Proving of bread dough: Modelling the growth of individual bubbles

Proving of bread dough was modelled using classical one-component diffusion theory, to describe the rate of growth of bubbles surrounded by liquid dough containing dissolved carbon dioxide. The resulting differential equation was integrated numerically to predict the effect of initial bubble size and system parameters (carbon dioxide concentration, surface tension at the bubble interface, temperature) on bubble growth. Two situations exist, potentially; the dough could be either supersaturated or subsaturated with carbon dioxide. When the dough is supersaturated, the model predicts a critical bubble size above which bubbles grow indefinitely, while below the critical bubble size bubbles reach a limiting size and stop growing. The critical bubble size decreases with increasing carbon dioxide concentration and increases with increasing surface tension. Below saturation, all bubbles reach an upper size limit proportional to their initial size. The final bubble size increases with carbon dioxide concentration and decreases with increasing surface tension. Higher temperatures increase the rate of bubble growth and reduce the critical bubble size for supersaturated doughs, by increasing the value of Henry's Law constant. Higher temperatures also increase the final bubble size for subsaturated systems. The model could be extended to include yeast kinetics and entire bubble size distributions, to develop a full simulation of the proving operation.