Concentration and Shear Rate

Up to 100 vortices can be observed at one time, dependent on molar mass, concentration and shear rate. The vortices are seen to rotate about their own axis at the same time moving in the direction of shear. Vortices were seen up to the highest achievable shear rate g=1000 s-1. Decreasing or increasing the shear rate has little or no influence on the generation of vortices. They appear or disappear in a few seconds. The vortices are not caused by air or vapour bubbles. Vortices were also observed in a solution to which a surfactant had been added, and the onset... 

Morris, E. R., Cutler, A. N., Ross-Murphy, S. B., Rees, D. A., and Price, J. (1981). Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions. Carbohydr. Polym. 1 5-21. 

The limiting viscosity number (LVN) of the polymers—i.e., the intrinsic viscosity at zero concentration and shear rate, was determined from the inherent viscosity measured at 0.05 to 0.2 grams/100 ml. concentration in decalin at 135° C. with a Schulken-Sparks viscometer. 

Experimental measurements of the normal stress differences A i and N2 for suspensions are rare, especially for hard spheres. According to a recent theory by Brady and Vicic (1995), in the dilute regime the low shear-rate values of the normal stress differences are M,o/hoK = O.8996 7r0 Pe and Af2,o/r/oy = —O.78867T0 Pe. These values are quite small at concentrations and shear rates where the theory might apply (0 0.15 Pe 0.1). The... 

Wecker, A. and Onken, V. (1991). Influence of dissolved oxygen concentration and shear rate on the production of pullulan by Aureobasidium pullulans. Biotechnol. Lett. 13,155-160. Wheatley, A. (1990). Anaerobic digestion A waste treatment technology. Elsevier Applied Science, London. 

Figure 6.16. Steady viscosity of liquid crystalline polymers as a function of concentration and shear rate. (From Doi, 1982.)...

Hoffman [1972, 1974], Strivens [1976], van de Ven [1984, 1985], Tomita et al. [1982, 1984], and Otsubo [1994] reported pseudoplastic/dilatant flow of concentrated suspensions of uniform and polydispersed spheres. A dramatic change in light diffraction pattern was systematically observed at the shear rate corresponding to the onset of dilatancy. Van de Ven and his collaborators demonstrated that, depending on concentration and shear rate, the distance between the sliding layers of uniform spheres in a parallel plate rheometer can vary by as much as 10%. 

Copolymers with sites for association in aqueous solutions were pre-pared by copolymerizing acrylamide with N-alkylacrylamides or with the ampholytic monomer pairs sodium 2-acrylamido 2 methylpro-panesulfonate (NaAMPS) and 2-acrylamido-2-methylpropane-dimethylammonium chloride (AMPDAC). The copolymers were characterized by elemental analysis, NMR and Fourier transform infrared spectroscopy, and lowhangle laser and quasielastic lightscattering measurements. Rheological properties were studied as a function of microstructure, molecular weight, polymer concentration, electrolyte concentration, and shear rate. On the basis of those results, a conceptual model that is based on microheterogeneous domain formation in aqueous solutions is proposed. 

Regression analysis techniques were applied to determine the regression coefficients associated with abrasion as a function of particle size, polymer concentration, and shear rate in the following three models ... 

Figure 3.2 Dependency of viscosity upon concentration and shear rate for a typical... 

Fig. 4. Viscosity of ABS as a function of CO2 concentration and shear rate at 370 F (Courtesy of Trexel, Inc.). Note that the relative viscosity change is most pronounced at low shear rates.

Figure 3.273. Influence of the inhibitor concentration and shear rate on the shear...

Let us consider a simple case in which the settling velocity is independent of concentration and shear rate, i.e., /" (C, 7) = 1. Then, from Eq. (27.52)... 

The Metzner and Reed approach requires the engineer to assume a value of the shear stress at the waU to calculate x. Such assumptions are very difficult to make for engineers outside a research lab. It may be more practical to send samples of the slurry to a rheology lab and to go from plots of yield stress versus weight concentration, as well as from plots of viscosity versus weight concentration and shear rates to a more straightforward computation of friction factors (Figure 5-3). 

Fig. 12 shows the effects of Kelzan M concentration and shear-rate on polymer water viscosity. The effect of shear rate was determined by varying spindle speed on an LVT Brookfield viscosimeter with the U.L. attachment. The decrease in viscosity at high shear rates is desirable from an injectivity standpoint. It is conceivable that polymers having strong friction reducing properties might show higher injectivities than water alone. 

A further complication in understanding the rheology of hydrophobically associating polymers is the unique response to shear rate and solvent quality (e.g. salt content). As shown in Fig. 3.8, the viscosity can be independent (Newtonian), decrease (pseudoplastic) or even increase (dilatant) with shear rate depending on the polymer concentration and shear rate. As the hydrophobe level and polymer concentration increase beyond a critical value, a shear rate region in... 

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