Flow Instability in Tubular Film Blowing. 1. Experimental Study Chang Dae Han* and R. Shetty Department of Chemical Engineering, Polytechnic institute of New York, Brooklyn, New York 1120 1
An experimental study was carried out to investigate the effect of processing variables on unstable flow behavior in tubular film blowing. For the study, a laboratory blown film apparatus was constructed, and low- and highdensity polyethylenes were used in producing tubular films. After the process had been stabilized, disturbances in either the take-up speed or air pressure inside the bubble were introduced, and motion pictures of the disturbed bubble were taken. In order to investigate the effect of the rheological properties of the polymer melt on flow instability, melt temperature was varied. The present study indicates that a disturbance in the take-up speed influences bubble stability much more than a disturbance in air pressure inside the bubble does, and that a decrease in melt temperature tends to stabilize the bubble after it has been disturbed. A rheological interpretation of the experimental results is presented to explain flow instability in tubular film blowing.
Introduction In recent years, the tubular film blowing process has attracted great interest in the plastics industry for the production of thermoplastic films. As schematically shown in Figure 1, in tubular film blowing a molten polymer is first extruded upward through an annular die, and the extruded tubing is inflated to form a bubble by air introduced a t the bottom of the die. An air cooling ring is often used to rapidly solidify the molten tubular film a t some distance above the die exit. The nip rolls, driven by a variable-speed motor, provide the axial tension needed to pull the film upward, and they form an air-tight seal so that a constant pressure, slightly above atmospheric, is maintained in the inflated bubble. Figure 2 gives photographs of some representative tubular blown films of low- and high-density polyethylenes. The tubular film blowing process has the advantage over the flat film process in that the former produces biaxially oriented film, whereas the latter produces uniaxially oriented film. Biaxially oriented film has better mechanical/physical properties (e.g., tensile strength, tear resistance, heat seal characteristics) than uniaxially oriented film has. The biaxial orientation is realized by stretching the tubular film in both the transverse and axial (machine) directions, the former by inflating the bubble and the latter by use of a take-up device. As may be surmised, a theoretical treatment of the tubular film blowing process is far more complex than that of the flat film process. Pearson and Petrie (1970a,b,c)are the first to have studied the tubular film blowing process from the point of view of fluid mechanics, but they restricted their attention to isothermal operation of the process with Newtonian fluids. More recently, Petrie (1975) has considered nonisothermal operation with Newtonian fluids, and Han and Park (1975b) have considered the nonisothermal film blowing process with a rheological model of the power-law type, which describes the dependence of rheological properties on both the temperature and the rate of strain in biaxial stretching. Still others (Ast, 1973;Farber and Dealy, 1974; Menges and Predohl, 1975) have studied the heat transfer problems involved in the tubular film blowing process. In his recent monograph, Han (1976) discusses various aspects of the tubular film-blowing process from both the practical and fundamental points of view, including an extensive survey of literature. From the rheological point of view, tubular film blowing is an interesting process in that it gives rise to a biaxial elongational flow. As a matter of fact, Han and Park (1975a) have suggested the use of the tubular film blowing process in de-
termining elongational viscosities, and have presented some experimental results. Stevenson and Chung (1975) have suggested use of the tubular film blowing process in determining the material constants of rheological equations of state. In production of tubular films, the film producers are often confronted with the difficulty of maintaining a constant (i.e., uniform) bubble diameter. Maintaining a uniform bubble diameter is of paramount importance, because a nonuniform bubble diameter gives rise to a nonuniform film thickness and hence nonuniform mechanical/physical properties. Therefore, a better understanding of the cause (or causes) of nonuniform bubble diameter, hereafter referred to as “flow instability” (or “bubble instability”), is of fundamental importance in controlling the tubular film blowing process. As a matter of fact, a theoretical attempt has been made by Yeow (1972),who has performed a linear hydrodynamic stability analysis of the phenomenon of bubble instability in isothermal operation with a Newtonian fluid. However, in practice, tubular film blowing always requires a cooling step, and the polymers in use (e.g., low-density polyethylene, ethylene-vinyl acetate) exhibit non-Newtonian, viscoelastic flow behavior under typical processing conditions. On the other hand, there is little experimental data available in the literature (Han and Park, 1 9 7 5 ~that ) can be used as a guide to developing a theory for describing the phenomenon of bubble instability in terms of the rheological properties of the melt and processing variables. As our continuing effort on studying the unstable nature of the tubular film blowing process, we have recently performed a further experimental study of bubble instability. The purpose of this paper is to present some new experimental results, with the hope that they will be useful to future theoretical study. At present, a theoretical study is being carried out to predict the critical conditions of bubble instability in terms of the rheological properties (both viscosity and elasticity) of the fluid concerned and processing variables. In future publications, we shall report the results of the theoretical study. Experimental Section The apparatus consisted of a 1-in. single screw extruder, a die, nip rolls (driven by a variable-speed motor and located a t about 6 ft above the die exit), a take-up device, and temperature controllers. Figure 3 shows a photograph of the apparatus. The compressed air for inflating the tubular film was introduced a t the bottom of the die. Figure 4 gives a schematic of the die design. The die is baInd. Eng. Chern., Fundarn., Vol. 16, No. 1, 1977
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Figure 1. Schematic of the tubular film-hlowingprocess.
