Non-Newtonian polymer solutions

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 ... 

Meter, D.M., Bird, R.B., 1964. Tube flow of non-Newtonian polymer solutions. Parts 1 and 11—Laminar Flow and Rheological Models. AlChE J. (November), 878—881, 1143— 1150. 

In the case of non-Newtonian polymer solutions (and narrow gaps) the stability limit increases. In situations where the outer cylinder is rotating, stable Couette flow may be maintained rmtil the onset of turbulence at a Reynolds nmnber. Re, of ca. 50 000 where Re = pQR2(R2 — R )/p- [Van Wazer et al, 1963],... 

For both heat and mass transfer in laminar boimdaiy layers, it has been assumed that the momentum boimdary layer is everywhere thicker than the thermal and diffusion boundary layers. For Newtonian fluids (n = 1), it can readily be seen that s varies as Pr / and Sm oc Sc. Most Newtonian liquids (other than molten metals) have the values of Prandtl number > 1 and therefore the assumption of < 1 is justified. Likewise, one can justify this assumption for mass transfer provided Sc > 0.6. Most non-Newtonian polymer solutions used in heat and mass transfer studies to date seem to have large values of Prandtl and Schmidt numbers [Ghosh et al., 1994], and therefore the assumptions of 1 and m 1 are valid. 

For particle-liquid heat and mass transfer in non-Newtonian polymer solutions flowing over spheres fixed in tubes (0.25 < d/D, < 0.5), Ghosh et al. [1992, 1994] invoked the usual heat and mass transfer analogy, that is, Sh = Nu and... 

Bird, R.B. Dodson, P.J. Johnson, J.L. Non-newtonian polymer solution rheology based on a finitely extensible bead-spring chain model. J. Non Newt. FI. Mech. 7 (1980) 213... 

DeKee, D., R. P. Chhabra, and A. Dajan, Motion and Coalescence of Gas Bubbles in Non-Newtonian Polymer Solutions, J. Non-Newtonian Fluid Mech., yi, 1 (1990). 

In most studies dealing with heat and mass transfer, it has been generally assumed that the thermo-physical properties, such as thermal conductivity, specific heat, molecular diffusivity of non-Newtonian polymer solutions, are the same as that for water, except for their non-Newtonian viscosity. Intuitively, one would expect the surface tension to be an important variable by way of influence on bubble dynamics and shape, but only a few investigators have controlled/measured/included it in their results. The available correlations can be broadly classified into two types first, those which directly relate the volumetric mass transfer coefficient with the liquid viscosity and gas velocity. The works of Deckwer et al. [36], Godbole et al. [42] and Ballica and Ryu [60] illustrate the applicability of this approach. All of them have correlated their results in the following form ... 

Once again, the reasoning is that the non-Newtonian polymer solution, with its blunted profile, will move toward a solid where plug flow definitely holds. This assumption is, of course, quite useful if the heat- or mass-transfer situation with respect to a filament is treated. 

Venu Madhav, G. and R. P. Chhabra, Settling velocities of non-spherical particles in non-Newtonian polymer solutions. Powder Technol. 78 11-93 (1994). 

Hydrodynamics of Free-Rise Bubbles in Non-Newtonian Polymer Solutions... 

When surface tension effects are small, as will be the case for large bubbles at high Reynolds number, Eqs. (12) and (13) and virtually the same. The experimental results of Astarita and Apuzzo (1965). Calderbank et al. (1970), Acharya et al. (1977), and Haque et al. (1988) on bubble velocities in non-Newtonian polymer solutions are well represented by Eq. (12) and (13) at high Reynolds number, thereby lending support to the notion that the liquid rheology plays little role in high Reynolds number bubble motion. 

T. Gillespie, T. Johnson, The penetration of aqueous surfactant solutions and non-Newtonian polymer solutions into paper by capillary action, J Colloid Interface Sci 36 (1971) 282-285. 

In this chapter, we have discussed the rheological behaviour of non-Newtonian polymer solutions in flow through porous media. The practical objective of this is to establish the apparent viscosity versus flow rate vs. Q or vs. 7pjn) expressions that can be used in polymer simulations in reservoirs. How this information is used in the numerical simulation of polymer flooding is discussed in more detail in Chapter 8. Much work has been reported on the in-situ rheology of inelastic polymers such as xanthan and flexible coil synthetic polymers such as HPAM, PEO etc. 

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