Viscous flow polymer solutions

Because of these characteristics electromagnetic flow meters have been widely appHed to the measurement of difficult Hquids such as raw sewage and wastewater flows, paper pulp slurries, viscous polymer solutions, mining slurries, milk, and pharmaceuticals. They ate also used in less demanding apphcations such as the measurement of large domestic water volumes. 

Materials such as metals are nearly elastic and show almost no flow or viscous component. Polymers and many of their solutions are both viscous and elastic, and both types of deformation must be taken into account to explain their behavior. 

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. 

The motion occurring during viscous flow consists of a shear in which different layers of the solution move with different velocities. The large polymer molecule finds it impossible to adjust its motions so as to coincide with the velocities of the different layers of the liquid through which it extends. Its situation is depicted in Fig. 139, where vectors representing the unperturbed velocity of the liquid relative to the position of the center of gravity of the molecule are shown. Let the velocity gradient be 7 ... 

Torrest, R.S. "The Flow of Viscous Polymer Solutions for Gravel Packing Through Porous Media," SPE paper 11010, 1962 Annual Fall Technical Conference and Exhibition of the SPE of AIME, New Orleans, September 26 29. 

Rules—solutions containing polymer chains are more viscous, slower flowing, than solutions that do not contain polymers. 

The overlaps between SPs in semidilute concentrations can be thought of in very similar terms to the entanglements defined above. Supramolecular interactions create large stmctures that physically interact to determine the mechanical response (in this case, viscous flow). The primary relaxation is the diffusion of an SP that is effectively intact on the timescale of the diffusion process. Thus, at a fixed concentration, the SP properties in dilute solution are therefore quite similar to those of covalent polymers of the same molecular weight and molecular weight distribution. 

Here a is the elastic stress which arises from the change in the (dynamic) free energy in the macroscopic flow, while o(V) and a(S) are the viscous stresses produced by the polymer-solvent friction and the solvent-solvent friction, respectively. In concentrated isotropic polymer solutions, the elastic stress overwhelms the viscous stresses, so the latter are often neglected. However, it should be noticed that the viscous stresses may become significant in more dilute solutions as well as in nematic solutions where the elastic stress diminishes. 

Berner C, Scrivener O (1980) Drag reduction and structure of turbulence in dilute polymer solutions Prog. Astronaut. Aeronaut., Vol 72 Viscous flow drag reduction (AIAA), 290... 

Ellis AT, Ting RY, Napolink RH (1970) Some effects of storage and shear history on the friction reducing properties of dilute polymer solutions Prog Astronaut Aeronaut 70 Viscous flow flow drag reduction (AIAA) 532... 

Falco RE, Wiggert DC (1980) Effects of dilute polymer solutions in vortexring/wall interactions — a mechanism of drag reduction Prog Astronaut Aeronaut 72 Viscous flow drag reduction (AIAA) 275... 

M. L. Booy, A Noniterative Numerical Solutions of Poisson s and Laplace s Equations with Applications to Slow Viscous Flow , Trans. ASME Series D, 88, 725-733 (1966) also, Isothermal Flow of Viscous Liquids in Corotaing Twin Screw Devices, Polym. Eng. Sci., 20, 1220 (1980). 

Further on, we shall consider the case of shear stress when one of the components of the velocity gradient tensor has been specified and is constant, namely V12 0. This situation occurs in experimental studies of polymer solutions (Ferry 1980). In order to achieve such a flow, it is necessary that the stresses applied to the system should be not only the shear stress a 12, as in the case of a linear viscous liquid, but also normal stresses, so that the stress tensor 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. 

Polymer solutions may have the memory effects observed in viscoelastic phenomena. This requires additional relaxation terms in the constitutive equations for the viscous pressure tensor, which may be affected by the changes in the velocity gradient. Besides this, the orientation and stretching of the macromolecules may have an influence on the flow. 

Polymer solutions generally exhibit viscous behavior when flowing in capillary tubes with constant diameters. However, in porous media where capillary diameters change rapidly, polymer chains are pulled or contracted to exhibit elastic behavior. The elastic behavior leads to a higher apparent viscosity, as described by Eq. 6.8. 

This condition is readily satisfied for the apparatus and liquids usually used for measurements of the viscosities of polymer solutions. However, in addition to the requirements of viscous flow, the derivation of Eq. (4.128) relies on the following assumptions. 

The effect of temperature on the flow behaviour of polymethacrylate and polyacrylate blends in mineral oil demonstrated that it is strongly controlled by the entropy of activation for viscous flow [51], confirming early speculations [52]. The increased negative entropy was presumably a result of the very sluggish translational motion of the polymer coils. On the other hand, the enthalpy of activation for viscous flow of the polymer solutions was, for the most part, very nearly the same as that of the oil solvent. Only the most efficient systems exhibited decreased enthalpy, suggesting that coil expansion at high temperatures may be a factor, but the effect was very small relative to the entropy effect. 

A thermopolastic elastomer based on sulfonated-EPDM, S-EPDM, was developed in the 1970 s by Exxon and more recently by Uniroyal. Unlike the synthesis of the carboxylate ionomers described above, S-EPDM is prepared by a post-polymerization sulfonatlon reaction(28). Compared to the metal neutralized S-EPDM, the sulfonic acid derivative is not highly associated. The free acid materials possess low strengths and are less thermally stable. The metal salts of S-EPDM have properties comparable to crosslInked elastomers, but they do exhibit viscous flow at elevated temperatures. In the absence of a polar cosolvent, such as methanol, hydrocarbon solutions of the metal salts of S-EPDM are solid gels at polymer concentrations above several percent(31). With the addition of 1 to 5% alcohol the polymer solution becomes fluid with solution viscosities of the order of 10 to 100 poise. 

---