New fundamental concepts in emulsion rheology

doi:10.1016/S1359-0294(99)00035-7

Current Opinion in Colloid & Interface Science

Volume 4, Issue 3, 1 June 1999, Pages 231-238

https://doi.org/10.1016/S1359-0294(99)00035-7 Get rights and content

Abstract

The field of emulsion rheology is developing rapidly due to investigations involving monodisperse emulsions having narrow droplet size distributions. The droplet uniformity facilitates meaningful comparisons between experiments, theories, and simulations.

Introduction

Emulsions consist of droplets of one liquid dispersed in another immiscible liquid. By contrast to microemulsion phases, emulsions are not thermodynamic states. Instead, emulsions are metastable dispersions; external shear energy is used to rupture large droplets into smaller ones during emulsification. Surfactants that provide a stabilizing interfacial repulsion are typically introduced to inhibit droplet coalescence [1]. If the liquids are highly immiscible, molecules of the dispersed phase cannot be exchanged between droplets, so coarsening of the droplet size distribution due to Ostwald ripening is negligible. When coalescence and ripening are suppressed, the emulsion can remain stable for years even when osmotically compressed to form a biliquid foam.

Emulsions exhibit highly varied rheological behavior that is useful and fascinating [2]•[3], [4], [5]. An emulsion's macroscopic constitutive relationships between the stress and strain depend strongly on its composition, microscopic droplet structure, and interfacial interactions. By controlling the droplet volume fraction, φ, an emulsion can be changed from a simple viscous liquid at low φ to an elastic solid having a substantial shear modulus at high φ, as shown schematically in Fig. 1. This elasticity results from the work done against interfacial tension, σ, to create additional droplet surface area when the shear further deforms the already compressed droplets. The elasticity of foams [6]•, the gas-in-liquid counterpart to concentrated emulsions, results from the same mechanism, although Ostwald ripening of gas bubbles usually causes the foam to age and its elasticity to become weaker over time. The rheological properties of such products as lotions, sauces, and creams are typically adjusted by varying the composition or the emulsification process to alter the droplet size distribution and hence packing. Additives such as polymers can also modify emulsion rheology by raising the viscosity of the continuous phase or by causing adhesion between droplets without coalescence [7]. Emulsions comprised of viscoelastic polymeric liquids, or blends, exhibit a rich rheological complexity arising from the interplay of bulk and interfacial elastic contributions [8]•.

For years, measurements of emulsion rheology [9], [10], [11], [12], [13] were not quantitatively understood because the droplet size distributions had not been controlled and no two emulsions had either the same distribution of Laplace pressures, Π_L=2σ/a, where a is the droplet radius, or the same critical volume fractions, φ_c, at which droplet packing would occur. Recently, measurements using monodisperse emulsions have established a conceptual foundation for quantitatively understanding emulsion rheology, especially at high φ [2]•, [14]••, [15]••, [16]. In contrast to a recent opinion [17], these studies show that polydispersity is important in emulsion rheology. The monodispersity has facilitated comparisons between rheological experiments, theories, and simulations, and sparked a comparison with uniform hard sphere (HS) suspensions for φ<φ_c and foams as φ→1.

Section snippets

Monodisperse emulsions

Traditional methods of emulsification, such as stirring and shaking typically lead to droplet size distributions that are uncontrolled and have a large polydispersity, defined as $P_{a} =δa/ a ̄$ , where $a$ is the average droplet radius and δa is the S.D. However, many methods for making monodisperse emulsions with P_a≈0. 1 now exist. These include depletion flocculation fractionation [18], controlled shear rupturing [19]•, [20], controlled coalescence [21]••, membrane emulsification [22]•,

Droplet interactions

Interactions between the deformable interfaces of droplets play an important role in emulsion rheology. For incompressible dispersed phases, the most basic interaction is that of excluded volume. The second basic repulsive interaction results from work done against σ to create additional droplet surface area when two droplets deform as they are forced together. Finally, the surfactant typically provides a short-range repulsion (disjoining pressure) that prevents droplet coalescence. The net

Dilute emulsion rheology

Predictions of the viscosity, η, of dilute monodisperse emulsions have been tested empirically at low enough shear rates that the shear stress, τ, is less than Π_L and there is little droplet deformation and no rupturing. Steady shear viscosity measurements for φ_eff<0.4 [15] agree with simulations of monodisperse HS suspensions [29] at large Peclet numbers, Pe=η $γ ̇$ /(k_BT/a³)⪢1, where convection dominates diffusion, yet at small Capillary numbers, Ca=η $γ ̇$ /(σ/a)≪1, where the droplets are not greatly

