Steady shear solution viscosities

Steady Shear Solution Viscosities of Polymers Crosslinked by Micelles. 

Consistent with the Newtonian flow of concentrated PAMAM solutions, it was found that all three types of dendrimers [40, 41, 50] under steady-shear conditions, and both PAMAMs [40] and PPIs [50] under creep [16,50] showed typical viscous behavior at all applied stress levels and testing temperatures. For example, as illustrated in Figure 14.9 [40], all of the first seven generations of PAMAMs showed constant viscosities over the entire ranges of shear rates investigated, and in addition to this, there was no hysteresis between the forward and the reverse stress sweeps in steady shearing, indicating the absence of thixotropy. 

Fig. 2.5. Steady-state and dynamic oscillatory flow measurements on a 2 wt. per cent solution of polystyrene S 111 in Aroclor 1248 according to Philippoff (57). ( ) steady shear viscosity (a) dynamic viscosity tj, ( ) cot 1% from flow birefringence, (A) cot <5 from dynamic measurements, all at 25° C. (o) cot 8 from dynamic measurements at 5° C. Steady-state flow properties as functions of shear rate q, dynamic properties as functions of angular frequency m. Shift factor aT which is equal to unity for 25° C, is explained in the text, cot 2 % and cot 8 are expressed in terms of shear (see eqs. 2.11 and 2.22)...

The bulk rheological properties of the PFPEs, including the melt viscosity (p), storage modulus (G ), and loss modulus (G"), were measured at several different temperatures via steady shear and dynamic oscillation tests. Note that we denoted p as melt viscosity and r as solution viscosity. An excellent description of the rheology is available in Ferry [99]. 

FIG. 16.33 Steady shear flow results for 12% PBLG solution in m-cresol at 293K (O) viscosity (A) positive N, (A) negative Nv Reproduced with permission from Mewis J and Moldenaers P (1987) Mol Cryst Liq Cryst 153, 291. Copyright Taylor and Francis Ltd., http //www.informaworld.com. 

Fig. 40. Steady shear viscosities of aqueous dispersions of polystyrene latices in nonadsorbing dextran solutions (Patel and Russel, 1989b) (a) a/r, = 6.9, 0 = 0.20. A, single phase, 4nR J/3pb = 0.15 B, two-phase, 4jtR /3pb = 0.30 C, two-phase, 4jtRj/3pb = 0.45 D, two-phase, 4jtRj/3pb = 0.65. (b) a/R, = 1.9, 0 = 0.10. F, single phase, 4jtR /pb = 0.65 G, fluid-fluid, 4jtR /3pb = 0.75 H, fluid-solid, 4nR /3p = 0.95 I, fluid-solid, 4jiR3/3p = 1.25.

Beyond the percolation limit, the bridging network is more concentrated. Below the critical volume fraction, no continuously bridging networks are formed and the viscosity is low. As shown in Figure 12.7, this bridging network breaks up as the shear rate increases, giving different viscosities at different shear rates. As a result, this gives low and high shear limit viscosities observed at steady state for concentrated poljmier solutions and concentrated particulate suspensions (discussed later). 

A single-relaxation-time response is also observed for this fluid in other flow histories, including start-up and cessation of steady shearing, if the shear rate y is low enough. At higher shear rates, the viscoelastic response is more complex. Figure 12-11 shows the time-dependence of the shear viscosity r] after start-up of steady shearing for a solution... 

Figure 12.11 Viscosity (stress divided by shear rate) after start-up of steady shearing at various shear rates for a solution of 0.1 M CTAB and 0.4 M NaSal. (Reprinted from J Non-Newt Fluid Mech 28 171, Shikata et al. (1988), with kind permission from Elsevier Science - NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

The viscosity of pectin solutions is influenced by the conditions of measurement. Steady shear is used to study the dependence of shear stress (or shear viscosity) on... 

A standard commercial film blowing LLDPE resin, LPX-30, was blended at different ratios with either other LLDPE s or a LDPE polymer. The characteristic properties of these materials are listed In Table II. The resins were generously donated to the project by Esso Chem., Canada. Prior to blending the polymers were thoroughly characterized by SEC, SEC/LALLS, solution viscosity, CNMR, Atomic Absorbance, and their rheological behavior was characterized In steady state and dynamic shear flow as well as In the uniaxial extenslonal deformation (44-46). 

