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This model characterises the flow behaviour of suspended particles when swallowing through oesophagus. Transport of particle-fluid mixture induced by dilating peristaltic waves on a circular cylindrical tube was considered for investigation. Unsteady closed-form solutions for pressure gradient, velocity and stream function are obtained by applying regular perturbation technique up to the first order of wavenumber (the ratio of the tube radius to the wavelength). It is observed that the axial velocity of the fluid is greater than that of the solid particles almost everywhere. However, at the wall the axial velocity of the fluid is zero due to the no-slip condition imposed on it; but the suspended particulate material has non-zero positive axial velocity. Thus, the axial velocity of the suspended particles near the tube wall is more than that of the fluid velocity. It is further observed that the axial velocity is negative in the regions close to maximum occlusions giving way to instantaneous backward flow. It is also inferred that the maximum axial velocity of the particle-fluid suspension with non-zero wavenumber is more than that of the particle-free fluid with zero wavenumber. We examined the effect of volume fraction of suspended particulate matter on pressure gradient and velocity. An increase in the volume fraction diminished the pumping performance and also the axial and radial velocities. The results are also compared with those which were obtained for zero wavenumber. The outcome of the investigation endorses the doctors’ advice to patients suffering from achalasia, oesophageal stricture and oesophageal tumors to take liquid or food items with lesser solid contents. Streamline patterns are changed by increasing the flow rate while trapping occurs at high flow rates.

Unsteady Peristaltic Transport of a Particle-Fluid Suspension: Application to Oesophageal Swallowing