Rheology non-Newtonian

Pearson,. I.R.A., 1994. Report on University of Wales Institute of Non-Newtonian Fluid Mechanics Mini Symposium on Continuum and Microstructural Modelling in Computational Rheology. /. Non-Newtonian Fluid Mech. 55, 203 -205. 

Rheology and elastohydrodynamic lubrication, Jacobson B.O, Elsevier, 1991, 175.75 Rheology non-Newtonian flow, Harris J, Bks Demand (reprint soon), 107.20 Rheology for Chemists - An Introduction, Goodwin JW Hughes, R.W, Royal Society of Chemistry, Cambridge, 2000, 27.50. 

The strongest appeal of NEMD, however, is its scope and versatility. In particular, the technique allows one to compute the rich and varied nonlinear behavior of systems far from equilibrium. This asset has been used to great advantage to study the atomic basis of the rheological non-Newtonian behavior of liquids. There was no practical technique to investigate the rheological properties of fluids from an atomistic viewpoint before NEMD. (Indeed the word rheology was rarely mentioned in a statistical-mechanical context.)... 

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)... 

Note that convected derivatives of the stress (and rate of strain) tensors appearing in the rheological relationships derived for non-Newtonian fluids will have different forms depending on whether covariant or contravariant components of these tensors are used. For example, the convected time derivatives of covariant and contravariant stress tensors are expressed as... 

Viscous Hquids are classified based on their rheological behavior characterized by the relationship of shear stress with shear rate. Eor Newtonian Hquids, the viscosity represented by the ratio of shear stress to shear rate is independent of shear rate, whereas non-Newtonian Hquid viscosity changes with shear rate. Non-Newtonian Hquids are further divided into three categories time-independent, time-dependent, and viscoelastic. A detailed discussion of these rheologically complex Hquids is given elsewhere (see Rheological measurements). 

Rheology. Both PB and PMP melts exhibit strong non-Newtonian behavior thek apparent melt viscosity decreases with an increase in shear stress (27,28). Melt viscosities of both resins depend on temperature (24,27). The activation energy for PB viscous flow is 46 kj /mol (11 kcal/mol) (39), and for PMP, 77 kJ/mol (18.4 kcal/mol) (28). Equipment used for PP processing is usually suitable for PB and PMP processing as well however, adjustments in the processing conditions must be made to account for the differences in melt temperatures and rheology. 

Viscosity is equal to the slope of the flow curve, Tf = dr/dj. The quantity r/y is the viscosity Tj for a Newtonian Hquid and the apparent viscosity Tj for a non-Newtonian Hquid. The kinematic viscosity is the viscosity coefficient divided by the density, ly = tj/p. The fluidity is the reciprocal of the viscosity, (j) = 1/rj. The common units for viscosity, dyne seconds per square centimeter ((dyn-s)/cm ) or grams per centimeter second ((g/(cm-s)), called poise, which is usually expressed as centipoise (cP), have been replaced by the SI units of pascal seconds, ie, Pa-s and mPa-s, where 1 mPa-s = 1 cP. In the same manner the shear stress units of dynes per square centimeter, dyn/cmhave been replaced by Pascals, where 10 dyn/cm = 1 Pa, and newtons per square meter, where 1 N/m = 1 Pa. Shear rate is AH/AX, or length /time/length, so that values are given as per second (s ) in both systems. The SI units for kinematic viscosity are square centimeters per second, cm /s, ie, Stokes (St), and square millimeters per second, mm /s, ie, centistokes (cSt). Information is available for the official Society of Rheology nomenclature and units for a wide range of rheological parameters (11). 

Dimensions. Most coUoids have aU three dimensions within the size range - 100 nm to 5 nm. If only two dimensions (fibriUar geometry) or one dimension (laminar geometry) exist in this range, unique properties of the high surface area portion of the material may stiU be observed and even dominate the overaU character of a system (21). The non-Newtonian rheological behavior of fibriUar and laminar clay suspensions, the reactivity of catalysts, and the critical magnetic properties of multifilamentary superconductors are examples of the numerous systems that are ultimately controUed by such coUoidal materials. 

