Mathematical models have been extensively used in veterinary science to analyse data collected from experiments measuring the flow of digesta through the gastrointestinal tract (GIT) of ruminants. In this paper a classic two compartment digesta flow model is reformulated into a two compartment CSTR (continuous stir tank reactor) model. A segregated reactor model is then obtained by incorporating 'non-mixing' stagnant regions into the ideal CSTR model. The ability to incorporate non-ideal mixing into the model allows a more accurate representation of the conditions within the GIT. In analyzing this model our main focus is on the cumulative excretion curve, as this is used to estimate the mean residence time through the GIT. The mean residence time is an important indicator of animal nutrition, directly affecting the feeding strategy of an animal. The effects of stagnant regions in a 'two stomach' GIT model are investigated by comparing the cumulative excretion curve with that obtained from an equivalent ideal 'two stomach' GIT model. This comparison characterises a trend that non-ideal mixing delays the excretion of waste from the GIT. The effect upon the cumulative excretion curve of small changes in parameter values is then investigated. Small changes in the size of the first stomach, and the division of the initial digesta ingested between the 'well-mixed' and stagnant regions of the first stomach, are found to substantially effects the cumulative excretion of digesta from the GIT of a ruminant animal. This investigation is a good example of the applications of chemical engineering to a problem outside the traditional definition of the discipline. (C) 2010 Elsevier B.V. All rights reserved.