Newtonian fluid mechanics

Non-Newtonian flow processes play a key role in many types of polymer engineering operations. Hence, formulation of mathematical models for these processes can be based on the equations of non-Newtonian fluid mechanics. The general equations of non-Newtonian fluid mechanics provide expressions in terms of velocity, pressure, stress, rate of strain and temperature in a flow domain. These equations are derived on the basis of physical laws and... 

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. 

Herschel, W.H. and Bulkley, R., 1927. See Rudraiah, N, and Kaloni, P.N. 1990. Flow of non-Newtonian fluids. In Encyclopaedia of Fluid Mechanics, Vol. 9, Chapter 1, Gulf Publishers, Houston. 

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. 

G. Bohme, Non-Newtonian Fluid Mechanics, Elsevier Science Publishing Co., New York, 1987. 

Example 4 Plnne Poiseuille Flow An incompressible Newtonian fluid flows at a steady rate in the x direction between two very large flat plates, as shown in Fig. 6-8. The flow is laminar. The velocity profile is to he found. This example is found in most fluid mechanics textbooks the solution presented here closely follows Denn. 

For laminar flow of power law fluids in channels of noncircular cross section, see Schecter AIChE J., 7, 445 48 [1961]), Wheeler and Wissler (AJChE J., 11, 207-212 [1965]), Bird, Armstrong, and Hassager Dynamics of Polymeric Liquids, vol. 1 Fluid Mechanics, Wiley, New York, 1977), and Skelland Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). 

Astarita G, Marrucci G (1974) Principles of non-Newtonian fluid mechanics. McCrow-Hill... 

Astarita. G. and Marrucci, G. Principles of Non-Newtonian Fluid Mechanics (McGraw-Hill, New York. 1974). 

Chhabra, R. P. and Richardson, J. F. In Encyclopedia of Fluid Mechanics, Volume 3, Gas-Liquid Flow Cheremisinoff, N, P. eds (Gulf Publishing Co. 1986). Co-current horizontal and vertical upwards flow of gas and non-Newtonian liquid. 

Watanabe K, Udagawa Y, Udagawa H (1999) Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall. J Fluid Mech 381 225-238 White FM (1994) Fluid mechanics, 3rd edn. McGraw-HiU, New York... 

A. B. Metzner, Non-Newtonian Technology Fluid Mechanics, Mixing, and Heat Transfer R. Byron Bird, Theory of Diffusion... 

Barnes, A.A. (2000) A handbook of elementary rheology. University of Wales, Institute of Non Newtonian Fluid Mechanics Department, pp 199... 

Runnels and Eyman [41] report a tribological analysis of CMP in which a fluid-flow-induced stress distribution across the entire wafer surface is examined. Fundamentally, the model seeks to determine if hydroplaning of the wafer occurs by consideration of the fluid film between wafer and pad, in this case on a wafer scale. The thickness of the (slurry) fluid film is a key parameter, and depends on wafer curvature, slurry viscosity, and rotation speed. The traditional Preston equation R = KPV, where R is removal rate, P is pressure, and V is relative velocity, is modified to R = k ar, where a and T are the magnitudes of normal and shear stress, respectively. Fluid mechanic calculations are undertaken to determine contributions to these stresses based on how the slurry flows macroscopically, and how pressure is distributed across the entire wafer. Navier-Stokes equations for incompressible Newtonian flow (constant viscosity) are solved on a three-dimensional mesh ... 

Non-Newtonian Technology Fluid Mechanics, Mixing, and Heat Transfer... 

Figure 5.2. Non-Newtonian behavior of suspensions (a) viscosity as a function of shear rate, 0.4 wt % polyacrylamide in water at room temperature (b) shear stress as a function of shear rate for suspensions of TiOz at the indicated vol % in a 47.1 wt % sucrose solution whose viscosity is 0.017 Pa sec (Denn, Process Fluid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1980).

Bames, H.A. 2000. A Handbook of Elementary Rheology. The University of Wals Institute of Non-Newtonian Fluid Mechanics, Aberysthyth, U.K. 

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