Similarity apparent viscosity

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

In general, for shear-thinning pseudoplastic fluids the apparent viscosity will gradually decrease with time if there is a step increase in its rate of shear. This phenomenon is known as thixotropy. Similarly, with a shear-thickening fluid the apparent viscosity increases under these circumstances and the fluid exhibits rheopexy or negative-thixotropy. 

The native sample E (Fig. 3) contains a relatively large amount of aggregated structures. Most of them appear to rearrange into perfectly matched double-stranded chains after incubation at 80 °C for 2 months (27). This rearrangement is reported to result in a fivefold increase in the apparent viscosity at a shear rate of 1 s-1 (27). A similar rearrangement of xanthan assemblies is also observed in a unpasteurized fermentation broth after exposure of the sample... 

For non-Newtonian liquids and suspensions, an apparent viscosity is determined using correlations which include power input and the Reynolds number. Scale-up comparisons based on heat generation data only were determined by comparison of results from RC1 experiments and from a 675-liter reactor [208]. In the experiments, a Bingham plastic fluid was used to determine the film heat transfer coefficient. This presents a worst case because of the low thermal conductivity of the Bingham plastic. Calculated inside film heat transfer coefficients determined in the RC1 tests were about 60% lower than the values determined in the pilot plant reactor, even though substantial effort was made to obtain both geometric and kinematic similarity in the pilot reactor. 

The second category, time-dependent behaviour, is common but difficult to deal with. The best known type is the thixotropic fluid, the characteristic of which is that when sheared at a constant rate (or at a constant shear stress) the apparent viscosity decreases with the duration of shearing. Figure 1.21 shows the type of flow curve that is found. The apparent viscosity continues to fall during shearing so that if measurements are made for a series of increasing shear rates and then the series is reversed, a hysteresis loop is observed. On repeating the measurements, similar behaviour is seen but at lower values of shear stress because the apparent viscosity continues to fall. 

Thixotropy is the time-dependent analogue of shear-thinning and plastic behaviour, and arises from somewhat similar causes. If a thixotropic system is allowed to stand and is then sheared at a constant rate, the apparent viscosity decreases with time until a balance between structural breakdown and structure re-formation is reached. If the sheared system is then allowed to stand, it eventually regains its original structure. A thixotropic hysteresis loop (Figure... 

A dilatant flow is characterized by the opposite type of pseudoplastic flow in which the apparent viscosity increases with the increase in shear stress (i.e., shearthickening). The empirical equation described for the dilatant flow is similar to Equation (4.84) but the exponent n is greater than 1. This behavior is not common for all pharmaceutical solutions and dispersions but it is exhibited by pastes of small, deflocculated particles (solid content > 50%). There is only a limited amount of fluid that can till the interparticulate voids. 

The studies indicated that for all foaming agents the efficiency of oil recovery increased with the rise in foam quality. The authors explained this with the apparent viscosity of the foam. The analysis of other studies of the same authors showed that similar increase was observed in unconsolidated porous media with high porosity (0 > 0.35) and high permeability (K > 10 mm2). For consolidated pores with low porosity (0 < 0.25) and low permeability (K < 0.2 pm2) a decrease in oil recovery with the increase in foam quality occurred. 

The mobility-control surfactant increased the apparent viscosity of CO2 sufficiently to prevent gravity override and viscous fingering. The bulk CO2 phase passed through the core in a piston-like manner. Oil and most of the brine were displaced from the core ahead of the bulk-phase CO2. Differential pressure measurement across the length of the core indicated an average gradient, 1.3 psi/ft, similar to that observed during the brine flood. 

The role of insoluble solids can be also studied in terms of the relative viscosity [r]t = apparent viscosity of COJ/apparent viscosity of serum) and pulp fraction (Figure 2-12) and, as expected, such a plot has the limiting value of 1.0 at zero pulp fraction (serum). The curve in Figure 2-12 illustrates the strong influence of pulp fraction on the viscosity of COJ. The values of )a,ioo also, as expected, follow a profile similar to that of % (Figure 2-12). The two curves are described by the equations ... 

