Peristaltic pumping of a second-order fluid in a planar channel

The peristaltic motion of a non-Newtonian fluid represented by the constitutive equation for a second-order fluid was studied for the case of a planar channel with harmonically undulating extensible walls. A perturbation series for the parameter δ (δ ≡ half-width of channel/wave length) obtained explicit terms of 0(δ2), 0(δ2Re2) and 0(λ1Reδ2) respectively representing curvature, inertia and the non-Newtonian character of the fluid. Numerical computations were performed and compared to the perturbation analysis in order to determine the range of validity of the terms.

[1]  S. Takabatake,et al.  Numerical Analysis of Two-Dimensional Peristaltic Flows : 1st Report, Flow Pattern , 1982 .

[2]  M. Webster.  A technique to solve incompressible non-Newtonian flow problems , 1986 .

[3]  K. Raju,et al.  Peristaltic motion of a non-Newtonian fluid , 1972 .

[4]  Steven Weinberg,et al.  An experimental study of peristaltic pumping , 1971, Journal of Fluid Mechanics.

[5]  R. Bird.  Dynamics of Polymeric Liquids , 1977 .

[6]  L M Srivastava,et al.  Peristaltic transport of blood: Casson model--II. , 1984, Journal of biomechanics.

[7]  R. Tanner,et al.  Numerical Simulation of Non-Newtonian Flow , 1984 .

[8]  S. Weinberg,et al.  Peristaltic pumping with long wavelengths at low Reynolds number , 1968, Journal of Fluid Mechanics.

[9]  J. B. Shukla,et al.  Peristaltic transport of a power-law fluid with variable consistency. , 1982, Journal of biomechanical engineering.

[10]  B. D. Coleman,et al.  An approximation theorem for functionals, with applications in continuum mechanics , 1960 .

[11]  Michel Y. Jaffrin,et al.  Inertia and streamline curvature effects on peristaltic pumping , 1973 .

[12]  S. Ostrach,et al.  A long wave approximation to peristaltic motion. , 1970, Journal of biomechanics.

[13]  R. Devanathan,et al.  Peristaltic motion of a non-Newtonian fluid , 1974 .

[14]  Frank C. P. Yin,et al.  Comparison of theory and experiment in peristaltic transport , 1971, Journal of Fluid Mechanics.

[15]  W. Schwarz,et al.  Stability of a Plane Poiseuille Flow of a Second‐Order Fluid , 1968 .

[16]  Thomas D. Brown,et al.  Computational and experimental investigations of two-dimensional nonlinear peristaltic flows , 1977, Journal of Fluid Mechanics.

[17]  K. Ayukawa,et al.  Numerical study of two-dimensional peristaltic flows , 1982, Journal of Fluid Mechanics.

[18]  T. Brown,et al.  Solid-particle motion in two-dimensional peristaltic flows , 1976, Journal of Fluid Mechanics.