension γ=4 mN m−1\gamma = 4\,\mathrm{mN\,m^{-1}}, equilibrium solubility ϕ∞=1×10−7\phi_\infty = 1\times10^{-7}, molecular volume vm=2.5×10−28 m3v_m = 2.5\times10^{-28}\,\mathrm{m^3} and diffusion coefficient of dissolved oil D=4×10−10 m2 s−1D = 4\times10^{-10}\,\mathrm{m^2\,s^{-1}}, at T=298 KT = 298\,\mathrm{K} (kBT=4.11×10−21 Jk_BT = 4.11\times10^{-21}\,\mathrm{J}). ((a)) Find the capillary length ℓc=2γvm/kBT\ell_c = 2\gamma v_m/k_BT and the Lifshitz-Slyozov rate constant ω=49Dϕ∞ℓc\omega = \tfrac49D\phi_\infty\ell_c. ((b)) Estimate the time for droplets to reach R=300 nmR = 300\,\mathrm{nm} by Ostwald ripening, using R3≈ωtR^3 \approx \omega t.

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