Abstract
Fluid mechanical peristaltic transport through esophagus is studied in the paper. A mathematical model has been developed to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths. The Ostwald-de Waele power law of a viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid. The model is formulated and analyzed specifically to explore some important information concerning the movement of food bolus through esophagus. The analysis is carried out by using the lubrication theory. The study is particularly suitable for the cases where the Reynolds number is small. The esophagus is treated as a circular tube through which the transport of food bolus takes place by periodic contraction of the esophageal wall. Variation of different variables concerned with the transport phenomena such as pressure, flow velocities, particle trajectory, and reflux is investigated for a single wave as well as a train of periodic peristaltic waves. The locally variable pressure is seen to be highly sensitive to the flow index “n”. The study clearly shows that continuous fluid transport for Newtonian/rheological fluids by wave train propagation is more effective than widely spaced single wave propagation in the case of peristaltic movement of food bolus in the esophagus.
Similar content being viewed by others
Abbreviations
- R, θ,Z :
-
cylindrical coordinates
- a :
-
average radius of the food bolus
- H :
-
displacement of the esophageal wall in the radial direction
- n :
-
fluid index
- k :
-
reciprocal of n
- P :
-
fluid pressure
- Q 1 :
-
volume flow rate
- t :
-
time
- δ :
-
wave number
- U :
-
velocity component in the Z-direction
- V :
-
velocity component in the R-direction
- W :
-
velocity component in the θ-direction
- V B :
-
volume of fluid within a single peristaltic wave (the bolus)
- ΔP :
-
pressure difference between the ends of the esophagus
- ɛ :
-
minimum vessel radius (during occlusion)
- ρ :
-
fluid density
- λ :
-
wave length of the travelling wave motion in the esophagus
- μ :
-
viscosity of the fluid (food bolus)
- ν :
-
kinematic viscosity of the fluid (food bolus)
- ϕ :
-
wave amplitude
References
Misra, J. C. and Pandey, S. K. Peristaltic transport of a non-Newtonian fluid with a peripheral layer. International Journal of Engineering Science, 37, 1841–1858 (1999)
Misra, J. C. and Pandey, S. K. A mathematical model for esophageal swallowing of a food bolus. Mathematical and Computer Modelling, 33(8–9), 997–1009 (2001)
Misra, J. C., Maiti, S., and Shit, G. C. Peristaltic transport of a physiological fluid in an asymmetric porous channel in the presence of an external magnetic field. Journal of Mechanics in Medicine and Biology, 8(4), 507–525 (2008)
Maiti, S. and Misra, J. C. Peristaltic flow of a fluid in a porous channel: a study having relevance to flow of bile. International Journal of Engineering Science, 49, 950–966 (2011)
Guyton, A. C. and Hall, J. E. Text Book of Medical Physiology, Elsevier, Philadelphia (2006)
Jaffrin, M. Y. and Shapiro, A. H. Peristaltic pumping. Annual Review of Fluid Mechanics, 3, 13–36 (1971)
Nadeem, S. and Akbar, N. S. Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel. Applied Mathematics and Mechanics (English Edition), 31(8), 969–978 (2010) DOI 10.1007/s10483-010-1332-6
Hayat, T. and Javed, M. Exact solution to peristaltic transport of power-law fluid in asymmetric channel with compliant walls. Applied Mathematics and Mechanics (English Edition), 31(10), 1231–1240 (2010) DOI 10.1007/s10483-101-1356-7
Brasseur, J. G. A fluid mechanical perspective on esophageal bolus transport. Dysphagia, 2, 32–39 (1987)
Li, M. and Brasseur, J. G. Non-steady peristaltic transport in finite-length tubes. Journal of Fluid Mechanics, 248, 129–151 (1993)
Patel, P. D., Picologlou, B. F., and Lykoudis, P. S. Biorheological aspects of colonic activity, II, experimental investigation of the rheological behaviour of human faces. Biorheology, 10, 441–445 (1973)
Bird, R. B., Stewart, W. E., and Lightfoot, E. N. Transport Phenomena, John Wiley and Sons, Singapore (1960)
Jaffrin, M. Y. Inertia and streamline curvature on peristaltic pumping. International Journal of Engineering Science, 11, 681–699 (1973)
Dusey, M. Numerical Analysis of Lubrication Theory and Peristaltic Transport in the Esophagus, Ph. D. dissertation, Pennsylvania State University, University Park, Pennsylvania (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Misra, J.C., Maiti, S. Peristaltic transport of rheological fluid: model for movement of food bolus through esophagus. Appl. Math. Mech.-Engl. Ed. 33, 315–332 (2012). https://doi.org/10.1007/s10483-012-1552-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-012-1552-7
Key words
- non-Newtonian fluid
- food bolus
- esophagus
- peristaltic transport
- flow reversal
- single wave
- wave train
- particle trajectory