Rheology application transient flow

Using finite element techniqnes, a mathematical model was developed for the two-dimensional analysis of non-isothermal and transient flow and mixing of a generalised Newtonian fluid with an inert filler. The model could incorporate no-slip, partial-slip or perfect-slip wall conditions using a universally applicable numerical technique. The model was used to simulate the convection of carbon black with flowing rubber in the dispersive section of a tangential rotor (Banbury) mixer. The Carreau equation was used to model the rheological behaviour of the fluid in this example. 31 refs. 

The fundamental assumption of the classical rheological theories is that the liquid stmcture is either stable (Newtonian behavior) or its changes are well dehned (non-Newtonian behavior). This is rarely the case for flow of multiphase systems. For example, orientation of sheared layers may be responsible for either dilatant or pseudoplastic behavior, while strong interparticle interactions may lead to yield stress or transient behaviors. Liquids with yield stress show a plug flow. As a result, these liquids have drastically reduced extrudate swell, B = d/d (d is diameter of the extrudate, d that of the die) [Utracki et al, 1984]. Since there is no deformation within the plug volume, the molecular theories of elasticity and the relations they provide to correlate, for example either the entrance pressure drop or the extmdate swell, are not applicable. 

Akay, G., Rheology of reinforced thermoplastics and its application to irijection molding IV. Transient injection capillary flow and injection rmflditig, Pofym. Eng. ScL, 22,1027 (1982). 

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