Newtonian flow Polymer solutions

In the case of internal flows extensive experimental data are available for turbulent pipe flow. The study of turbulent-friction coefficients in pipe flow has brought forth a number of effects displayed by flowing polymer solutions. Furthermore, many hydro-dynamic investigations in pipe flow have been made to elucidate the flow behavior (laminar and turbulent) of Newtonian fluids. Thus, the pipe is one of the most investigated and traditional pieces of test apparatus and one can easily compare the flow behavior of Newtonian fluids and polymer solutions under constant boundary conditions. 

Polymer melts and solutions show pronounced non-Newtonian flow behavior. In rotational flows, polymer solutions typically show a shear-thinning behavior (2i, 22) where the apparent viscosity reduces as the shear rate is increased. In extensional, or stretching flows, however, polymer solutions often show a marked increase in viscosity as the shear rate is increased, termed dilatancy (23-26), Stretching flows are of considerable importance and generally occur in flows through orifices, filters, porous media, constrictions in pipes, and in any flow possessing turbulence or vorticity, in fact as a component of most real flow systems. 

Simple liquids such as solvents have the same viscosity no matter how fast they are stirred (Barnes, 2000). These are Newtonian liquids. Polymer solutions differ from simple liquids in the way they react to stirring (Wicks et al., 2007). Polymer molecules impart a structure to the liquid. The structure is disturbed while the solution is stirred vigorously. There are a number of different behaviours on stirring. Viscosity can reduce on stirring (shear thinning) as the molecules line up in the direction of flow, so reducing the viscosity... 

The practical and computational complications encountered in obtaining solutions for the described differential or integral viscoelastic equations sometimes justifies using a heuristic approach based on an equation proposed by Criminale, Ericksen and Filbey (1958) to model polymer flows. Similar to the generalized Newtonian approach, under steady-state viscometric flow conditions components of the extra stress in the (CEF) model are given a.s explicit relationships in terms of the components of the rate of deformation tensor. However, in the (CEF) model stress components are corrected to take into account the influence of normal stresses in non-Newtonian flow behaviour. For example, in a two-dimensional planar coordinate system the components of extra stress in the (CEF) model are written as... 

Capillary viscometers are useful for measuring precise viscosities of a large number of fluids, ranging from dilute polymer solutions to polymer melts. Shear rates vary widely and depend on the instmments and the Hquid being studied. The shear rate at the capillary wall for a Newtonian fluid may be calculated from equation 18, where Q is the volumetric flow rate and r the radius of the capillary the shear stress at the wall is = r Ap/2L. 

The following qualitative picture emerges from these considerations in weak flow where the molecular coils are essentially undeformed, the polymer solution should behave approximately as a Newtonian fluid. In strong flow of a highly dilute polymer solution where the macroscopic velocity field can still be approximated by the Navier-Stokes equation, it should be expected, nevertheless, that in the immediate proximity of a chain, the fluid will be slowed down because of the energy intake to stretch the molecular coil thus, the local velocity field may deviate from the macroscopic description. In the general case of polymer flow,... 

Rheology deals with the deformation and flow of any material under the influence of an applied stress. In practical apphcations, it is related with flow, transport, and handling any simple and complex fluids [1], It deals with a variety of materials from elastic Hookean solids to viscous Newtonian liquid. In general, rheology is concerned with the deformation of solid materials including metals, plastics, and mbbers, and hquids such as polymer melts, slurries, and polymer solutions. 

These values can now be used to calculate the smooth pipe friction factor from Eq. (6-100). Excluding the vVDe term gives the friction factor for the Newtonian solvent (/s), and including the, VDe term gives the friction factor for the polymer solution (fp) under the same flow conditions ... 

The main result was that regardless of dendrimer generation (i.e. molecular weight) and concentration, all of the examined solutions exhibited characteristic Newtonian flow behavior, as shown in Figure 14.6. This was in striking contrast to the typical behavior of either chain-type polymers of comparable molecular weights [33], or suspensions of spherical particles [34-37], both of which exhibit... 

Onogi,S., Kobayashi,Y., Kojima,Y., Taniguchi,Y. Non-Newtonian flow of concentrated solutions of high polymers. J. Appl. Polymer Sci.7,847-859 (1963). 

Kotaka,T., Osaki,K. Normal stresses, non-Newtonian flow, and dynamic mechanical behavior of polymer solutions. J. Polymer ScL Pt.C 15,453-479 (1966). 

Fig. 1. Schematic representation of the different flow behavior of a NEWTONian liquid (N) in comparison to a polymer solution (P). Under equal energy conditions, it can be seen that the polymer solution in addition to a higher volumetric flow also attains a greater length of forward travel and a higher degree of beam focusing for the jet...

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. 

Analyzing the flow in a single screw extruder using analytical solutions can only be done if we assume a Newtonian polymer melt. As can be seen in these sections, the flow inside the screw channel is a three dimensional flow made up of a combination of pressure and drag flows. Non-Newtonian flow can be solved for using numerical techniques and will be covered in Chapters 8 to 11 of this book. 

Thurston GB, Peterlin A (1967) Influence of finite number of chain segments, hydrodynamic interaction, and internal viscosity on intrinsic birefringence and viscosity of polymer solutions in an oscillating laminar flow field. J Chem Phys 46(12) 4881 4884 Treloar LRG (1958) The physics of rubber elasticity. Oxford University Press, London Tsenoglou C (2001) Non-Newtonian rheology of entangled polymer solutions and melts. Macromolecules 34 2148-2155... 

Doi and Edwards (1986) characterized a dilute solution as one of sufficiently low concentration that the polymer molecules are separated from each other. Dilute sols are normally characterized by a linear dependence of P on ct and often by Newtonian flow. A constant rate of change of iq, vs c, is... 

Solutions, including many polymer solutions, are well behaved. If poured from a container they flow. If they are quite viscous, they will still flow, just more slowly. Solutions such as these are called Newtonian fluids. Consider water flowing out of a garden hose. Newton s second law states in essence that the flow of water depends directly upon the pressure behind it. If we double the pressure, we get twice the flow (the water coming out of the end shoots twice as far). The viscosity remains constant and is independent of the pressure (force/unit area). As we mentioned above, the viscosity of many solutions depends upon the nature of the components, their concentrations, the temperature, and, if the solute is a polymer, its molar mass. 

The sedimentation of pharmaceutical dispersions in non-Newtonian polymer solutions is of some practical interest. These polymers are used not only to stabilize colloidal particles but also to slow down (or prevent) settling, thus preventing cake formation. Newtonian fluids are defined as simple fluids that show a linear relationship between the rate of flow or shear (G) and the applied (or shearing) stress (F) at a constant viscosity (p) as shown in Figure 4.38 ... 

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