Complex phenomena occur during production of sorbet in a scraped surface heat exchanger: fluid flow, heat transfer, phase change (ice crystallization), rheological modification and fragmentation of bubbles. In a previous work, all these coupled phenomena except bubble fragmentation were simulated by CFD. The objective of the present work is to predict the bubble break-up. Locally, the critical radius for bubble break-up can be estimated as a function of the shear rate, the extension rate, the apparent viscosity of the 'continuous' phase, the viscosity of the gas and the surface tension, by using correlations based on the capillary number. The 'continuous' phase surrounding the bubbles is in fact constituted by a concentrated liquid and ice crystals; its non-Newtonian rheology sharply depends on ice-fraction, which in turn depends on temperature. The CFD simulation allowed analyzing all the parameters influencing the critical radius. It appears that the smallest bubbles are generated a) near the contact between the blades and the scraped surface where the highest shear rate is reached, and b) in the coldest region (near to the outlet) where the continuous phase has the maximum apparent viscosity. The order of magnitude of the smallest crystals predicted by CFD corresponds to the observed values.