Apparent viscosity Extension

Researchers have investigated the nature of the foam flow by examining the mechanisms of foam generation (l ). An extensive study (1 ), that is quite relevant to the mechanism of foam flow in porous media, has shown that the apparent viscosity of foam in a capillary tube decreases rapidly as the ratio of bubble radius-to-tube radius is increased. 

Most previous work has been reviewed by Grace (G13) and Schiigerlet al. (in D5). Botterill (B12) and Hetzler and Williams (H8) correlated the apparent viscosity of liquid- and gas-fluidized systems, applying a free-volume theory which may be used successfully for glass-forming (polymeric) liquids. Saxton et al. (S3) proposed another approach to a free-volume theory. They compared theoretical expectations with the experimental data obtained in liquid-fluidized systems. Their extension to gas-fluidized systems (in cgs units) became, for sand. 

Appendix B explains how polymer melt flow curves can be derived, and defines apparent (shear) viscosity. It is difficult to correlate the apparent viscosity with a single molecular weight average, because it depends on the width of the molecular weight distribution. However, in the limit of very low shear strain rates 7, when the entanglements between polymer chains produce negligible molecular extension, the apparent viscosity approaches a limiting value... 

Most recent, extensive rheological studies [59] on the stabilized NMMO-water solution proved that the apparent viscosity of the anisotropic solutions is relatively high (see Figure 10.26). Therefore, most commercial Lyocell spinning dopes usually have concentrations less than 17% and are isotropic. 

Many mathematical expressions of varying complexity and form have been proposed in the literature to model shear-thinning characteristics some of these are straightforward attempts at cmve fitting, giving empirical relationships for the shear stress (or apparent viscosity)-shear rate curves for example, while others have some theoretical basis in statistical mechanics - as an extension of the application of the kinetic theory to the liquid state or the theory of rate processes, etc. Only a selection of the more widely used viscosity models is given here more complete descriptions of such models are available in many books [Bird et al., 1987 Carreau et al., 1997] and in a review paper [Bird, 1976],... 

In conclusion, it should be emphasised that most of the cmrently available information on heat transfer to non-Newtonian fluids in stirred vessels relates to specific geometrical arrangements. Few experimental data are available for the independent verification of the individual correlations presented here which, therefore, must be regarded somewhat tentative. Reference should also be made to the extensive compilations [Edwards and Wilkinson, 1972 Poggermann et al., 1980 Dream, 1999] of other correlations available in the literature. Although the methods used for the estimation of the apparent viscosity vary from one correlation to another, especially in terms of the value of ks, this appears to exert only a moderate influence on the value of h, at least for shear-thinning fluids. For instance, for n = 0.3 (typical of suspensions and polymer solutions), a two-fold variation in the value of ks will give rise to a 40% reduction in viscosity, and the effects on the heat transfer coefficient will be further diminished because Nu [Pg.371]

The salinity at which the middle phase microemulsion contains equal volumes of oil and brine is defined as the optimal salinity. The oil recovery is found to be maximum at or near the optimal salinity (8,10). At optimal salinity, the phase separation time or coalescence time of emulsions and the apparent viscosity of these emulsions in porous media are found to be minimum (11,12). Therefore, it appears that upon increasing the salinity, the surfactant migrates from the lower phase to middle phase to upper phase in an oil/brine/surfactant/alcohol system. The -> m u transition can be achieved by also changing any of the following variables Temperature, Alcohol Chain Length, Oil/Brine Ratio, Surfactant Solution/Oil Ratio, Surfactant Concentration and Molecular Weight of Surfactant. The present paper summarizes our extensive studies on the low and high surfactant concentration systems and related phenomena necessary to achieve ultralow interfacial tension in oil/brine/surfactant/alcohol systems. 

One method is based on the measurement of viscosity. 1° 105 Fig. 5.7610 shows an example measurement with a Brookfield viscometer, In this procedure, the gel solution is mixed in a thermally Jacketed beaker and then the viscometer is turned on with a specified spindle at a set shear rate. Apparent viscosity is measured as a function of time and typically yields a curve like that shown in Fig. 5,76. There is no apparent increase in viscosity for a period of time, and then a period of rapid increase occurs. Gel time may be arbitrarily defined as the time at which viscosity starts to increase, the tirne at which the extensions of the two approximately straight lines intersect, or the time at which the apparent viscosity reaches a specified value. This method has been found to give reproducible results for gel times of up to 10 days or more, l ... 

Figure 7.7.7 shows data collected in suction (uniaxial extension) and expulsion (biaxial or compression) plotted as apparent viscosity versus apparent extension rate. The liquid was Newtonian a glycerin-water mixture with shear viscosity of 1.6 poise. The dashed line gives Stjo, the value we would expect for pulling of the sample in air. We see that the values are closer to Ar)o because of the departure of the flow from ideal extensional flow. The solid lines represent calculations by Schunk et ai. (1990), who have carried out a fairly complete analysis of this flow, solving the Na-vier-Stokes equations via the finite element method. 

A detailed and intricate scaling analysis for the Couette flow of nematics, similar in style to that contained in Section 5.5.5, has been carried out by Atkin and Leslie [6]. We do not pursue this aspect of the analysis in this text and refer the reader to Reference [6] for comments on possible experimentally determined quantities such as an apparent viscosity. As already mentioned, solutions for unequal elastic constants can also be found in [6]. A more extensive analysis of Couette flow incorporating the effects of an applied magnetic field has been provided by Currie [57], who also comments on other types of solutions which may be possible. 

---