Elasticity of Compressed Emulsions

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Title of Original Work: Elasticity of Compressed Emulsions

Journal of Original Work: PRL, Volume 75, Number 10, Sept 4, 1995

Authors: T.G. Mason, J. Bibette, D.A. Weitz

Author of Review: Joseph Muth - AP 225 - Fall 2012 - 11/11/2012

Soft Matter Keywords

Emulsions, Laplace Pressure, Disjoining Pressure


Emulsions consist of a fluid dispersed in a second immiscible fluid where the first fluid is stabilized in the second fluid by a surfactant. Despite the liquid nature of emulsions, the elastic response of such material systems mimics the characteristics of an elastic solid. As a pressure (π) is applied to an emulsion, the volume fraction (Φ) of droplets increases. When the π is sufficiently high so as to force the droplets to touch, Φ approaches one and any subsequent pressure increase results in deformation of the droplets. Deformation leads to stored strain energy and thus elasticity. Deformation of the droplets is governed by the Laplace pressure, σ/r, where σ is the surface tension of the drop and r is the radius of the undeformed drop. Clearly the elastic modulus (E) of the drop will depend on the degree of stored strain energy in the drop interface. Thus if the drops are not touching, then E = 0 because there can be no interfacial deformation. If Φ = 1 then the drops are maximally touching and the emulsion behaves like a dry elastic foam. However, the transition of the emulsions elastic properties between these two limiting cases is not well understood. It is the author's goal to elucidate the elastic property transition of emulsions by measuring the Φ dependence of E using monodisperse emulsions. By creating monodisperse emulsions, differences in Laplace pressure between drops is eliminated - enabling direct comparisons of experimental results with theoretical predictions.


All emulsions were made using silicone oil dispersed in oil. 0.01 M of sodium dodecylsulphate was added as the surfactant. The linear viscoelastic moduli, G' and G, were measured by applying a periodic strain and measuring the stress response.


Figure 1 shows G' and G" as a function of strain for several emulsions of Φ ranging from 0.60 - 0.80. G' increases by four decades over this Φ range. For small strains, G' dominates. At large strains G" dominates. At small strains the emulsion can maintain contact between each drop making the mechanical response more elastic. However, at large strains, the yield limit of the emulsion is reached and flow initiates, thus G" becomes dominant.

Figure 2 shows the frequency (ω)dependence of G' and G" for emulsions with Φ ranging from 0.60 - 0.80. G' remains nearly constant for each emulsion, especially so for higher Φ. However, each G' curve does exhibit some curvature. As such, G' can be calculated at the inflection point - G'p. G" behaves much differently, each G" curve is characterized by a distinct minimum G" value - G"m. The frequency at which G"m occurs increases with increasing Φ. G'p and G"m provide useful reference points for characterizing the elastic and loss moduli, respectively.

To describe the Φ dependence