Rheological Properties. Materials must have suitable flow properties in order to be used in production. Both Newtonian and non-Newtonian fluids and their viscoelasticity properties play a critical role in the performance of the embedding materials. 

The flow of compressible and non-compressible liquids, gases, vapors, suspensions, slurries and many other fluid systems has received sufficient study to allow definite evaluation of conditions for a variety of process situations for Newtonian fluids. For the non-Newtonian fluids, considerable data is available. However, its correlation is not as broad in application, due to the significant influence of physical and rheological properties. This presentation is limited to Newtonian systems, except where noted. 

Appearance of rheological effects — yield stress, non-Newtonian viscosity, thixotropy... 

The flow of plastics is compared to that of water in Fig. 8-5 to show their different behaviors. The volume of a so-called Newtonian fluid, such as water, when pushed through an opening is directly proportional to the pressure applied (the straight dotted line), the flow rate of a non-Newtonian fluid such as plastics when pushed through an opening increases more rapidly than the applied pressure (the solid curved line). Different plastics generally have their own flow and rheological rates so that their non-Newtonian curves are different. 

Linear novolac resins prepared by reacting para-alkylphenols with paraformaldehyde are of interest for adhesive tackifiers. As expected for step-growth polymerization, the molecular weights and viscosities of such oligomers prepared in one exemplary study increased as the ratio of formaldehyde to para-nonylphenol was increased from 0.32 to 1.00.21 As is usually the case, however, these reactions were not carried out to full conversion, and the measured Mn of an oligomer prepared with an equimolar phenol-to-formaldehyde ratio was 1400 g/mol. Plots of apparent shear viscosity versus shear rate of these p-nonylphenol novolac resins showed non-Newtonian rheological behavior. 

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. 

An understanding of non-Newtonian behaviour is important to the chemical engineer from two points of view. Frequently, non-Newtonian properties are desirable in that they can confer desirable properties on the material which are essential if it is to fulfil the purpose for which it is required. The example of paint has already been given. Toothpaste should not flow out of the tube until it is squeezed and should stay in place on the brush until it is applied to the teeth. The texture of foodstuffs is largely attributable to rheology. 

For a Newtonian fluid, the data for pressure drop may be represented on a pipe friction chart as a friction factor = (R/pu2) expressed as a function of Reynolds number Re = (udp/n). The friction factor is independent of the rheological properties of the fluid, but the Reynolds number involves the viscosity which, for a non-Newtonian fluid, is... 

A Newtonian liquid of viscosity 0.1 N s/m2 is flowing through a pipe of 25 mm diameter and 20 m in lenglh, and the pressure drop is 105 N/m2. As a result of a process change a small quantity of polymer is added to the liquid and this causes the liquid to exhibit non-Newtonian characteristics its rheology is described adequately by the power-law model and the flow index is 0.33. The apparent viscosity of the modified fluid is equal to ihc viscosity of the original liquid at a shear rate of 1000 s L... 

Cross, M. M. J. Colloid Sci. 20 (1965) 417. Rheology of non-Newtonian fluids a new flow equation for pseudoplastic systems. 

Because concentrated flocculated suspensions generally have high apparent viscosities at the shear rates existing in pipelines, they are frequently transported under laminar flow conditions. Pressure drops are then readily calculated from their rheology, as described in Chapter 3. When the flow is turbulent, the pressure drop is difficult to predict accurately and will generally be somewhat less than that calculated assuming Newtonian behaviour. As the Reynolds number becomes greater, the effects of non-Newtonian behaviour become... 

Molecularly motivated empiricisms, such as the solubility parameter concept, have been valuable in dealing with mixtures of weakly interacting small molecules where surface forces are small. However, they are completely inadequate for mixtures that involve macromolecules, associating entities like surfactants, and rod-like or plate-like species that can form ordered phases. New theories and models are needed to describe and understand these systems. This is an active research area where advances could lead to better understanding of the dynamics of polymers and colloids in solution, the rheological and mechanical properties of these solutions, and, more generally, the fluid mechaiucs of non-Newtonian liquids. 

Complex liquids seldom behave as classical Newtonian fluids thus, analysis of their behavior requires a thorough understanding of non-Newtonian rheology. The importance of this knowledge is illustrated by the following two examples ... 

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