Peristaltic transport of non-Newtonian fluid in a diverging tube with different wave forms

The present study investigates the peristaltic transport of non-Newtonian fluid, modeled as power law and Bingham fluid, in a diverging tube with different wall wave forms: sinusoidal, multi-sinusoidal, triangular, trapezoidal and square waves. Fourier series is employed to get the expressions for temporal and spatial dependent wall shapes. Solutions for time average pressure rise — flow rate relationship are computed for different amplitude ratios, φφ, power law indices, nn, yield stresses, τ0τ0, and wave shapes. Results indicate that φφ and n play a vital role in peristalsis. When φφ of the sinusoidal wave is increased from 0.6 to 0.8, the maximum pressure rise, ΔPLmax, increased by a factor of 10. Increasing n from 0.6 to 1 increased the ΔPLmax by a factor of 3. For Bingham fluid with φ=0.5φ=0.5, a 25% increase in ΔPL,max is obtained when τ0τ0, is reduced from 1 (non-Newtonian) to 0 (Newtonian). Of all the wave shapes considered, ΔPLmax obtained is maximum for the square wave and minimum for the triangular wave (4–15 times less depending on φφ). Finally, pathlines of massless particles are traced to investigate the occurrence of reflux. It is observed that, even for zero flow rate, reflux occurs near the tube wall and the thickness and shape of the reflux region strongly depends on φφ, nn, and shape of the peristaltic waves.