Rheologica Acta

, Volume 55, Issue 8, pp 683–697 | Cite as

Entropic, electrostatic, and interfacial regimes in concentrated disordered ionic emulsions

  • Ha Seong Kim
  • Frank Scheffold
  • Thomas G. MasonEmail author
Original Contribution


We develop a free energy model that describes two key thermodynamic properties, the osmotic pressure Π and the linear elastic shear modulus Gp (i.e. plateau storage modulus), of concentrated monodisperse emulsions which have isotropic, disordered, droplet structures, and are stabilized using ionic surfactants. This model effectively incorporates the concept of random close packing or jamming of repulsive spheres into a free energy F that depends on droplet volume fraction ϕ and shear strain γ both below and above the a critical jamming point ϕ c ≈ 0.646. This free energy has three terms: entropic, electrostatic, and interfacial (EEI). By minimizing F with respect to an average droplet deformation parameter that links all three terms, we show that the entropic term is dominant for ϕ well below ϕ c, the electrostatic term is dominant for ϕ near but below ϕ c, and the interfacial term dominates for larger ϕ. This EEI model describes measurements of Gp(ϕ) for charge-stabilized uniform emulsions having a wide range of droplet sizes, ranging from nanoscale to microscale, and it also is consistent with measurements of Π(ϕ). Moreover, it describes Gp(ϕ) for similar nanoemulsions after adding non-amphiphilic salt, when changes in the interfacial tension and the Debye screening length are properly taken into account. By unifying existing approaches, the EEI model predicts constitutive properties of concentrated ionic emulsions that have disordered, out-of-equilibrium structures through near-equilibrium free energy minimization, consistent with random driving Brownian excitations.


Disorder Droplet deformation Surfactant Storage modulus Emulsion Constitutitve equation 



The authors thank the UCLA for financial support.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ha Seong Kim
    • 1
  • Frank Scheffold
    • 2
  • Thomas G. Mason
    • 1
    • 3
    Email author
  1. 1.Department of Chemistry and BiochemistryUniversity of California-Los AngelesLos AngelesUSA
  2. 2.Physics DepartmentUniversity of FribourgFribourgSwitzerland
  3. 3.Department of Physics and AstronomyUniversity of California-Los AngelesLos AngelesUSA

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