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Research Papers: Fundamental Issues and Canonical Flows

Pumping Flow in a Channel With a Peristaltic Wall

[+] Author and Article Information
Yeng-Yung Tsui

Professor
e-mail: yytsui@mail.nctu.edu.tw

Shi-Wen Lin

Department of Mechanical Engineering,
National Chiao Tung University,
Hsinchu 300, Taiwan

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 4, 2012; final manuscript received October 10, 2013; published online December 18, 2013. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 136(2), 021202 (Dec 18, 2013) (9 pages) Paper No: FE-12-1496; doi: 10.1115/1.4026077 History: Received October 04, 2012; Revised October 10, 2013

Simplified models were widely used for analysis of peristaltic transport caused by contraction and expansion of an extensible tube. Each of these models has its own assumptions, and therefore, weakness. To get rid of the limitations imposed by the assumptions, a numerical procedure is employed to simulate this pumping flow in the present study. In earlier studies, the frame of reference adopted moves with the peristaltic speed of the vibrating wall so that the flow becomes steady. The flow characteristics in a wavelength were the main concern. In our calculations, a channel of finite length with a flexible wall is considered. Pressures are prescribed at the inlet and outlet boundaries. The computational grid is allowed to move according to the oscillation of the wall. Another state-of-the-art technique employed is to construct the grid in an unstructured manner to deal with the variable geometry of the duct. The effects of dimensionless parameters, such as amplitude ratio, wave number, Reynolds number, and back pressure on the pumping performance are examined. Details of the peristaltic flow structure are revealed. Also conducted is the comparison of numerical results with the theoretical predictions obtained from the lubrication model to determine the suitability of this theory.

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References

Shapiro, A. H., Jaffrin, M. Y., and Weinberg, S. L., 1969, “Peristaltic Pumping With Long Wavelengths at Low Reynolds Number,” J. Fluid Mech., 37, pp. 799–825. [CrossRef]
Weinberg, S. L., Eckstein, E. C., and Shapiro, A. H., 1971, “An Experimental Study of Peristaltic Pumping,” J. Fluid Mech., 49, pp. 461–479. [CrossRef]
Mishra, M., and Rao, A. R., 2003, “Peristaltic Transport of a Newtonian Fluid in an Asymmetric Channel,” Z. Angew. Math. Phys., 54, pp. 532–550. [CrossRef]
Hayat, T., and Ali, N., 2008, “Effect of Variable Viscosity on the Peristaltic Transport of a Newtonian Fluid in an Asymmetric Channel,” Appl. Math. Modelling, 32, pp. 761–774. [CrossRef]
Reddy, M. V. S., Mishra, M., Sreenadh, S., and Rao, A. R., 2005, “Influence of Lateral Walls on Peristaltic Flow in a Rectangular Duct,” ASME J. Fluids Eng., 127, pp. 824–827. [CrossRef]
Ravi Kumar, Y. V. K., Krishna, S. V. H. N., Ramana Murthy, M. V., and Sreenadh, S., 2010, “Unsteady Peristaltic Pumping in a Finite Length Tube With Permeable Wall,” ASME J. Fluids Eng., 132, p. 101201. [CrossRef]
Srinivas, S., and Kothandapani, M., 2008, “Peristaltic Transport in an Asymmetric Channel With Heat Transfer - A Note,” Int. Commun. Heat Mass Transfer, 35, pp. 514–522. [CrossRef]
Jiménez-Lozano, J., and Sen, M., 2010, “Streamline Topologies of Two- Dimensional Peristaltic Flow and Their Bifurcations,” Chem. Eng. Process., 49, pp. 704–715. [CrossRef]
Misra, J. C., and Pandey, S. K., 2002, “Peristaltic Transport of Blood in Small Vessels: Study of a Mathematical Model,” Comput. Math. Appl., 43, pp. 1183–1193. [CrossRef]
Misra, J. C., and Maiti, S., 2012, “Peristaltic Pumping of Blood through Small Vessels of Varying Cross-Section,” ASME J. Appl. Mech., 79, p. 061003. [CrossRef]
Rao, A. R., and Mishra, M., 2004, “Peristaltic Transport of a Power-Law Fluid in a Porous Tube,” J. Non-Newtonian Fluid Mech., 121, pp. 163–174. [CrossRef]
Ravi Kumar, Y. V. K., Krishna KumariP., Ramana Murthy, M. V., and Sreenadh, S., 2011, “Peristaltic Transport of a Power-Law Fluid in an Asymmetric Channel Bounded by Permeable Walls,” Adv. Appl. Sci. Res., 2, pp. 396–406. Available at http://www.pelagiaresearchlibrary.com/advances-in-applied-science/vol2-iss3/AASR-2011-2-3-396-406.pdf
Nadeem, S., Akram, S., Hayat, T., and Hendi, A. A., 2012, “Peristaltic Flow of a Carreau Fluid in a Rectangular Duct,” ASME J. Fluids Eng., 134, p. 041201. [CrossRef]
Noreen, S., Alsaedi, A., and Hayat, T., 2012, “Peristaltic Flow of Pseudoplastic Fluid in an Asymmetric Channel,” ASME J. Appl. Mech., 79, p. 054501. [CrossRef]
Ali, N., and Hayat, T., 2008, “Peristaltic Flow of a Micropolar Fluid in an Asymmetric Channel,” Comput. Math. Appl., 55, pp. 589–608. [CrossRef]
Tripathi, D., 2011, “Numerical Study on Creeping Flow of Burgers' Fluids Through a Peristaltic Tube,” ASME J. Fluids Eng., 133, p. 121104. [CrossRef]
Fung, Y. C., and Yih, C. S., 1968, “Peristaltic Transport,” ASME J. Appl. Mech., 45, pp. 669–675. [CrossRef]
Yin, F. C. P., and Fung, Y. C., 1971, “Comparison of Theory and Experiment in Peristaltic Transport,” J. Fluid Mech., 47, pp. 93–112. [CrossRef]
Wilson, D. E., and Panton, R. L., 1979, “Peristaltic Transport due to Finite Amplitude Bending and Contraction Waves,” J. Fluid Mech., 90, pp. 145–159. [CrossRef]
Selverov, K. P., and Stone, H. A., 2001, “Peristaltically Driven Channel Flows With Applications Toward Micromixing,” Phys. Fluids, 13, pp. 1837–1859. [CrossRef]
Yi, M., Bau, H. H., and Hu, H., 2002, “Peristaltically Induced Motion in a Closed Cavity With Two Vibrating Walls,” Phys. Fluids, 14, pp. 184–197. [CrossRef]
Abd Elnaby, M. A., and Haroun, M. H., 2008, “A New Model for Study the Effect of Wall Properties on Peristaltic Transport of a Viscous Fluid,” Commun. Nonlinear Sci. Numer. Simul., 13, pp. 752–762. [CrossRef]
Usha, S., and Rao, A. R., 2000, “Effects of Curvature and Inertia on the Peristaltic Transport in a Two-Fluid System,” Int. J. Eng. Sci., 38, pp. 1355–1375. [CrossRef]
Rao, A. R., and Mishra, M., 2004, “Nonlinear and Curvature Effects on Peristaltic Flow of a Viscous Fluid in an Asymmetric Channel,” Acta Mech., 168, pp. 35–59. [CrossRef]
Brown, T. D., and Hung, T.-K., 1977, “Computational and Experimental Investigations of Two-Dimensional Nonlinear Peristaltic Flows,” J. Fluid Mech., 83, pp. 249–272. [CrossRef]
Takabatake, S., and Ayukawa, K., 1982, “Numerical Study of Two-Dimensional Peristaltic Flows,” J. Fluid Mech., 122, pp. 439–465. [CrossRef]
Tong, P., and Vawter, D., 1972, “An Analysis of Peristaltic Pumping,” ASME J. Appl. Mech., 39, pp. 857–862. [CrossRef]
Rathish Kumar, B. V., and Naidu, K. B., 1995, “A Numerical Study of Peristaltic Flows,” Comput. Fluids, 24, pp. 161–176. [CrossRef]
Pozrikidis, C., 1987, “A Study of Peristaltic Flow,” J. Fluid Mech., 180, pp. 515–527. [CrossRef]
Demirdzic, I., and Peric, M., 1988, “Space Conservation Law in Finite Volume Calculations of Fluid Flow,” Int. J. Numer. Methods Fluids, 8, pp. 1037–1050. [CrossRef]
Tsui, Y.-Y., and Pan, Y.-F., 2006, “A Pressure-Correction Method for Incompressible Flows Using Unstructured Meshes,” Numer. Heat Transfer, Part B, 49, pp. 43–65. [CrossRef]
Tsui, Y.-Y., and Wu, T.-C., 2010, “Use of Characteristic-Based Flux Limiters in a Pressure-Based Unstructured-Grid Algorithm Incorporating High-Resolution Schemes,” Numer. Heat Transfer, Part B, 55, pp. 14–34. [CrossRef]
Tsui, Y-Y., and Chang, T.-C., 2012, “A Novel Peristaltic Micropump With Low Compression Ratios,” Int. J. Numer. Methods Fluids, 69, pp. 1363–1376. [CrossRef]
Issa, R. I., 1986, “Solution of the Implicitly Discretised Fluid Flow Equations by Operator-Splitting,” J. Comput. Phys., 62, pp. 40–65. [CrossRef]

