Peristaltic transport of a physiological fluid. Part-I. Flow in non-uniform geometry

The problem of peristaltic transport of a fluid of variable viscosity in a non-uniform tube and channel has been investigated under zero Reynolds number, and long wavelength approximation. It is found that, the pressure rise decreases as the fluid viscosity decreases at zero flow rate, is independent of viscosity variation at a certain value of flow rate, and increases if flow rate exceeds further. The difference between two corresponding values (for constant and variable viscosity) of pressure rise, under a given set of conditions increases with increasing amplitude ratio at zero flow rate. Further, for a given zero pressure rise, the flow rate increases as viscosity of fluid decreases. The pressure rise, in the case of non-uniform geometry is found to be much smaller than the corresponding value in the case of uniform geometry. In Part II (a companion paper), results for uniform tube and channel are obtained and comparison with other theories are made in detail. Finally, the models developed in Part I and Part II are applied and compared with observed flow rates in vas deferens of rhesus monkeys, the small intestine, and the ductus deferens of the male reproductive tract in the other companion paper, Part III.