Bubble growth model and its influencing factors in a polymer melt under nonisothermal conditions

Prediction of the Bubble Growth Behavior by Means of the Time-, Temperature-, Pressure- and Blowing Agent Concentration-Dependent Transient Elongational Viscosity Function of Polymers

Bubble growth processes are highly complex processes, which are not only dependent on the foaming process parameters (temperature, pressure and blowing agent concentration) but also on the type and structure of the polymer used. Since the elongational viscosity at the bubble wall during bubble growth also depends on these influencing factors, the so-called transient elongational viscosity plays a key role in describing the gas bubble growth behavior in polymer melts. The model-based description of the transient elongational viscosity function is difficult due to its dependence on time, Hencky strain and strain rate. Therefore, representative viscosities or shear viscosity models are usually used in the literature to predict the bubble growth behavior. In this work, the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth is described holistically for the first time. This is achieved by extending the so-called molecular stress function (MSF) model by superposition principles (temperature, pressure and blowing agent concentration) and by using the elongational deformation behavior (Hencky strain and strain rate) at the bubble wall during the initial, and thus viscosity-driven, bubble growth process. Therefore, transient uniaxial elongational viscosity measurements are performed and the non-linear MSF model parameters of the two investigated polymers PS (linear polymer chains) and PLA (long-chain branched polymer chains) are determined. By applying the superposition principles and by changing the strain mode parameter to the equibiaxial case in the MSF model, the transient equibiaxial viscosity master curve is obtained and used to describe the bubble growth process. The results show that the extended MSF model can fully predict the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth processes. The bubble growth behavior over time can then be realistically described using the defined transient equibiaxial elongational viscosity function at the bubble wall. This is not possible, for example, with a representative viscosity and therefore clearly demonstrates the influence and importance of knowing the transient deformation behavior that prevails at the bubble wall during bubble growth processes.

A Novel In-Line Measurement and Analysis Method of Bubble Growth-Dependent Strain and Deformation Rates during Foaming

Bubble growth processes are highly influenced by the elongational viscosity of the blowing agent-loaded polymer melt. Therefore, the elongational viscosity is an important parameter for the development of new polymers for foaming applications, as well as for the prediction of bubble growth processes. Thus, knowledge of the initial expansion and deformation behavior in dependency on the polymer, the blowing agent concentration, and the process conditions is necessary. This study presents a novel method for the in-line observation and analysis of the initial expansion and deformation behavior within the bead foam extrusion process. For this purpose, nitrogen as the blowing agent was injected into the polymer melt (PS and PLA) during the extrusion process. The in-line observation system consists of a borescope equipped with a camera, which was integrated into the water box of an underwater pelletizer. The camera is controlled by a developed trigger by means of angular step signal analysis of a rotary encoder on the cutter shaft of the underwater pelletizer. Thus, images can be taken at any time during the foaming process depending on the cutter position to the die outlet. It is shown that the developed method provides reliable results and that the differences of the initial expansion and deformation behavior during bubble growth can be analyzed in-line in dependency on real foaming process conditions and the type of polymer used.