Figures

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Fig. 1

Schematic sketch of the peristaltic channel

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Fig. 2

Illustration of a typical control volume

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Fig. 3

A control volume adjacent to the open boundary

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Fig. 4

Comparison with theoretical solutions and experiments for two amplitudes

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Fig. 5

Variation of mean flow rate against Reynolds number with ɛ = 0.3 for (a) two wave numbers (Pb = 0) and (b) different back pressures (α = 0.0907)

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Fig. 6

Variation of mean flow rate against amplitude ratio with α = 0.0907 for (a) different Reynolds numbers (Pb = 0) and (b) different back pressures (Re = 20)

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Fig. 7

Variation of mean flow rate against wave number with ɛ = 0.3 for (a) different Reynolds numbers (Pb = 0) and (b) different back pressures (Re = 10)

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Fig. 8

Variation of mean flow rate against back pressure with Re = 10 for (a) two wave numbers (ɛ = 0.3) and (b) two amplitude ratios (α = 0.0907)

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Fig. 9

Streamlines at times t = 0, T/4, T/2, and 3T/4 in a time period for ɛ = 0.3 (a) in wave frame and (b) in laboratory frame (α = 0.0907, Re = 20, and Pb = 1.5)

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Fig. 10

Streamlines at times t = 0, T/4, T/2, and 3T/4 in a time period for ɛ = 1 (a) in wave frame and (b) in laboratory frame (α = 0.0907, Re = 20, and Pb = 1.5)

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Fig. 11

Variation of pressure at the fixed wall for two amplitude ratios (α = 0.0907, Re = 20, and Pb = 1.5)

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Fig. 12

Variation of pressure at the fixed wall for two wave numbers (ɛ = 0.3, Re = 20, and Pb = 1.5)

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Fig. 13

Path lines for three particles (ɛ = 0.3)

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Fig. 14

Velocity profiles along a vertical line in a time period (ɛ = 0.3)

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Fig. 15

Path lines for three particles (ɛ = 1)

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Fig. 16

Velocity profiles along a vertical line in a time period (ɛ = 1)

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