Application of variational principles in modeling of the film blowing process for high stalk bubbles

Investigation of convective heat transfer in 9-layer film blowing process by using variational principles

“…This model was chosen in this work because it provides analytical expression for the bubble shape, utilizes small number of physical parameters, is able to describe experimental film blowing data for variety of polymers and processing conditions and was successfully used in the film blowing stability analyses [2,[44][45][46][47]. Note that even if the principle of stationary potential energy approach, widely used in the mechanics of deformable solids, can Table 1 Parameters A and / for different bubble shapes (y) (adapted from [43]).…”

“…The melt stretching in the transverse direction is predominantly controlled by the blow-up ratio, BUR, defined as a ratio of the final bubble diameter at the freezeline height to the die diameter, which usually varies from 1 to 5. In order to control the melt stretching in the axial machine direction, the take-up ratio, TUR, is usually kept between 5 and 40 and it is expressed as a ratio between the film velocity above the freezeline height and melt velocity at the die exit [1][2][3][4]. In order to reach stable film blowing process conditions and required final film properties, it is necessary to properly adjust bubble cooling (i.e.…”

“…In order to reach stable film blowing process conditions and required final film properties, it is necessary to properly adjust bubble cooling (i.e. heat transfer coefficient between the blown film and cooling air) [1,2,4]. Probably the first study considering heat transfer in film blowing process was presented in 1975 by Petrie [5] using non-isothermal film blowing model and Menges and Predohl [6] utilizing simple one parametric heat transfer coefficient model.…”

Modeling of Non-Isothermal Film Blowing Process for Polyolefines by Using Variational Principles

“…After the bubble deformation the element length is given by the following equation [28,31]: (14) It has been shown in [28] that if the constant bubble compliance is assumed along the bubble, one can derive the analytical equation for the bubble shape satisfying the minimum-energy requirements by using variational principles. This model can be applied for description of different bubble types including high stalk bubbles [30]. In this work, bubble without neck will be considered only.…”

Investigation of heat transfer in 9-layer film blowing process by using variational principles

“…The melt stretching in the transverse direction is predominantly controlled by the blow-up ratio, BUR, defined as a ratio of the final bubble diameter at the freezeline height to the die diameter, which usually varies from 1 to 5. In order to control the melt stretching in the axial machine direction, the take-up ratio, TUR, is usually kept between 5 and 40 and it is expressed as a ratio between the film velocity above the freezeline height and melt velocity at the die exit [1][2][3][4].…”