Influence of whip speed ratios on the inclusion of air into a bakery foam produced with a planetary mixer device
Résumé
In the present study, dimensional analysis has been developed in order to identify the ratios governing the foam development network, with mixers combining dual whip revolution speeds. It is first suggested that, for a given planetary whip mixer and foaming solution, the set of dimensionless ratios characterizing the course of gas hold-up can be reduced to modified Froude and revolution numbers, as in the case of a classical mixing system. This requires the introduction of a characteristic velocity, instead of the two individual rotational speeds of the whip, in the corresponding list of governing parameters. An analytical expression for this characteristic velocity is then proposed, and gas hold-up measurements are made at various whip speed ratios, using a given food model-recipe, containing whole eggs and sugar. Our experimental results were evaluated, in order to validate the proposed dimensional analysis. It is shown that the aeration process requires a very low, modified revolution number to reach steady state values. It is also shown that the asymptotic values of gas hold-up are influenced by the modified Froude number. Depending on the values of the modified Froude number, it is noted that coalescence can occur, which then contributes to a reduction in gas hold-up. It has also been established that the modified Froude number can account for the eccentricity of planetary mixers, and consequently, that this number is a robust indicator for the determination of the optimum gas hold-up value, when air incorporation is produced by various planetary whipping devices. The results described in this paper enable foaming processes using planetary whipping mixers to be optimized, by proposing a framework in which the impeller speed ratio and aeration time can be set in such a way as to control the simultaneous entrainment and disentrainment of gas. Finally, this work can be further extended to other gas/liquid applications in which planetary mixers are used, such as surface aeration in wastewater treatment plants.