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Issue 36, 2014

Crossover between entropic and interfacial elasticity and osmotic pressure in uniform disordered emulsions

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Abstract

We develop a simple predictive model of the osmotic pressure Π and linear shear elastic modulus Gp of uniform disordered emulsions that includes energetic contributions from entropy and interfacial deformation. This model yields a smooth crossover between an entropically dominated GpkBT/a3 for droplet volume fractions ϕ below a jamming threshold for spheres, ϕc, and an interfacially dominated Gpσ/a for ϕ above ϕc, where a and σ are the undeformed radius and interfacial tension, respectively, of a droplet and T is the temperature. We show that this model reduces to the known ϕ-dependent jamming behavior Gp(ϕ) ∼ (σ/a)ϕ(ϕϕc) as T → 0 for ϕ > ϕc of disordered uniform emulsions, and it also produces the known divergence for disordered hard spheres Gp(ϕ) ∼ (kBT/a3)ϕ/(ϕcϕ) for ϕ < ϕc when σ → ∞. We compare predictions of this model to data for disordered uniform microscale emulsion droplets, corrected for electrostatic repulsions. The smooth crossover captures the observed trends in Gp and Π below ϕc better than existing analytic models of disordered emulsions, which do not make predictions below ϕc. Moreover, the model predicts that entropic contributions to the shear modulus can become more significant for nanoemulsions as compared to microscale emulsions.

Graphical abstract: Crossover between entropic and interfacial elasticity and osmotic pressure in uniform disordered emulsions

Article information


Submitted
23 May 2014
Accepted
22 Jul 2014
First published
11 Aug 2014

Soft Matter, 2014,10, 7109-7116
Article type
Paper

Crossover between entropic and interfacial elasticity and osmotic pressure in uniform disordered emulsions

T. G. Mason and F. Scheffold, Soft Matter, 2014, 10, 7109 DOI: 10.1039/C4SM01125B

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