Film blowing process is a flexible mass production technology used for manufacturing thin polymeric films. Its flexibility in using an existing die to produce films of different width and thickness, just by controlling process conditions such as, extrudate velocity, excess pressure, and line speed, makes it an attractive process with less capital investment. Controlling the process conditions to obtain a stable bubble, however, is not a trivial task. It is a costly trial and error procedure, which could result is a large wastage of material and other resources. Hence, it is necessary to develop methods to simulate the process and design it using numerical experiments. This important need of the industry defines the objective of this work. In this dissertation, a transient, axisymmetric, nonisothermal, viscoelastic model is developed to simulate the process, and it is solved using finite element method. Material behavior of polymer melt is described using a modified Phan-Thien-Tanner model in the liquid??like region, and anisotropic Kelvin??Voight model in the solid zone, and the transition is modeled using a simple mixture theory. Crystallization kinetics is described using a modified Avrami model with factors to account for the influence of temperature and strain. Results obtained are compared with available experimental results and the model is used to explore stability issues and the role of different parameters. Software developed using this model comes with a GUI based pre- and post-processor, and it can be easily adapted to use other constitutive models.

Film blowing is a highly complex industrial process used to manufacture thin plastic films for uses in a wide range of applications; for example, plastic bags. The mathematical modelling of this process involves the analysis of highly nonlinear differential equations describing the complex phenomena arising in the film blowing process, and requires a sophisticated mathematical approach. This dissertation applies an innovative combination of tools, namely analytic, numerical and heuristic mathematical techniques to the analysis of the film blowing process. The research undertaken examines, in particular, a two-point boundary value problem arising from the modelling of the radial profile of the polymer film. For even the simplest modelling of this process, namely the isothermal Newtonian model, the resulting differential equation is a highly nonlinear, second order one, with an extra degree of difficulty due to the presence of a small parameter multiplying the highest derivative. Thus, the problem falls into the category of a nonlinear singular perturbation problem. Analytic techniques are applied to the isothermal Newtonian blown film model to obtain a closed form explicit approximation to the film bubble radius. This is then used as a base approximation for an iterative numerical scheme to obtain an improved numerical solution of the problem. The process is extended to include temperature variations, varying viscosity (Power law model) and viscoelastic effects (Maxwell model). As before, closed form approximations are constructed for these models which are used to launch numerical schemes, whose solutions display good accuracy. The results compare well with results obtained by purely numerical solutions in the literature.

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This paper presents experimental data and a mathematical model for the radiant heat transfer operation used in the production of biaxially oriented polypropylene (BOPP) films by the Double Bubble process. The data was obtained from an industrial pilot plant fully instrumented for the purpose of the study. In the mathematical model the effect of the view factor is considered, along with the effects of natural and forced convection on the heat transfer coefficients. Experiments were also conducted in a laboratory radiant heater to determine the range of heat transfer coefficients experienced under different heating conditions, and analytical methods to determine these are discussed.

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Το αντικείμενο της παρούσας εργασίας είναι η μαθηματική μοντελοποίηση της εφαπτομενικής ροής του ψυχρού αέρα, ο οποίος παρέχεται εξωτερικά της διεργασίας εκβολής πολυμερούς με εμφύσηση (film blowing) και η αριθμητική επίλυση των εξισώσεων που προκύπτουν. Η διεργασία εκβολής πολυμερών με εμφύσηση είναι η βασική μέθοδος παραγωγής φύλλων πλαστικού μεγάλης επιφάνειας τα οποία χρησιμοποιούνται κυρίως ως υλικά συσκευασίας και σε θερμοκήπια. Στην παρούσα εργασία αναπτύχθηκε μεθοδολογία η οποία επιτρέπει την μοντελοποίηση της ροής και της μεταφοράς θερμότητας του αέρα καθώς και του πολυμερούς και μας δίνει τη δυνατότητα να μελετήσουμε την επίδραση που έχει τόσο η ροή όσο και η ψύξη που προκαλεί ο αέρας στο φιλμ που σχηματίζει το πολυμερές. Αρχικά οι διέπουσες εξισώσεις του αέρα και του πολυμερούς απλοποιήθηκαν με την βοήθεια της θεωρίας των διαταραχών. Η μαθηματική ανάλυση και οι παραδοχές που έγιναν είχαν ως αποτέλεσμα i) η ροή και η παραμόρφωση του πολυμερούς να περιγράφεται από τις εξισώσεις του “λεπτού φιλμ” και ii) η ροή του αέρα να προσομοιάζεται με συνοριακό στρώμα, του οποίου η λύση προκύπτει με την μέθοδο ομοιότητας. Η επίδραση της θερμοκρασίας του αέρα στο πολυμερές μελετήθηκε θεωρώντας την αρχικά σταθερή, ενώ στην περίπτωση που και ο αέρας θεωρείται ότι θερμαίνεται από το πολυμερές, η κατανομή της θερμοκρασίας του προσεγγίζεται με ένα πολυώνυμο 4ου βαθμού στην ακτινική διεύθυνση. Τα αποτελέσματα που προκύπτουν εξαιτίας της ψύξης του φιλμ δείχνουν ότι οι παραμορφώσεις και οι μεταβολές του πάχους μειώνονται επιτρέποντας στο φιλμ που σχηματίζει το πολυμερές να αποκτά σωληνοειδή μορφή. Η λύση της εφαπτομενικής ροής του αέρα κατά μήκος του φιλμ έδειξε ότι στο φιλμ ασκούνται τάσεις οι οποίες μετατοπίζουν το φιλμ προς τον άξονα συμμετρίας και έτσι λαμβάνονται πιο ομοιόμορφα σχήματα σε σχέση με τα σχήματα που λαμβάνονται χωρίς την επίδραση του αέρα. Η επίδραση της ροής του αέρα φαίνεται να συμβαίνει στο χαμηλότερο τμήμα του φιλμ και κυρίως μέχρι ύψους . Τέλος, η σύγκριση μεταξύ του θεωρητικού μοντέλου που αναπτύχθηκε με πειραματικά αποτελέσματα δείχνει ότι υπάρχει, τουλάχιστον ποιοτικά, συμφωνία. / The object of present work is the mathematical modelling of tangential flow of cold air, which is provided externally to the polymer film produced in the well-known industrial process for manufacturing biaxial stretched films, Film Blowing Process, and the numerical solution of equations as well. In the present work was developed methodology which describes the flow and heat transfer of air as well as polymer. This analysis gives us the possibility of studying the effect of the flow as well as refrigeration that causes the air in the film of the polymer. Initially the governing equations of air and polymer were simplified with the help of theory of perturbations. The mathematic analysis and the assumptions that became had as result i) the flow and deformation of polymer described with the equations of "thin film" and ii) the flow of air simulated as a boundary layer, which its solution obtained by method of similarity. The effect of temperature of air in polymer was studied considering initially constant, while in the case where also the air is considered that is heated from polymer, the temperature distribution is approached with a polynomial of 4th degree in the radial direction. The results that arise because of refrigeration of film show that the deformations and the changes of thickness are decreased allowing in the film makes solenoids shape. The solution of tangential flow of air along the film showed that stresses in the film shift the film to the axis of symmetry and thus are received more uniform shapes in regard the shapes which are received without the air effect. The air flow effect appears to happen in the lower part of film and mainly until height . Finally, the comparison between the theoretical model that was developed with experimental results shows that exists qualitatively agreement.