Pseudoplastic liquid

A simple relationship has been shown to exist, however, between much of the data on power consumption with time-independent non-Newtonian liquids and Newtonian liquids in the laminar region. This link, which was first established by Metzner and Otto 1 2 for pseudoplastic liquids, depends on the fact that there appears to be an average angular shear rate y mt, for a mixer which characterises power consumption, and which is directly proportional to the rotational speed of impeller ... 

Plastic fluids are Newtonian or pseudoplastic liquids that exhibit a yield value (Fig. 3a and b, curves C). At rest they behave like a solid due to their interparticle association. The external force has to overcome these attractive forces between the particles and disrupt the structure. Beyond this point, the material changes its behavior from that of a solid to that of a liquid. The viscosity can then either be a constant (ideal Bingham liquid) or a function of the shear rate. In the latter case, the viscosity can initially decrease and then become a constant (real Bingham liquid) or continuously decrease, as in the case of a pseudoplastic liquid (Casson liquid). Plastic flow is often observed in flocculated suspensions. 

It is important when using the term yield stress to distinguish between an extrapolated value, sometimes called the dynamic yield stress and a true or static yield stress . The latter can only be observed for plastic solids whilst the former is readily obtained with pseudoplastic liquids. In practical terms this can be critical in evaluating the performance of a material. 

Pseudoplastic liquids have a r-y plot that is concave downward. The simplest mathematical representation of such relations is a power law... 

Figure 6.5. Friction factors in laminar and turbulent flows of power-law and Bingham liquids, (a) For pseudoplastic liquids represented by tw = K [WID) , with K and n constant or dependent on r l/V/ = [4.0/(n )0 75] log10[Re /( "2)] — 0.40/(k )1 2j, [Dodge and Metzner, AIChE J. 5, 159 (7959)]. (b) For Bingham plastics, ReB = DVp/pB, He = 10D2plp% [Hanks and Dadia, AIChE J. 17, 554 (J971)].

In most pseudoplastic liquids, Newtonian flow behavior is observed at sufficiently low and at high shear rates y, see Fig. 18. Viscosity approaching a constant value with low shear rates is called the zero-shear viscosity, p0> and its constant value at very high shear rates is called the infinite shear viscosity, p°°. 

Homogenization characteristics of a mechanically agitated polymerization reactor in terms of NO = /(Reeff = Ndfp/pe( ) have been published for various stirrer types and pseudoplastic liquids with power-law behavior (Opara, 1975, Tebel et al, 1986). The homogenization time is compared to that for Newtonian fluids (Opara, 1975), and the homogenization properties of a... 

Figure 6.5. Friction factors in laminar and turbulent flows of power-law and Bingham liquids, (a) For pseudoplastic liquids represented by = K (WID f, with K and n constant or dependent on 1/Vf= -0.40/(n ) [Dodge and Metzner,...

FIG. 155. Types of rheological behaviour (a) Newtonian liquid (b) anomalous (pseudoplastic) liquid (c) Bingham body (d) real plastic body (e) thixotropic body (f) dilatant body. The viscosity is given by the tangent of the indicated angle. 

If in non-Newtonian liquids the structure of the liquid is destroyed upon increasing y, hysteresis curves are observed as shown in Fig. 1.29. The behaviour of these liquids depends not only on the time of shear but also on the past shear and thermal history. Pseudoplastic liquids of this kind are named thixotropic, and dilatant liquids are referred to as rheopectic. The longer the duration of shear, the stronger is the destruction of the liquid structure, and the longer it takes to restore it. 

In the top graph of Fig. 2.9 the Ga number for the pseudoplastic liquid CMC is formed with the effective viscosity after Metzner-Otto (k = 11.5), whereupwn good consistency with the experimental values for glycerine is achieved. 

