direct‎ ‎mathematical‎ ‎models‎ ‎for‎ ‎estimating‎ ‎the‎ ‎shelf‎ life of second‎- ‎and zero-order degradation relationships of food and drugs

‎recently‎, ‎a direct model for evaluating the shelf life of lemon juice‎, ‎depending on the loss of ascorbic acid concentration with time was derived by al-zubaidy and khalil (food chem‎. ‎101 (2017) 254–259)‎. ‎by using this model‎, ‎one could directly estimate the expiration date at any residual ratio and any specific temperature of the first-order degradation rate‎. ‎but‎, ‎in general‎, ‎the kinetic model for degradation process is not limited to first-order reactions‎, ‎as it could be second-‎, ‎or zero-order according to the experimental data‎. ‎therefore‎, ‎two direct models have been developed to evaluate shelf life based on these orders‎. ‎these models have been verified using previously published results for vitamins c (zero-order) and d3 (2nd-order) in coconut powder‎. ‎the results indicate that the prediction of shelf life for food‎, ‎drugs and so on can also be evaluated directly for second-‎, ‎and zero-order degradation processes using the developed models in the same way to that of pre-published for first order‎. ‎a characteristic feature of the presented degradation orders is that the input data for determining the rate constant must be in percentage (%) rather than the real concentration in contrast to that of first order‎. ‎it was concluded that the use of the derived equations avoids the complications resulting from changing the unit of the rate constant with the change in the reaction order‎. ‎in addition to the gained simplicity when dealing with the developed models‎.