Viscoelastic fluid, mixing

Ulbrecht, J. The Chemical Engineer (London) No. 286 (1974) 347. Mixing of viscoelastic fluids by mechanical agitation. 

Carreav. P, J.. Patterson, I., and Yap, C. Y. Can J. Chem. Eng. 54 (1976) 135. Mixing of viscoelastic fluids with helical ribbon agitators 1. Mixing time and flow pattern. 

Niederkom, T. C, and Ottino, J. M., Mixing of viscoelastic fluids in time-periodic flows. J. Fluid Mech. 256, 243-268 (1993). 

Cheng J, Carreau PJ, Chhabra RP. On the effect of wall and bottom clearance on mixing of viscoelastic fluids. In Tatterson GB, Calabrese RV, Penny WR, eds. Industrial Mixing Fundamentals with Applications. New York Amer Inst Chem Eng, 1995 115-122. 

M. Kawahara and N. Takeuchi. Mixed finite element method for analysis of viscoelastic fluid flow. Comput. Fluids., 5 33, 1977. 

The high normal stress differences in comparison to the shear stress cause flow phenomena which may influence many technical processes. One example is the Weissenberg Effect (see Fig. 3.10), which arises when a shaft rotates within a viscoelastic fluid. The first normal stress difference leads to a pressure distribution which causes the fluid to climb up the stirrer shaft. This effect occurs when processing polymer color dispersions or mixing cake dough. 

Conventional stirred-tank polymeric reactors normally use turbine, propeller, blade, or anchor stirrers. Power consumption for a power-law fluid in such reactors can be expressed in a dimensionless form, Ne = Reynolds number based on the consistency coefficient for the power-law fluid. Various forms for the function f(m) in terms of the power-law index have been proposed. Unlike that for Newtonian fluid, the shear rate in the case of power-law fluid depends on the ratio dT/dt and the stirrer speed N. For anchor stirrers, the functionality g developed by Beckner and Smith (1962) is recommended. For aerated non-Newtonian fluids, the study of Hocker and Langer (1962) for turbine stirrers is recommended. For viscoelastic fluids, the works of Reher (1969) and Schummer (1970) should be useful. The mixing time for power-law fluids can also be correlated by the dimensionless relation NO = /(Reeff = Ndfpjpti ) (Tebel et aL 1986). 

For viscoelastic fluids, the formalism of a viscous fluid and an elastic solid are mixed [31]. The equations for the effective viscosity, dynamic viscosity, and the creep compliance are given in Table 12.4 for a viscous fluid, an elastic solid, and a visco-elastic solid and fluid. For the viscoelastic fluid model the dynamic viscosity, >j (tu), and the elastic contribution, G (ti)), are plotted as a function of (w) in Figure 12.31. With one relaxation time, X, the breaks in the two curves occur at co. 

Figure 6.29 compares the flow streamlines in a mixing tank of a Newtonian fluid and a viscoelastic fluid. The flow streamlines of polymer solution are different from those of water. The blind area at the bottom of the tank is much larger for polymer solution. There is a difference in speed between the blade tip and the surrounding polymer solution, but approximately the same for water. These problems increase the energy requirement to rotate the blade and the time to dissolve polymer powder. After the blade was redesigned, the energy... 

FIGURE 6.29 Comparison of flow streamlines in a mixing tank with (a) a Newtonian fluid and (b) a viscoelastic fluid. Source Wang (2001). 

There have been contradictory results reported in the literature, however, regarding the influence of fluid elasticity on the mixing unit operation [49-52], Further research is apparently required to define adequately the influence of viscoelasticity on mixing in agitated vessels, for a broad range of fluid properties and mixer configurations. 

In addition to the above, some materials behave in part as a viscous liquid and in part as an elastic solid, i.e. they can exhibit elastic recovery. These liquids are known as viscoelastic fluids. Although rather little has been done to establish the effect of viscoelasticity on mixing phenomena in a quantitative way, some effects are clear". 

Viscoelasticity leads to flow pattern dampening and reports of both decreased and increased mixing rates have been made. It seems therefore that viscoelastic properties affect the performance of different mixer designs in different ways and that there may be some opportunities to exploit viscoelastic properties in mixer design. It also seems that operating conditions, e.g. direction of impeller rotation , can also have an important effect when viscoelastic fluids are being mixed. More work is required to resolve these issues. 

The promotion of viscoelastic instability by utilizing microchannels with abrupt contraction-expansion geometiy for mixing has been exploited by Gan et al. [17, 18]. They employed a microchannel with a depth of 150 pm and an abmpt ctuitraction-expansion of 1,000 pm 125 pm 1,000 pm to introduce the con-vergent/divergent flow. The viscoelastic fluids utilized consisted of 1 wt% poly(ethylene oxide)... 

Gan et al. [18] further examined the flow of viscous fluid streams with no measurable elastic effects in an identical channel, but with the same viscosity ratio as the viscoelastic fluid streams. No mixing of the streams was observed. Thus, the necessity of fluid elasticity for flow instability and mixing was demonstrated. 

Chaotk Mixing Based on Viscoelasticity, Fig. 3 Consecutive snapshots of viscoelastic fluids flow at Q = 12ml/h. Each fluorescent tracer s snapshots, (a) and (b) or (c) and (d), were collected at 50 ms interval. Viscoelastic instability (whipping) upstream and... 

Gan HY, Lam YC, Nguyen NT (2006) Polymer-based device for efficient mixing of viscoelastic fluids. Appl Phys Lett 88 224103... 

Hsiao, K. L. (2007). Conjugate heat transfer of magnetic mixed convection with viscous dissipation effects for second-grade viscoelastic fluid past a stretching sheet, Appl. Therm. Eng., 27, pp. 1895-1903, ISSN 1359-4311. 

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