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

Abstract

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, φ , power law indices, n , yield stresses, τ 0 , and wave shapes. Results indicate that φ and n play a vital role in peristalsis. When φ of the sinusoidal wave is increased from 0.6 to 0.8, the maximum pressure rise, Δ P L max , increased by a factor of 10. Increasing n from 0.6 to 1 increased the Δ P L max by a factor of 3. For Bingham fluid with φ = 0.5 , a 25% increase in Δ P L , max is obtained when τ 0 , is reduced from 1 (non-Newtonian) to 0 (Newtonian). Of all the wave shapes considered, Δ P L max obtained is maximum for the square wave and minimum for the triangular wave (4–15 times less depending on φ ). 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 φ , n , and shape of the peristaltic waves.