Flow Phenomena and Viscosity

F. Schneider and H. Kneppe, Flow Phenomena and Viscosity, in Handbook of Liquid Crystals, Volume 1, D. Demus, J. Goodby, G.W. Gray, H.-W. Spiess and V. Vill (Eds.), 454-476, Wiley-VCH, Weinheim, Germany, 1998. 

Fig. 2 shows the flow curve for the neat exact 5361 at loot). The instability problem of the metallocene based polymers with narrow molecular distribution is well known. Fig. 3 shows the photographs of the extrudate samples with varying Dechlorane concentration collected during the capillary rheometers measurement. It is interesting to see that while the severe instabilities such as slip-stick and gross-melt fracture were observed at the shear rate from 177.8 s to 3162.2 s for the neat Exact resin, the severe instability appeared at the shear rate between 177.8 s and 562.2 s but disappeared at the shear rate above 1000.1 s for Exact/10% Dechlorane suspension. The shark-skin like instabilities were observed above the Dechlorane concentration of 20% and the shear rate at which the instability started to appear was decreased as the Dechlorane concentration was increased. Since the viscosity of the Dechlorane-filled systems was higher than that of the neat resin at all rates of shear, the instabilities are expected to develop the melt fracture at even lower shear rates. The shear viscosity vs. shear rate relationships measured with plate-plate rheometers and capillary rheometers are shown in Fig. 4. In this figure it is seen that both sets of data are reasonably matched. It is observed that at low shear rate range the viscosity increment due to the increase in the filler concentration is more pronounced than that at high shear rate. Both plate-plate and capillary measurements were carried out with constant shear rate (CSR) mode. While the capillary rheometer could accurately follow the preset shear rate values the plate-plate rheometer couldn t keep up with the preset shear rate values. Above two observations are due to the yield stress developed at low shear rate. At low shear rate particle-particle interaction dominates the flow phenomena and the yield stress was observed. At high shear rate hydrodynamic effect dominates the flow phenomena.

Shear viscosity vs. shear rate relationship was measured with plate-plate rheometers and capillary rheometers and it is observed that at low shear rate range the viscosity increment due to the increase in the filler concentration is more pronounced than that at high shear rate. At low shear rate particle-particle interaction dominates the flow phenomena and the yield stress was observed. At high shear rate hydrodynamic effect dominates the flow phenomena. 

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. 

In fluid dynamics the behavior in this system is described by the full set of hydrodynamic equations. This behavior can be characterized by the Reynolds number. Re, which is the ratio of characteristic flow scales to viscosity scales. We recall that the Reynolds number is a measure of the dominating terms in the Navier-Stokes equation and, if the Reynolds number is small, linear terms will dominate if it is large, nonlinear terms will dominate. In this system, the nonlinear term, (u V)u, serves to convert linear momentum into angular momentum. This phenomena is evidenced by the appearance of two counter-rotating vortices or eddies immediately behind the obstacle. Experiments and numerical integration of the Navier-Stokes equations predict the formation of these vortices at the length scale of the obstacle. Further, they predict that the distance between the vortex center and the obstacle is proportional to the Reynolds number. All these have been observed in our 2-dimensional flow system obstructed by a thermal plate at microscopic scales. ... 

As mentioned before in Eq. (3), the most common source of SGS phenomena is turbulence due to the Reynolds number of the flow. It is thus important to understand what the principal length and time scales in turbulent flow are, and how they depend on Reynolds number. In a CFD code, a turbulence model will provide the local values of the turbulent kinetic energy k and the turbulent dissipation rate s. These quantities, combined with the kinematic viscosity of the fluid v, define the length and time scales given in Table I. Moreover, they define the local turbulent Reynolds number ReL also given in the table. 

The flow phenomena in TBR are not easy to predict, because of the large number of variables such a bed porosity, size and shape of the catalyst, viscosity, density, interfacial tension, flowrates, and reactor dimensions. 

An analogy can be seen between these phenomena and the decrease in volume-averaged viscosity in the flow of a polymerizing liquid through a tubular reactor as described in Eq. (4.14). In real situations, the flow of a polymerizing liquid is always non-isothermal, which leads to a very... 

A generalized kinetic model of cure is developed from the aspect of relaxation phenomena. The model not only can predict modulus and viscosity during the cure cycle under isothermal and non-isothermal cure conditions, but also takes into account filler effects on cure behavior. The increase of carbon black filler loading tends to accelerate the cure reaction and also broadens the relaxation spectrum. The presence of filler reduces the activation energy of viscous flow, but has little effect on the activation energy of the cure reaction. 

All transport processes (viscous flow, diffusion, conduction of electricity) involve ionic movements and ionic drift in a preferred direction they must therefore be interrelated. A relationship between the phenomena of diffusion and viscosity is contained in the Stokes-Einstein equation (4.179). 

In the story of numerical flow simulation, the ability to predict observed and significant viscoelastic flow phenomena of polymer melts and solutions in an abrupt contraction has been unsuccessful for many years, in relation to the incomplete rheological characterization of materials, especially in elongation. The numerical treatments have often been confined to flow of elastic fluids with constant viscosity, described by differential constitutive equations as the Upper Convected Maxwell and Oldroyd-B models. Fortunately, the recent possibility to use real elastic fluids with constant viscosity, the so-called Boger fluids [10], has narrowed the gap between experimental observation and numerical prediction [11]. 

The use of local theories, incorporating parameters such as the eddy viscosity Km and eddy thermal conductivity Ke, has given reasonable descriptions of numerous important flow phenomena, notably large scale atmospheric circulations with small variations in topography and slowly varying surface temperatures. The main reason for this success is that the system dynamics are dominated primarily by inertial effects. In these circumstances it is not necessary that the model precisely describe the role of turbulent momentum and heat transport. By comparison, problems concerned with urban meso-meteorology will be much more sensitive to the assumed mode of the turbulent transport mechanism. The main features of interest for mesoscale calculations involve abrupt... 

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