Oldroyd’s 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 frequently used example of Oldroyd-type constitutive equations is the Oldroyd-B model. The Oldroyd-B model can be thought of as a description of the constitutive behaviour of a fluid made by the dissolution of a (UCM) fluid in a Newtonian solvent . Here, the parameter A, called the retardation time is de.fined as A = A (r s/(ri + s), where 7]s is the viscosity of the solvent. Hence the extra stress tensor in the Oldroyd-B model is made up of Maxwell and solvent contributions. The Oldroyd-B constitutive equation is written as... 

Shearing flows of the convected Jeffreys model. The convected Jeffreys model [6] or Oldroyd s B-fluid [54] is given by,... 

At low shear rate (3.3 s ), experimental and computed free surfaces are compared in Fig. 26. The final extrudate swell values are equivalent, but the experimental shape of the free surface is different from the computed ones. In addition, a slight overswelling at the die exit is observed for the (JOB model, which is observed neither experimentally, nor using a classic Oldroyd-B model. 

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