Rheology Newtonian flow

Incorporation of viscosity variations in non-elastic generalized Newtonian flow models is based on using empirical rheological relationships such as the power law or Carreau equation, described in Chapter 1. In these relationships fluid viscosity is given as a function of shear rate and material parameters. Therefore in the application of finite element schemes to non-Newtonian flow, shear rate at the elemental level should be calculated and used to update the fluid viscosity. The shear rale is defined as the second invariant of the rate of deformation tensor as (Bird et at.., 1977)... 

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. 

Caustic Waterflooding. In caustic waterflooding, the interfacial rheologic properties of a model crude oil-water system were studied in the presence of sodium hydroxide. The interfacial viscosity, the non-Newtonian flow behavior, and the activation energy of viscous flow were determined as a function of shear rate, alkali concentration, and aging time. The interfacial viscosity drastically... 

Newtonian flow, and their viscosity is not constant but changes as a function of shear rate and/or time. The rheological properties of such systems cannot be defined simply in terms of one value. These non-Newtonian phenomena are either time-independent or time-dependent. In the first case, the systems can be classified as pseudoplastic, plastic, or dilatant, in the second case as thixotropic or rheopective. 

Keywords. Viscoelasticity, Molecular rheology. Branched polymers. Tube model, Non-Newtonian flow... 

Rheologically, the flow of many non-Newtonian materials can be characterized by a time-independent power law function (sometimes referred to as the Ostwald-deWaele equation)... 

Leaderman.H., Smith,R.G., Williams,L.C. Rheology of polyisobutylene. III. Elastic recovery, non-Newtonian flow, and molecular weight distribution. J. Polymer Sci. 36,233 257 (1959). 

Y. Cohen, Apparent Slip Flow of Polymer Solutions, in "Encyclopedia of Fluid Mechanics. Rheology and Non-Newtonian Flows", N.P. Cheremisinoff (ed.), Gulf Publishing, Houston, TX, vol. 7,1988, pp. 407-457. 

Uppuluri, S., Keinath, S. E., Tomalia, D. A., Dvornic, P. R., Rheology of dendrimers. I. Newtonian flow behavior of medium and highly concentrated solutions of polyamidoamine (PAMAM) dendrimers in ethylenediamine (EDA) solvent. Macromolecules 1998, 31, 4498-4510. 

I would also like to list some of the challenges that will provide the foundation for where the profession has to go (Fig. 2). This is not meant to be comprehensive, but to suggest some of what we should be doing. This wish list derives from work Bob Brown and I have done on modeling flows of polymer fluids. The first item has to do with the need to understand the effects of polymer structure and rheology on flow transitions in polymeric liquids and on polymer processing operations. In the past, we ve studied extensively the behavior of Newtonian fluids and how Newtonian flows evolve as, say, the Reynolds number is varied. We have tools available to... 

Krieger, I.M., and Dougherty, T.J. (1959). A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheology 3, 137-152. 

Non-Newtonian flows need much more attention since in many industrial applications the chemical engineer has to deal with materials that exhibit a complex rheological behavior that cannot (even approximately) be described with Newtonian closure models. 

The viscosity of microemulsions has been studied several times in order to determine hydration and interactions between the dispersed droplets. It was found that an increase in hydration of the surfactant molecules resulted in rheological behavior more similar to that of suspensions containing solid particles in low concentrations. In any case, the microemulsions showed Newtonian flow characteristics. 

Liquid crystals can be classified into lyotropic and thermotropic systems. The rheology of thermotropic liquid crystals is less documented, but in general, nematic liquid crystals were found to show Newtonian flow, whereas smectic and cholesteric liquid crystals demonstrated more or less pronounced plug flow. Plug flow is typical for non-Newtonian, shear thinning liquids. ... 

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. 

Rheology is a powerful method for the characterization of HA properties. In particular, rotational rheometers are particularly suitable in studying the rheological properties of HA. In such rheometers, different geometries (cone/plate, plate/plate, and concentric cylinders) are applied to concentrated, semi-diluted, and diluted solutions. A typical rheometric test performed on a HA solution is the so-called "flow curve". In such a test, the dynamic viscosity (q) is measured as a function of the shear rate (7) at constant strain (shear rate or stress sweep). From the flow curve, the Newtonian dynamic viscosity (qo), first plateau, and the critical shear rate ( 7 c), onset of non-Newtonian flow, could be determined. 

Many important coating processes are of liquids that are not Newtonian, and so the effects of non-Newtonian rheology on flow between rolls is of great interest. The code used here has been applied to the simplest non-Newtonian model, namely the purely viscous, shear-thinning fluid. Viscoelasticity, though also important, is more difficult to treat and is not considered here. 

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