We have developed a mathematical and asymptotic model to simulate the transport of an intestinal mixture in a deformable cylindrical conduit representing the colon. The radius of the colon varies in both time and space, mimicking peristaltic movements. The mixture consists of mucus, luminal fluid, dietary fibers, and bacteria, whose volume fractions change under the influence of variable viscosity, peristaltic wall motion and physiologically relevant boundary conditions. The governing equations combine incompressible Stokes equations coupled to transport equations for each component, where the effective viscosity depends strongly on the mucus concentration. We consider physiological boundary conditions: secretion of mucus by the wall, absorption of luminal fluid, and confinement of fibers and bacteria... 

 After non-dimensionalization and asymptotic expansion in the small radius versus length regime, we derive a reduced system that captures the first-order behavior of the mixing dynamics. The analysis reveals how wall deformation and mucus-induced viscosity gradients shape the axial and radial flow profiles, directly influencing the efficiency of intestinal content transport. These simulations explore the impact of different wall deformations (e.g., peristaltic patterns) on the spatial distribution and transport efficiency of the mixture. However, in this presentation, we only focus on a preliminary stage of this work in which only the mucus component is considered.  Following on from the talk given at TOP's day at Tour, in this talk we will explore several types of gut geometry, but for each type, we will carry out a comparative analysis between two types of radial disturbance of the gut: one stationary and the other time-dependent. Our aim is to understand how the mobile or immobile nature of intestinal contractions or dilations influences transport mechanisms. In particular, we aim to determine whether a mobile perturbation is more effective at driving mucus flow or modifying its distribution.