Figure 3. Photograph of the experimental apparatus.
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Figure 2. Typical bubbleshapes (Ha", 1976): (a) high-density polyethylene at extrusion conditions: T = 200 "C, Q = 9.13 celmin, Va = 0.375 cmls, V,./V0 = 36.5, M = 3.57 X 10V psi; (b) low-density polyethylene at extrusion conditions: T = 200 OC, Q = 25.11 cdmin, Vi] = 0.347 cm/s, VLIVO= 17.9, AP = 3.57 X lO-:'psi.
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sically an annulus, the inner diameter being 2.002 in. and the outer diameter being 2.062 in. In order to ensure uniform flow within the annular space, the molten polymer from the extruder is split into two streams which are fed to the die through two feed-ports located diametrically opposite each other (see Figure 4a). Also, shallow grooves (about %in. deep) were provided at the converging section of the die (see Figure 4b) so that they might function as areservoir section, similar to that of a capillary die. In other words, the grooves were provided to help the molten polymer spread as uniformly as possible through the annular space. The die and feed lines were electrically heated, and the temperature was controlled by thermistor-regulated controllers. The mass flow rate of the melt was determined by collectingthe extrudate for a predetermined time interval, and the pressure in the blown bubble was measured using a water manometer. The materials used were low- and high-density polyethylenes, The rheological properties of these materials a t different melt temperatures are given in Figure 5 for low-density polyethylene (Union Carbide, DYNF l), and in Figure 6 for high-density polyethylene (Union Carbide, DMDJ 4306). These rheological measurements were made on a capillary 50
Ind. Eng. Chem, Fundam.. VoI. 16. No. 1,1977
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Figure 4. Schematic of the design of the blown film die. rheometer (Han e t al., 1971). Readers who are not familiar with the experimental technique may consult the recent monograph by Han (1976). In the bubble instability experiment, the tubular film traveling upward was cooled by blowing air with a fan from a distance of about 10 ft from the die. In this way, the motion of the traveling tubular film was minimally disturbed by the cooling device. In the present study, a t one time a step change in take-up speed was introduced, and a t other times a step change in air pressure inside the bubble was introduced into the steady tubular film. Upon introducing a disturbance, motion pictures were taken of the traveling tubular film. The experiment was repeated, varying the magnitude of the disturbance and the extrusion temperature. The extrusion temperatures used were 160,180,and 200 "C for low-density polyethylene, and 200, 220, and 240 "C for high-density polyethylene. In order to obtain quantitative information of the motion of the tubular film, the movie films were projected on a screen
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100
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300
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Figure 5. Rheological properties of the low-density polyethylene used. 60
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Figure 8. Pictures of the bubble shape of high-densitypolyethylene (T = 240 "C)for a step change ~ntakeup speed from 1.53 cmls to 5.08 cmls: (a) before disturbance; (b) after 2.0 s; (c) after 5.0 s; (d)after 12.0
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Figure 6. Rheological properties of the high-density polyethylene used.
Figure 7. Pictures of the bubble shape of low-density polyethylene ( T = 200 "C) for a step change in takeup speed from 1.53cmls to 5.68 cmls: (a) before disturbance; (b) after 6.0 s; (c) after 15.0 s; (d) after 20.0 s.
and the tube (Le., huhhle) diameter was read off from the projected images of the motion pictures taken, at several different positions along the axis of the tubular film traveling upward. This was done by stopping the projector at a predetermined interval of projection time. With the relation between the projection time and real time known, it was possible to determine the time-dependent behavior of the hubhle while the phenomenon of bubble instability was observed
Results and Discussion Influence of Processing Variables on Bubble Instability. Figure 7 shows photographs taken of a bubble of low-
Figure 9. Pictures of the bubble shape of low-density polyethylene (?' = 200 "C) for a step change in air pressure inside the bubble from 0.2 in. of H20 to 0.3 in. of H20: (a) before disturbance; (b) after 4.0 s; (c) after 8.0 s; (d) after 14.0 s. density pulyerhylene ILDPEJ at 200 "C airer it was distiirlwd Iiynrhnngein rake-up