Steady shear flow measnrements, however, can measure only viscosity and the first normal stress difference, and it is difficult to derive information abont fluid structure from such measurements. Instead, dynamic oscillatory rheological measurements are nsed to characterize both enhanced oil recovery polymer solutions and polymer crosslinker gel systems (Prud Homme et al., 1983 Knoll and Pmd Homme, 1987). Dynamic oscillatory measurements differ from steady shear viscosity measnrements in that a sinusoidal movement is imposed on the fluid system rather than a continnons, nnidirectional movement. In other words, the following displacement is imposed ... 

The measurement of yield stress at low shear rates may be necessary for highly filled resins. Doraiswamy et al. (1991) developed the modified Cox-Merz rule and a viscosity model for concentrated suspensions and other materials that exhibit yield stresses. Barnes and Camali (1990) measured yield stress in a Carboxymethylcellulose (CMC) solution and a clay suspension via the use of a vane rheometer, which is treated as a cylindrical bob to monitor steady-shear stress as a function of shear rate. The effects of yield stresses on the rheology of filled polymer systems have been discussed in detail by Metzner (1985) and Malkin and Kulichikin (1991). The appearance of yield stresses in filled thermosets has not been studied extensively. A summary of yield-stress measurements is included in Table 4.6. 

In this section we investigate some of the properties of mixtures undergoing steady shearing flow. Specifically we consider the viscosity and normal stress functions for suspensions of rigid dumbbells of various lengths which have the same zero shear rate viscosity as a solution containing dumbbells of length L only. 

Here t, 4, and 4 2 are three important material functions of a nonnewtonian fluid in steady shear flow. Experimentally, the apparent viscosity is the best known material function. There are numerous viscometers that can be used to measure the viscosity for almost all nonnewtonian fluids. Manipulating the measuring conditions allows the viscosity to be measured over the entire shear rate range. Instruments to measure the first normal stress coefficients are commercially available and provide accurate results for polymer melts and concentrated polymer solutions. The available experimental results on polymer melts show that , is positive and that it approaches zero as y approaches zero. Studies related to the second normal stress coefficient 4 reveal that it is much smaller than 4V and, furthermore, 4 2 is negative. For 2.5 percent polyacrylamide in a 50/50 mixture of water and glycerin, -4 2/4 i is reported to be in the range of 0.0001 to 0.1 [7]. 

The steady shear viscosity measurements of representative solutions used in the study of the friction factor behavior are given in Fig. 10.23. For concentrations ranging from 50 to 1000 wppm, the viscosity is shear rate dependent. The viscosities for 10-wppm polyacrylamide solutions are relatively independent of shear rate. 

FIGURE 10.23 Steady-shear-viscosity measurements for polyacrylamide (Separan AP-273) solutions from Weissenberg rheogoniometer and capillary-tube viscometer. tp is the characteristic time calculated from the Powell-Eyring model [37]. 

FIGURE 10.32 Degradation effects on steady shear viscosity measurements for polyacrylamide 1000-wppm solution as a function of circulation time. 

FIGURE 10.34 Steady shear viscosity versus shear rate for polyacrylamide 1000-wppm solutions with four different solvents [100]. 

Figure 25. Steady shear viscosity variation with shear rate for 15% styrene-methyl acrylate copolymer suspension in a 2 wt% PAA solution (171).

Figure 1 Shear-induced aggregation of bovine serum albumin (BSA), ovalbumin (OV) and /3-lactoglobulin (BLG) in aqueous solution. Viscosity of the solutions was measured against time under a steady shear rate (10"3 s 1 for BSA, 6.3 10 3 s 1 for OV, and 10 4 s-1 for BLG). Solvent 0.1 M NaCI, pH 7, 20°C. The concentrations of the solutions were 0.75%, 1.25%, and 1.5% for BSA, OV, and BLG, respectively. (Replotted from Refs. 28 and 29.)...

A. Steady Shear Viscosity of Fluid Foods and Dilute Food Polymer Solutions... 

A. STEADY SHEAR VISCOSITY OF FLUID FOODS AND DILUTE FOOD POLYMER SOLUTIONS... 

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