Newtonian fluids flow behaviour

Numerous examples of polymer flow models based on generalized Newtonian behaviour are found in non-Newtonian fluid mechanics literature. Using experimental evidence the time-independent generalized Newtonian fluids are divided into three groups. These are Bingham plastics, pseudoplastic fluids and dilatant fluids. 

Chapter 5 deals with the aspects of the flow behaviour of polymer melts which are relevant to the processing methods. The models are developed for both Newtonian and Non-Newtonian (Power Law) fluids so that the results can be directly compared. 

Chapter 4 describes in general terms the processing methods which can be used for plastics and wherever possible the quantitative aspects are stressed. In most cases a simple Newtonian model of each of the processes is developed so that the approach taken to the analysis of plastics processing is not concealed by mathematical complexity. Chapter 5 deals with the aspects of the flow behaviour of polymer melts which are relevant to the processing methods. The models are developed for both Newtonian and Non-Newtonian (Power Law) fluids so that the results can be directly compared. 

The branch of science which is concerned with the flow of both simple (Newtonian) and complex (non-Newtonian) fluids is known as rheology. The flow characteristics are represented by a rheogram, which is a plot of shear stress against rate of shear, and normally consists of a collection of experimentally determined points through which a curve may be drawn. If an equation can be fitted to the curve, it facilitates calculation of the behaviour of the fluid. It must be borne in mind, however, that such equations are approximations to the actual behaviour of the fluid and should not be used outside the range of conditions (particularly shear rates) for which they were determined. 

As in the case of Newtonian fluids, one of the most important practical problems involving non-Newtonian fluids is the calculation of the pressure drop for flow in pipelines. The flow is much more likely to be streamline, or laminar, because non-Newtonian fluids usually have very much higher apparent viscosities than most simple Newtonian fluids. Furthermore, the difference in behaviour is much greater for laminar flow where viscosity plays such an important role than for turbulent flow. Attention will initially be focused on laminar-flow, with particular reference to the flow of power-law and Bingham-plastic fluids. 

At the molecular level there are several important differences between polymeric fluids and small-molecule fluids. Because of these differences the flow behaviour of polymeric fluids is not similar to that of small-molecule fluids, which are satisfactorily described by Newtonian fluid dynamics. There are several salient features of macromolecular architecture that influence the flow behaviour ... 

Equation 3.29 is helpful in showing how the value of the correction factor in the Rabinowitsch-Mooney equation corresponds to different types of flow behaviour. For a Newtonian fluid, n = 1 and therefore the correction factor has the value unity. Shear thinning behaviour corresponds to < 1 and consequently the correction factor has values greater than unity, showing that the wall shear rate yw is of greater magnitude than the value for Newtonian flow. Similarly, for shear thickening behaviour, yw is of a... 

Newtonian fluids containing a high concentration of rigid particles can show non-Newtonian flow behaviour with increasing shear rate, due to a break up of agglomerates in the shear field [4]. For many pseudoplastic fluid suspensions the... 

Equation (6.4) is applicable to a description of the flow behaviour of ideal fluids, or Newtonian fluids. Examples include water, mineral oils, bitumen, and molasses. However, many fluids, especially colloidal dispersions, do not obey Eq. (6.4), usually due to the mutual orienting and even structure formation of the dispersed species in the flow. 

M. M. Cross, Rheology of Non-Newtonian Fluids a New Flow Equation for Pseudoplastic Systems, J. Colloids Sci., 20, 417 137 (1965) also M. M. Cross, Relation Between Viscoe-lasiticity and Shear-thinning Behaviour in Liquids, Rheological Acta, 18, 609-614 (1979). 

Most emulsions, unless very dilute, display hoth plastic and pseudoplastic flow behaviour rather than simple Newtonian flow. The flow properties of fluid emulsions should have little influence on their biological behaviour, although the rheological characteristics of semisolid emulsions may affect their performance. The pourability, spreadability and syringeability of an emulsion will, however, be directly determined by its rheological properties. The high viscosity of w/o emulsions leads to problems with intramuscular administration of injectable formulations. Conversion to a multiple emulsion (w/o/w), in which the external oil phase is replaced by an aqueous phase, leads to a dramatic decrease in viscosity and consequent improved ease of injection. 

Many attempts have been made to obtain (semi-)analytical descriptions for non-Newtonian coating flows. These are necessarily approximate and the approximations made to obtain tractable mathematics are sometimes non-physical [58]. These models do not predict the coating behaviour very well from the rheological parameters. The thickness is usually considerably overestimated. It seems more advantageous to simulate non-Newtonian coating flows by computational fluid dynamic methods (see also Ref. [58]). 

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