Simple drag flow

Over the twentieth century, the mbber industry has developed special rheometers, essentially factory floor instmments either for checking process regularity or for quality control purposes, for instance, the well-known Mooney rheometer (1931), the oscillating disk rheometer (1962), and the rotorless rheometer (1976). All those instmments basically perform simple drag flow measurements but they share a common feature During the test, the sample is maintained in a closed cavity, under pressure, a practice intuitively considered essential for avoiding any wall slip effects. Indeed it has... 

In extrusion and polymer processing, shear and extensional flows occur. This section deals with basic flow shapes of pressure-driven pipe flows and simple drag flows, while the next section coversextensional flows. 

Table 3.3 provides a summary of the relations for simple drag flow (laminar, stationary). Here, even if the fluids show different rheological behaviors, the speed profiles do not change (see Fig. 3.19). The shear rate is also not dependent on rheological properties of the fluid. 

Melt conveying is the forward motion of the molten polymer through the extruder, due to the pumping action of the rotating screw. This simple drag flow Md is proportional to melt density, down-channel velocity, and cross-sectional area of the screw channel. In most cases, however, there is also a pressure gradient as the melt moves downstream, either... 

Figure 6.1.8. Simple drag flow of liquid due to the motion of the top plate at a velocity v while the bottom plate is stationary.

Chain degradation in turbulent flow has been frequently reported in conjunction with drag reduction and in simple shear flow at high Reynolds numbers [187], Using poly(decyl methacrylate) under conditions of turbulent flow in a capillary tube, Muller and Klein observed that the hydrodynamic volume, [r ] M, is the determining factor for the degradation rate in various solvents and at various polymer concentrations [188], The initial MWD of the polymers used in their experiments are, however, too broad (Mw/Iiln = 5 ) to allow for a precise... 

Simple pressure/drag flow. Here we treat an idealization of the down-channel flow in a melt extruder, in which an incompressible viscous fluid constrained between two boundaries of infinite lateral extent (2). A positive pressure gradient is applied in the X-direction, and the upper boundary surface at y - H is displaced to the right at a velocity of u(H) - U this velocity is that of the barrel relative to the screw. This simple problem was solved by a 10x3 mesh of 4-node quadrilateral elements, as shown in Figure 1. 

Knowledge of the geometry and mathematical description of a screw Is required to understand the analysis of the functional sections of the screw and the troubleshooting of case studies. In Chapter 1 the geometry and mathematical descriptions are presented. Also In this chapter, the calculation of the rotational flow (also known as drag flow) and pressure flow rates for a metering channel Is Introduced. Simple calculation problems are presented and solved so that the reader can understand the value of the calculations. 

Dynamic (Sinusoidally Varying) Drag Simple Shear Flows... 

The steady and dynamic drag-induced simple shear-flow rheometers, which are limited to very small shear rates for the steady flow and to very small strains for the dynamic flow, enable us to evaluate rheological properties that can be related to the macromolecular structure of polymer melts. The reason is that very small sinusoidal strains and very low shear rates do not take macromolecular polymer melt conformations far away from their equilibrium condition. Thus, whatever is measured is the result of the response of not just a portion of the macromolecule, but the contribution of the entire macromolecule. 

Let us next consider the simple isothermal drag flow (dP/dz = 0) of a shear-thinning fluid in the screw channel. The cross-channel flow, induced by the cross-channel component of the barrel surface velocity, affects the down-channel velocity profile and vice versa. In other words, the two velocity profiles become coupled. This is evident by looking at the components of the equation of motion. Making the common simplifying assumptions, the equation of motion in this case reduces to... 

Next, we explore some nonisothermal effects on of a shear-thinning temperature-dependent fluid in parallel plate flow and screw channels. The following example explores simple temperature dependent drag flow. 

Example 9.3 Nonisothermal Drag Flow of a Power Law Model Fluid Insight into the effect of nonisothermal conditions, on the velocity profile and drag flow rate, can he obtained by analyzing a relatively simple case of parallel-plate nonisothermal drag flow with the two plates at different temperatures. The nonisothermicity originates from viscous dissipation and nonuniform plate temperatures. In this example we focus on the latter. 

Estimation of Entrance Pressure-Pressure Losses from the Entrance Flow Field17 Consider the entrance flow pattern observed with polymer melts and solutions in Fig. 12.16(a). The flow can be modeled, for small values of a, as follows for 0 < a/2 the fluid is flowing in simple extensional flow and for a/2 < 0 < rc/2 the flow is that between two coaxial cylinders of which the inner is moving with axial velocity V. The flow in the outer region is a combined drag-pressure flow and, since it is circulatory, the net flow rate is equal to 0. The velocity V can be calculated at any upstream location knowing a and the capillary flow rate. Use this model for the entrance flow field to get an estimate for the entrance pressure drop. 

Since homogenous melts are covered in a later account of pressure build-up and power input in the extruder (Chapter 7), this chapter confines itself to the flow behavior of homogenous unfilled polymer melts and on the introduction of the most important rheological parameters such as viscosity, shear thinning, elasticity, and extensional viscosity. The influence of these rheological properties on simple pressure- and drag flows is demonstrated, while the influence of rheological parameters on pressure build-up and power input in the extruder is described in more detail in Chapter 7. 

Extensional flow takes place when the liquid is squeezed into a small opening (see Figure 15.6b). It occurs when the liquid enters (or exits) a chaimel or is pushed through a small hole (e.g., with high-pressure homogenization). In most praetieal cases, the flow pattern is a mixture of simple shear flow and extensional flow. A droplet in extensional flow will also experience a drag force exerted by the flow only now the external force exerted on the droplet is not equal to r ddvldz) but equal to t c dvldy), where y is the coordinate in the direction of the extension. We ean use the same relations as with simple shear flow, only in this ease the value of We, is different. So, also here. 

Flow of this type in simple shear is known as drag flow. ... 

Even though polypropylene composites exhibit non-Newtonian flow behavior with shear dependent melt viscosity, fundamental concepts of flow mechanisms can be visualized more easily in the limit of Newtonian flow characteristics. Consequently, both White (21) and Todd (26) have made an analogy between drag flow in a given kneading block of elements with the flow characteristics of a conventional single-screw extruder with the following simple expression ... 

The flow in Fig. 3 is called a drag flow, the top plate is dragging the material across the stationary plate to create the velocity profile that is shearing the fluid. In contrast, flow in a capillary rheometer is pressure-driven flow. All of the wall area inside the capillary is stationary so that the material has zero velocity at the walls and a maximum velocity along the centerline. Calculating the shear rate in a capillary is not as straightforward as with steady simple shear. Each fluid element still sees steady simple shear, but the shear rate is no longer constant it varies across the radius of the die. It runs... 

An elongated drop does not necessarily break. In simple shear flows, differences in surface drag establish an internal rotation or circulation within the drop that helps stabilize it. This circulation does not develop for the case of bulgy deformation. 

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