Structural Viscosity Models

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

The Carreau model (Carreau, 1972) is very useful for describing the viscosity of structural fluids  

This model contains four rheological parameters the low shear limiting viscosity (rj0), the high shear limiting viscosity a time constant (X), 

If r]oo 3C ( /. j/o), the Carreau model reduces to a three-parameter model ( 0,k, and p) that is equivalent to a power law model with a low shear limiting viscosity, also known as the Ellis model  

If r/0 (i], 1] ) and (ky)2 S 1, the Carreau model reduces to the equivalent of a power law model with a high shear limiting viscosity, called the Sisko model  

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The high structural viscosity of bimodal products means that advanced modeling methods are needed to optimize the pressure build-up zones. Calculation and evaluation of dimensionless parameters helps to keep the complexity within limits. 

Estimation of Liquid Viscosity of Organic Compounds with a Quantitative Structure-Property Model. 

The viscosity of some fluids (particle solutions or suspensions) measured at a fixed shear rate that places the fluid in the non-Newtonian regime increases with time as schematically shown by curve C of Figure 13.39. This behavior can be explained by assuming that in the Newtonian region the particles pack in an orderly manner, so flow can proceed with minimum interference between particles. However, high shear rates facilitate a more random arrangement for the particles, which leads to interparticle interference and thus to an increase in viscosity. Models that illustrate the thixotropic and rheopectic behavior of structural liquids can be found elsewhere (58,59). 

Ivanciuc, O., Ivanciuc, T, Filip, P.A. and Cabrol-Bass, D. (1999b). Estimation of the Liquid Viscosity of Organic Compounds with a Quantitative Structure-Property Model. J.Chem.Inf.Comput.Sci., 39,515-524. 

Quemada (1978a, 1978b) examined the rheology and modelling of concentrated dispersions and described simple viscosity models that incorporate the effects of shear rate and concentration of filler and separate effects of Brownian motion (or aggregation at low shear) and particle orientation and deformation (at high shear). The ratio of structure-build-up and -breakdown rates is an important parameter that is influenced by the ratio of the shear rate to the particle diffusion. A simple form of viscosity relation is given here ... 

There are a large number of models used for the correlation and/or prediction of the viscosity of liquid hydrocarbons and their mixtures. Since there is no exact statistical mechanical or molecular-level theory for liquid viscosity, all of the models available contain some degree of empiricism. Also, there is considerable variation in the structure of these models in that most have been formulated to address only a speeific viscosity estimation problem. For example, some liquid hydrocarbon viscosity models have been proposed only for predicting the viscosity of an undefined petroleum mixture, and their input parameters have been selected accordingly. There are models that use some experimental viscosity data, while others are completely predictive, at least within a class of substances. Some viscosity models are suitable for incompletely defined petroleum cuts, whereas others can be used only for well-defined hydrocarbons and their mixtures. Further, some models include the effects of pressure and dissolved gases on liquid hydrocarbon viscosity, while others are for use only at atmospheric pressure. 

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

The highly detailed results obtained for the neat ionic liquid [BMIM][PFg] clearly demonstrate the potential of this method for determination of molecular reorienta-tional dynamics in ionic liquids. Further studies should combine the results for the reorientational dynamics with viscosity data in order to compare experimental correlation times with correlation times calculated from hydrodynamic models (cf [14]). It should thus be possible to draw conclusions about the intermolecular structure and interactions in ionic liquids and about the molecular basis of specific properties of ionic liquids. 

Thermodynamic, statistical This discipline tries to compute macroscopic properties of materials from more basic structures of matter. These properties are not necessarily static properties as in conventional mechanics. The problems in statistical thermodynamics fall into two categories. First it involves the study of the structure of phenomenological frameworks and the interrelations among observable macroscopic quantities. The secondary category involves the calculations of the actual values of phenomenology parameters such as viscosity or phase transition temperatures from more microscopic parameters. With this technique, understanding general relations requires only a model specified by fairly broad and abstract conditions. Realistically detailed models are not needed to un-... 

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