Glass transition in colloidal emulsions

The identification of features of the colloidal glass transition [33], [34] in emulsion rheology is one of the most important recent conceptual advances [14]••. For hard spheres, the colloidal glass transition occurs when the spheres become sufficiently concentrated that a given droplet becomes caged by its neighbors indefinitely. Thermal excitations are insufficient to destroy these cages when φ exceeds the glass transition volume fraction, φ_g. Light scattering and rheology measurements for HS

Linear viscoelastic shear moduli of compressed emulsions

New developments in optical microrheology have enhanced our understanding of the frequency-dependent linear viscoelastic moduli of compressed emulsions. Diffusing wave spectroscopy (DWS) [39] has been used to measure the time-dependent mean square displacement, <Δr²(t)>, of droplets in concentrated turbid monodisperse emulsions, and G′(ω) and G″(ω) are obtained using a generalized Stokes–Einstein relation [40]••[41]. This method is approximate because it treats the emulsion as an isotropic

Elasticity of concentrated emulsions

The universal φ-dependence of the linear plateau elasticity of disordered concentrated monodisperse emulsions has been established. Measurements on four emulsions having different a are described by: G′_p(φ_eff)=1.5(σ/a)(φ_eff−φ_c) [14]•• where φ_c has been identified as random close packing of monodisperse spheres, φ_c=φ_RCP≈0.64 [48]. Although a quasi-linear rise in G′_P(φ_eff) had been previously measured [10], little insight into the reported φ_c=0.715 could be offered due to polydispersity. The

Non-linear rheology of concentrated emulsions

Basic concepts for understanding yielding, fracture flow, and emulsification are beginning to appear. A schematic illustration of these phenomena for a concentrated emulsion is shown in Fig. 5, along with a corresponding plot of τ( $γ ̇$ ). At low $γ ̇$ , the stress approaches a constant defined to be the yield stress, τ_y. For higher $γ ̇$ , the interplay of the fluid viscosities with the interfacial structures within the emulsion cause the shear stress to increase. For τ≪Π_L, droplet rearrangements occur,

Emulsions of viscoelastic materials

Emulsions need not be comprised solely of isotropic viscous liquids, but may include viscoelastic or anisotropic liquids such as polymers [8]• or liquid crystals [67]. Bulk and interfacial energy storage combine to provide a wide range of rheological behavior [68]•,[69], [70], [71]•. The measured G′(ω) and G″(ω) of copolymer blends [71]• have been successfully compared to a theory of spherical inclusions of an isotropic viscoelastic material in an isotropic viscoelastic matrix [72]••. In the

Conclusions

Monodisperse emulsions have provided much new insight into emulsion rheology, including the notion of colloidal glasses of deformable droplets, yet many challenges remain. Perhaps the most important is to understand how polydispersity affects emulsion rheology. This could be studied by combining different monodisperse emulsions to control the polydispersity. Other rheological frontiers lie in crystalline emulsions with ordered droplet structures, binary emulsions, emulsions of liquid crystals,

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New fundamental concepts in emulsion rheology

Abstract

Introduction

Section snippets

Monodisperse emulsions

Droplet interactions

Dilute emulsion rheology

Glass transition in colloidal emulsions

Linear viscoelastic shear moduli of compressed emulsions

Elasticity of concentrated emulsions

Non-linear rheology of concentrated emulsions

Emulsions of viscoelastic materials

Conclusions

Curr Opin Colloid Interface Sci

Curr Opin Colloid Interface Sci

Colloid Surfaces A

Colloids Surfaces A

J Colloid Interface Sci

J Colloid Interface Sci

J Colloid Interface Sci

Curr Opin Colloid Interface Sci

J Colloid Interface Sci

Physica A

J Colloid Interface Sci

J Colloid Interface Sci

J Colloid interface Sci

J Colloid Interface Sci

J Colloid Interface Sci

J Non-Newtonian Fluid Mech

Stability of emulsions with non-adsorbing polymers

Langmuir

Osmotic pressure of foams and highly concentrated emulsions theoretical considerations

Langmuir

Osmotic pressure of foams and highly concentrated emulsions determination from the variation in volume fraction with height in an equilibrated column

Elasticity of compressed emulsions

Phys Rev Lett

Depletion interactions and fluid–solid equilibrium emulsions

Phys Rev Lett

Emulsification in viscoelastic media

Phys Rev Lett

Nucleation of a binary liquid mixture under steady-state shear

Phys Rev Lett

A dynamical model of crystal structure

Proc R Soc A

Entropy driven phase separation in binary emulsions

Phys Rev Lett

Structure of adhesive emulsions

Langmuir

Adhesion of water droplets in organic solvent

Langmuir

Hydrodynamic transport coefficients of random dispersions of hard spheres

J Chem Phys

The viscosity of a fluid containing small drops of another fluid

Proc R Soc A