The purpose of this study is to represent a generic model of digestion in the small intestine. In the first part of this work, a model based on ordinary differential equations is used to represent the digestion : the equations describe the evolution of the position and composition of the bolus coming from the stomach. Each bolus is identified as a cylinder. This model considers simultaneously the different aspects of digestion i.e. transport of the bolus all along the small intestine, feedstuffs degradation according to the enzymes and local physical conditions, and nutrients absorption. In the second part of this study, we use the homogenization method to sustain the simplified digestion model developed in the first part. We show that this model can be considered as a macroscopic version of more realistic models which contain the biological phenomena at lower scales of the small intestine : (i) the high frequency peristaltic pulses (microcopic time scale) and their effects on the velocity of bolus, (ii) the presence of the intestinal villi (microscopic scale of space) and their influence on the digestion. Finally, in the third part of this study, we investigate the digestion of a non-homogeneous feedstuffs matrix by integrating the dietary fibre in the bolus. The two main physiochemical characteristics of dietary fibre which interact with the function of the small intestine, i.e. viscosity and water holding capacity are modelled. This leads us to consider some features of the digestion which have not been taken into account previously, particularly the interrelationship between the evolution of dry matter and water in the bolus. Although this model is generic and contains a large number of parameters, to our knowledge, it is among the first qualitative dynamical modelling of fibre influence on intestinal digestion.
