Melt velocity

The physical process of melt ascent during two-phase flow models is typically based on the separation of melt and solid described by Darcy s Law modified for a buoyancy driving force. The melt velocity depends on the permeability and pressure gradients but the actual microscopic distribution of the melt (on grain boundaries or in veins) is left unspecified. The creation of disequilibria only requires movement of the fluid relative to the solid. 

Where /yand ps are the melt and solid densities, respectively, bulk partition coefficient. Note that if the partition coefficient A is 1, the effective velocity approaches the melt velocity, and also that the difference in effective velocity between elements with different Di decreases at larger porosities. In the following text, the subscripts 0, 1, and 2 are taken to refer to °Th, and Ra, respectively. 

From the results in Figure A2, it is not clear that the analytic solutions using the average porosity and melt velocity do a very good job at approximating the numerical solution. Both the ( Ra/ °Th) and values are significantly different from... 

It is important to note that the Ra- °Th disequilibria do not preclude a partial melting origin for the Pa-excesses. However, they do require that the residence time of Ra in the melting column was short enough, and thus that the melt velocity was fast enough, to prevent Ra from decaying back to values solely attributable to partial... 

The melting velocities of the solid bed interfaces are the foundation of this new approach. The mathematical equality to calculate the rate of loss of the solid at the interface next to the barrel is found in Eq. 6.12. 

The new concepts presented here remove the literature assumption that the solid bed reorganizes, and it allows melting at all solid bed interfaces. The Tadmor model allows melting at only a single interface, that is, as specified by the melting velocity Filni C- The model presented here predicts melting at all four interfaces two in the y direction and two in the x direction. 

The thickness and width of the solid bed as a function of the helical downstream position z are calculated from the melting velocities at the interfaces over a small Az increment. The calculation is progressed down the transition section until the value approaches zero. The balances for the solid in the x and y directions for an increment in the z direction are as follows ... 

Assuming one-dimensional heat transfer is the mode of the solid bed heating due to the heating of the film by conduction and dissipation, the temperature will only change in the y direction. The same assumption that was made by Tadmor and Klein will be made here that the heat transfer model is a semi-infinite slab moving at a velocity Vsy c (melting velocity) with the boundary conditions T(0) = and j(-oo) = 7 , This assumption is not strictly correct because it will also be proposed that the other four surfaces are melting. The major error will occur at the corners of the solid bed. is the velocity of the solid bed surface adjacent to Film C as it moves toward the center of the solid bed in the y direction. 

Fig. 10.53 Mixing-chamber melt velocities at cross sections (B-B ) and (C-C ). (a) Velocity vectors at (B-B ) (b) axial velocity contours at (C-C ) (c) axial velocity contours at (C-C ) all at 500 kg/h. [Reprinted by permission from T. Ishikawa, S. Kihara, K. Funatsu, T. Amaiwa, and K. Yano, Numerical Simulation and Experimental Verification of Nonisothermal Flow in Counterrotating Nonintermeshing Continuous Mixers, Polym. Eng. Sci., 40, 365 (2000).]...

The bare wire is unwound, sometimes by a controlled tension device, and is preheated to a temperature above the Tg or Tm of the polymer to be extruded this is done so that the layer next to the bare wire adheres to it, and to drive moisture or oils off the conductor surface. The wire is fed in the back of the cross-heat die and into a guider tube. Upon exiting the guider, it meets the molten plastic, which covers it circumferentially. Since the wire speed, which is controlled by a capstan at the end of the line, is usually higher than the average melt velocity, a certain amount of drawdown is imposed on the melt anywhere from a value slightly greater than unity to 4. 

Lines can operate with different degrees of automation via computer-integrated PCs providing improvements in operating procedures and quality assurance with the result that rejects are reduced (if not eliminated) and fabricating costs are usually reduced. These closed loop systems maintain long term repeatability of factors such as melt velocity and pressure. All this action occurs independent of what could be occurring with equipment component wear, unbalance of equipment in the line, and/or plastic material variations. 

The melt velocity in these models at any height z in the column is of order... 

The melt velocity estimated from transport models is a bit slower but still comparable to estimates from the dynamic melting models. For example, if we assume that Ra-excesses are produced at the bottom of a column 90 km deep and need to move to the surface in —3 half-lives, then wq —20myr. It should be stressed that this is a constraint on the average melt velocity across the entire melting column rather than a constraint on the maximum velocity near the surface. Moreover, the constraint from Equation (9) assumes that there is only a single porosity near the surface. Two-porosity models (next section) relax this constraint somewhat. 

From our example, we could see that for our lab-scale furnace with only one impurity element, the segregation follows closely to the ideal case. The difference between the ideal case measured in the Czochralski material, where the stirring and resulting transport of solutes from the interface is good, and our casting furnace with relatively low melt velocities (V 1.5-2 mm s 1 Meese et al. [20]) is due to the build up of impurities during the solidification due to low transport of solute from the interface to bulk and due to recirculation... 

A conventional nozzle (Fig. 6.31) with a reverse taper can be used with FEP, PFA, and ETFE. The size of the bore should be as large as possible and it should be tapered in order to prevent stagnation and abrupt changes in the melt velocity. The sprue should extend into the nozzle a sufficient length (13-25 mm) to minimize the likelihood of cold slug formation in... 

Flows can be classified into streamline, when particles in the fluid follow paths (streamlines) that remain constant with time, and turbulent, when vortices cause unpredictable changes in the flow pattern with time. The changeover occurs at a critical value of the Reynolds number, which is defined as the melt velocity, divided by the viscosity times the channel diameter. The high viscosity of thermoplastic melts causes velocities to be low. Hence, the Reynolds number is very low and the flows are streamline. We will consider steady flows, and ignore the start and end of injection and blow-moulding flows, when the melt accelerates and decelerates, respectively. However, in the RIM process (Section 5.6.5), turbulent flow of the low viscosity constituents in the mixing head achieves intimate mixing. 

In the finite element solution, the melt viscosity tj is a function of position, due to its pressure and temperature dependence. Heat transfer as a result of material transport (the melt velocity has components u, v), diffusion in the thickness z direction, and viscous generation, is described by... 

We need to be able to convert data from a melt rheometer into a flow curve, and to use such a curve to estimate pressure drops in simple melt processing equipment. Figure B.l shows four types of flow in channels. These are assumed to be steady laminar flows. The first task is to quantify the shear strain rates. Polymer melts adhere to metal surfaces so the melt velocity is zero at the stationary channel walls. 

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