Oldroyd emulsion model

The viscosity ji, relaxation time x, and retardation time for Oldroyd s model, to low order in 0, are given in Table 9-1. The viscosity /r is the shear viscosity of the emulsion in the limit of high interfacial tension. 

The experimental data of dynamic testing in the kHz region for ionic emulsions could be equally well described using either model. The emulsion elasticity was found to originate in droplet deformation. For non-ionic emulsions, only one relaxation time was observed. The data were interpreted in terms of the second Oldroyd s model, in which the interfacial tension is more important than the viscoelasticity of the interphase. 

A linear viscoelastic constitutive model of dilute emulsion viscoelastic properties was proposed by Oldroyd [111, 112]. The model considered low deformation of monodispersed drops of one Newtonian liquid in another, with an interphase. Choi and Schowalter [113] extended their cell model to dilute emulsions with Newtonian matrix and viscoelastic drops under infinitesimally small oscillatory deformation. Oldroyd s model was modified by Palierne [126, 127] for dilute viscoelastic hquids emulsions with polydispersed spherical drops (thus, subject to small deformations) with constant interfacial tension coefficient, Vu, at concentrations below that where the drop-drop interactions start complicating the flow field, that is, < 0.1 ... 

A number of other models and theories have been proposed for evaluating viscosity data. Two models that are referred to as emulsion models predict the complex modulus or viscosity of an immiscible blend with spherical inclusions of one phase in a continuous phase (Oldroyd [263] and Paherne [264] models). The emulsion models can predict a positive deviation as noted in Fig. 6.21. Application of the Palierne model showed good agreement for viscosity data for EVAc/PE blends [265,266]. Another emulsion model proposed by Choi and Schowalter [267] is based on a cell model composed of a viscous matrix with viscous dispersed spheres (droplets). The viscosity of these models in the limit of zero shear viscosity can be expressed by the following equations. 

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