Freeze-line

In the tubular process a thin tube is extruded (usually in a vertically upward direction) and by blowing air through the die head the tube is inflated into a thin bubble. This is cooled, flattened out and wound up. The ratio of bubble diameter to die diameter is known as the blow-up ratio, the ratio of the haul-off rate to the natural extrusion rate is referred to as the draw-down ratio and the distance between the die and the frost line (when the extrudate becomes solidified and which can often be seen by the appearance of haziness), the freeze-line distance. 

Figure 10.14. Effect of freeze-line distance and other operating variables on the haze of low-density polyethylene film. (Reproduced by permission of ICI)...

Figure 14.19 (Solid + liquid) and (liquid + liquid) phase diagram for (xic-C6H 12 + X2CH3OH) at (a) p = 0.1 MPa and (b) as a function of pressure. In (a), the freezing curve extending to the eutectic is estimated and is represented by a dashed line to reflect this uncertainty. In (b), the freezing line at p = 229 MPa is estimated and is represented by a dashed line. The dash-dot line in (b) is the envelope enclosing the region with two liquid phases.

Film blowing. In film blowing, a tubular cross-section is extruded through an annular die, normally a spiral die, and is drawn and inflated until the freezing line is reached. Beyond this point, the stretching is practically negligible. The process is schematically depicted in Fig. 3.55 [14],... 

The bubble will grow to a maximum —or final— radius, Rf, when it freezes at a position z = Z, which is called the freeze-line. Since the bubble is pulled by a force Fz, which is usually referred to as the draw force, we can perform a force balance between a position z and Z to give,... 

Film blowing. A tubular 50 pm thick low density polyethylene film is blown with a draw ratio of 5 at a flow rate of 50 g/s. The annular die has a diameter of 15 mm and a die gap of 1 mm. Calculate the required pressure inside the bubble and draw force to pull the bubble. Assume a Newtonian viscosity of 800 Pa-s, a density of 920 kg/m3 and a freeze line at 300 mm. 

Figure 6.25 Schematic diagram of the thermoforming process of a conical geometry. Next, we can compute the dimensionless freeze line using,...

Following the principles of the Petrie model, and recalling that the film thickness <5 is much smaller than the radius S/R thin-film approximation, which implies that field equations are averaged over the thickness and that there are no shear stresses and moments in the film. The film is regarded, in fact, as a thin shell in tension, which is supported by the longitudinal force Fz in the bubble and by the pressure difference between the inner and outer surfaces, AP. We further assume steady state, a clearly defined sharp freeze line above which no more deformation takes place and an axisymmetric bubble. Bubble properties can therefore be expressed in terms of a single independent spatial variable, the (upward) axial position from the die exit,2 z. The object... 

Bubble instability is one of the complications of this process. Only recently did this matter receive theoretical attention. As pointed out by Jung and Hyun (28), there are three characteristic bubble instabilities axisymmetric draw resonance, helical instability, and metastability where the bubble alternates between steady states, and the freeze line moves from one position to another. Using linear stability analysis, Cain and Denn (62) showed that multiple steady state solutions are possible for the same set of conditions, as pointed out earlier. However, in order to study the dynamic or time-dependent changes of the process, transient solutions are needed. This was recently achieved by Hyun et al. (65), who succeeded in quite accurately simulating the experimentally observed draw resonance (28). 

POSTER TITLE Fundamental studies of freeze lining behaviour... 

One of the newer technologies to protect pyrometallurgical furnaces from corrosive slags is freeze lining. The present research focuses on the determination of the effect of several slag and process parameters on the... 

Does the change involve the use of one-time maintenance items such as chemical cleaning, hot tapping, jumpovers, freezing lines to temporarily plug, or the temporary repair of hazardous chemical leaks ... 

Figure 7.4 Phase diagram for adhesive hard spheres as a function of Baxter temperature rg. The solid line is the spinodal line for liquid-liquid phase separation (the dense liquid phase is probably metastable), the dot-dashed line is the freezing line for appearance of an ordered packing of spheres, and the dashed line is the percolation transition. (Adapted from Grant and Russel 1993, reprinted with permission from the American Physical Society.)...

See also Kuijk et al [46], who showed that the stress at the freeze line is the key morphological parameter in determining the mechanical properties of blown polyethylene films. 

Nonisothermal Maxwell model extended past the freeze line with the Hookean elastic behavior... 

From numerical solution of the set of equations that represent both processes, it is possible to predict the ribbon and film dimensions and temperature profiles from the die to the freeze line. Figure 24.3 shows two-dimensional simulations of a PA6/LDPE blown film (extruded at 250 °C and DR = 20) and a PS/FIDPE ribbon (extruded at... 

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