A Mathematical Model of Crunchiness/Crispness Loss in Breakfast Cereals1

Published sigmoid relationships between sensory crunchiness/crispness scores of five breakfast cereals and water activity (Sauvageot and Blond 1991) were fitted with the model Y(a w ) = Y o /{1 + exp [a w ‐ a wc )/b]}, where Y(a w ) is the sensory score at a given a w level, Y o the score of the cereal at the dry (glassy) state, a wc a critical water activity representing the inflection point of Y(a w ) and b a constant representing the steepness of Y(a w ) in the a w region where much of the plasticization occurs. In all five cases the fit of the model, which had previously been used with instrumental mechanical parameters of stiffness and crunchiness, was almost perfect (r 2 in the range of 0.997–0.999). All the cereals had similar Y o and a wc values, Y o between 7.5 and 7.9, on a scale of 10, and a wc between 0.62 and 0.68. The range of water activity in which most of the perceived crunchiness/crispness loss took place, however, varied considerably among the five cereals, with the constant b being in the range of 0.046–0.093. Since according to this model about 90% of the perceived crunchiness/crispness loss occurs within a wc ± 3b these numbers correspond to water activity spans between about 0.28 and 0.55, respectively.