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Droplet shape fluctuations in agitated emulsions—Beyond the dilute limit

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  • Frenkel, Gad

Abstract

The paper investigates the interaction between dispersed droplets in an emulsion under random stirring of the host fluid. The main interest is to examine the autocorrelation of the shape fluctuations in such randomly stirred host fluids, beyond the dilute limit regime. Keeping expressions to leading order in the density of droplets and in deviation of droplets shapes from spherical, the shape is expanded in spherical harmonic modes and the correlations of these modes are derived. The special case of droplets that are governed by surface tension is investigated in detail. The correlations of the deformations that are obtained for this special case are damped relative to the deformation correlations in the dilute regime. The dependence of the damping on frequency is also discussed.

Suggested Citation

  • Frenkel, Gad, 2015. "Droplet shape fluctuations in agitated emulsions—Beyond the dilute limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 251-261.
    • Handle: RePEc:eee:phsmap:v:427:y:2015:i:c:p:251-261
    DOI: 10.1016/j.physa.2015.02.045
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    References listed on IDEAS

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    1. Edwards, S.F. & Schwartz, Moshe, 1991. "Stochastic dynamics of a slightly deformed membrane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(2), pages 236-240.
    2. Edwards, Sam F. & Schwartz, Moshe, 2002. "Lagrangian statistical mechanics applied to non-linear stochastic field equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(3), pages 357-386.
    3. Seki, Kazuhiko & Komura, Shigeyuki, 1995. "Viscoelasticity of vesicle dispersions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 253-289.
    4. Schwartz, Moshe & Frenkel, Gad & Edwards, Sam F., 2014. "Does a particle swept by a turbulent liquid diffuse?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 229-233.
    5. Frenkel, Gady & Schwartz, Moshe, 2001. "Diffusion of a deformable body in a random flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 278-284.
    6. Brustein, Ram & Marianer, Shlomo & Schwartz, Moshe, 1991. "Langevin memory kernel and noise from Lagrangian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 47-58.
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