A mathematical model for the isothermal growth of bubbles in wheat dough

The objective of this research is to develop a set of mathematical relations that can describe the dynamics of a bubble inside an expanding viscoelastic fluid mass. The specific case of isothermal growth of a CO2 bubble in bread dough as the dough exits an extruder with a circular die and expands, is modeled. Inertia, mass transfer to the bubble, mass transfer to the atmosphere, viscoelasticity and surface tension were considered. The Cell Model proposed by Amon and Denson [Amon, M. & Denson, C. (1984). A study of the dynamics of foam growth: Analysis of the growth of closely spaced spherical bubbles. Polymer Engineering and Science, 24(13), 1026–1034] to consider the growth of a bubble in close proximity to other bubbles was modified and applied. The mathematical relations developed were solved by a commercial solver and the result compared to the model and experimental results of Alavi et al. [Alavi, S. H., Rizvi, S. S. H., & Harriot, P. (2003). Process dynamics of starch based microcellular foams produced by supercritical fluid extrusion. I: Model development and II: Numerical simulation and experimental evaluation. Food Research International, 36, 309–330]. During the solution process, a characteristic time was defined in terms of system parameters. It was found that the model developed in this research fit the available data better while considering more phenomena in the analysis.