Morris (1981) suggested that when the apparent viscosities of two gum dispersions at equal concentrations are substantially different, in order to account for the different viscosity-coneentration relationships for the two gums, the apparent viscosity of mixtures of solutions of two gums be studied by mixing solutions of the two biopolymers with eoneentrations adjusted to give similar viscosities. The steps in this procedure for peetin and LB gum dispersions were (Lopes da Silva et al., 1992) (1) the shear rate—apparent viscosity data of solutions of pectin and LB gum with different eoneentrations were obtained, and (2) the concentrations... 

A master curve of the rheological conditions applicable during spreading of lipophilic preparations with force on the skin using a method similar to that of Wood (1968) showed that the range of acceptable apparent viscosity was about 3.9 poise to 11.8 poise, with an optimum value of approximately 7.8 poise (Barry and Grace, 1972). The preferred region was approximately bounded by shear rates 400-700 s and shear stress 2,000-7,000 dyne cm (200-700 Pa, respectively). 

Similar to solutions of other random coil polysaccharides, the viscosity of pectin dispersion decreases with increasing temperature but increases with increasing concentration, and the effect of temperature is stronger at higher concentrations (Kar and Arslan, 1999b). The effect of temperature on apparent viscosity is usually analyzed by an Arrhenius-type relationship to calculate activation energy of flow... 

Different researchers have proposed formulae similar to Eq. 5.21 to calculate Yeq in porous media—for example, Christopher and Middleman (1965), Hirasaki and Pope (1974), Teeuw and Hesselink (1980), WiUhite and Uhl (1986), and CanneUa et al. (1988). CanneUa et al. used the following equations to estimate the equivalent shear rate (s ), Yeq, and apparent viscosity (mPa s), Papp, in porous media ... 

The activation energies for the backbone motion of P(4HB) and the 3HB and 4HB units in the P(3HB-co-4HB)s, derived from the DEM model analysis, are found to be similar and in the range 42-47 kJ/mol [79]. This range is typical of amorphous polymers at temperatures above Tg, but they are greater than typical ones for polymers in solution, possibly due to the increased apparent viscosity exerted by the amorphous matrix on the moving backbone segment [79]. The activation energy observed for the backbone motion of P(3HB) in chloroform solution is 17 kJ/mol [72]. 

We can see that Eqs. (2 101) (2-104) are sufficient to calculate the continuum-level stress a given the strain-rate and vorticity tensors E and SI. As such, this is a complete constitutive model for the dilute solution/suspension. The rheological properties predicted for steady and time-dependent linear flows of the type (2-99), with T = I t), have been studied quite thoroughly (see, e g., Larson34). Of course, we should note that the contribution of the particles/macromolecules to the stress is actually quite small. Because the solution/suspension is assumed to be dilute, the volume fraction is very small, (p 1. Nevertheless, the qualitative nature of the particle contribution to the stress is found to be quite similar to that measured (at larger concentrations) for many polymeric liquids and other complex fluids. For example, the apparent viscosity in a simple shear flow is found to shear thin (i.e., to decrease with increase of shear rate). These qualitative similarities are indicative of the generic nature of viscoelasticity in a variety of complex fluids. So far as we are aware, however, the full model has not been used for flow predictions in a fluid mechanics context. This is because the model is too complex, even for this simplest of viscoelastic fluids. The primary problem is that calculation of the stress requires solution of the full two-dimensional (2D) convection-diffusion equation, (2-102), at each point in the flow domain where we want to know the stress. 

Tanglertpaibul and Rao (AS) found that in the range of finisher screen openings (FSO) 0.508 to 1.143 mm, smaller FSO yielded lower apparent viscosities evaluated at a shear rate of 100 sec-1 (T ioo) However, concentrates from 0.686 mm screen had the highest apparent viscosity. Similar results were found for tomato juice also. This phenomena can be explained in that small screens reduced the size of solid particles and at the same time remove some of the large particles. The net result is that one obtains finished products with narrow particle size distribution and a small amount of large particles. 

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