In the gassing of viscoelastic fluids (e.g. PAA-solutions) the sorption characteristics for D/d > 2.5 (e.g. turbine stirrer) are also dependent upon the stirrer speed, since then the effect of the stirrer is ever more strongly limited by its immediate surroundings, and this even more so the more intensively the liquid is sheared. For D/d < 1.67 (e.g. MIG stirrer), on the other hand, the same results are obtained as in pseudoplastic liquids, see equation (4.41). 

For determining the sedimentation velocity of spherical particles in pseudoplastic liquids, whose viscosity obeys the power law according to Ostwald - de Waele, see [294]. 

Skelland and Kanel [513] established, that the relationship [512] given by them in Table 6.1 was also fully applicable, if a Newtonian liquid (diisobutyl ketone) was stirred into a pseudoplastic liquid (aqueous solutions of Carbopol 934, a stongly acidic acrylic acid polymer), if its apparent density, which obeys the power law of Metzner and Otto, was appropriately taken into consideration. 

Bertrand J., Couderc J.P., Evaluation of the power consumption in agitation of viscous Newtonian or pseudoplastic liquids by two-bladed, anchor or gate agitators, Chem. Eng. Res. Dev. 63 (1985) 7, p. 259-263... 

Takahashi K., Yokota T, Konno H., Mixing of pseudoplastic liquid in a vessel equipped with a variety of helical ribbon impellers, J. Chem. Engng. Japan 21 (1988) 1, p. 63-68... 

For a straight-blade turbine in pseudoplastic liquids it has been shown that the average shear rate in the vessel is directly related to the impeller speed. For a number of pseudoplastic liquids a satisfactory, though approximate, relation... 

Figure 9.14 shows the power number-Reynolds number correlation for a six-blade turbine impeller in pseudoplastic fluids. The dashed curve is taken from Fig. 9.12 and applies to newtonian fluids, for which = nDlpJix. The solid curve is for pseudoplastic liquids, for which is given by Eqs. (9.25) and... 

At Reynolds numbers below 10 and above 100 the results with pseudoplastic liquids are the same as with newtonian liquids. In the intermediate range of Reynolds numbers between 10 and 100, pseudoplastic liquids consume less power than newtonian fluids. The transition from laminar to turbulent flow in pseudoplastic liquids is delayed until the Reynolds number reaches about 40, instead of 10 as in newtonian liquids. 

The flow patterns in an agitated pseudoplastic liquid differ considerably from those in a newtonian liquid. Near the impeller the velocity gradients are large, and the apparent viscosity of a pseudoplastic is low. As the liquid... 

Plug flow is not a realistic model for newtonian fluids, but it does apply to highly pseudoplastic liquids ( 0) or to plastic liquids having a high value of the yield stress Zq. 

In dilatant liquids, increases less than proportionally with 021, while in pseudoplastic liquids increases more than proportionally (Figure 7-4). Expressed another way In pseudoplastic liquids, the apparent viscosity rjapp = as the shear stress increases (shear thinning), whereas in... 

When the shear stress changes in Newtonian, dilatant, or pseudoplastic liquids, as well as in Bingham bodies or fluids above the flow limit, the corresponding shear gradient or the corresponding viscosity is reached almost instantaneously. In some liquids, however, a noticeable induction time is necessary, i.e., the viscosity also depends on time. If, at a constant shear stress or constant shear gradient, the viscosity falls as the time increases, then the liquid is termed thixotropic. Liquids are termed rheopectic or antithixotropic, on the other hand, when the apparent viscosity increases with time. Thixotropy is interpreted as a time-dependent collapse of ordered structures. A clear molecular picture for rheopexy is not available. 

FIGURE 14 Rheological curves for Newtonian and pseudoplastic liquids. 

Fig. 1.21 Capillary breakup of pseudoplastic liquid jets [29]. (a) Suspension of 25% y-Fe203 particles in oil. (b) Suspension of 36% y-Fe203 particles in oil. (c) Aqueous suspension of clay (Courtesy of Pearson Education)...

Figure 8.7 Power curve for pseudoplastic liquids agitated by different types of impeller [from Skelland, 1983]...

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