A mathematical model for the movement of food bolus of varying viscosities through the esophagus

This mathematical model is designed to study the influence of viscosity on swallowing of food bolus through the esophagus. Food bolus is considered as viscous fluid with variable viscosity. Geometry of esophagus is assumed as finite length channel and flow is induced by peristaltic wave along the length of channel walls. The expressions for axial velocity, transverse velocity, pressure gradient, volume flow rate and stream function are obtained under the assumptions of long wavelength and low Reynolds number. The impacts of viscosity parameter on pressure distribution, local wall shear stress, mechanical efficiency and trapping are numerically discussed with the help of computational results. On the basis of presented study, it is revealed that swallowing of low viscous fluids through esophagus requires less effort in comparison to fluids of higher viscosity. This result is similar to the experimental result obtained by Raut et al. [1], Dodds [2] and Ren et al. [3]. It is further concluded that the pumping efficiency increases while size of trapped bolus reduces when viscosity of fluid is high.