Skip to main content
SpringerLink
Log in

DTM Simulation of Peristaltic Viscoelastic Biofluid Flow in Asymmetric Porous Media: A Digestive Transport Model

  • Published:
Journal of Bionic Engineering Aims and scope Submit manuscript

Abstract

A biofluid dynamics mathematical model is developed to study peristaltic flow of non-Newtonian physiological liquid in a two-dimensional asymmetric channel containing porous media as a simulation of obstructed digestive (intestinal) transport. The fractional Oldroyd-B viscoelastic rheological model is utilized. The biophysical flow regime is constructed as a wave-like motion and porous medium is simulated with a modified Darcy-Brinkman model. This model is aimed at describing the digestive transport in intestinal tract containing deposits which induce impedance. A low Reynolds number approximation is employed to eliminate inertial effects and the wavelength to diameter ratio is assumed to be large. The differential transform method (DTM), a semi-computational technique is employed to obtain approximate analytical solutions to the boundary value problem. The influences of fractional (rheological material) parameters, relaxation time, retardation time, amplitude of the wave, and permeability parameter on peristaltic flow characteristics such as volumetric flow rate, pressure difference and wall friction force are computed. The present model is relevant to flow in diseased intestines.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

h 1 :

Transverse vibration of the upper wall

h 2 :

Transverse vibration of the lower wall

b 1 :

Upper half-width of the channel

b 2 :

Lower half-width of the channel

a 1 :

Amplitude of upper wall

a 2 :

Amplitude of lower wall

ξ:

Axial displacement

u:

Axial velocity

ν:

Transverse velocity

η:

Transverse coordinate

p:

Pressure

Re:

Reynolds number

c:

Wave velocity

K:

Permeability parameter

q:

Volumetric flow rate in the wave frame

δ:

Wave number

ϕ 1 :

Ratio of upper wall wave amplitude to upper channel half width

ϕ 2 :

Ratio of lower wall wave amplitude to upper channel half width

ϕ:

Phase difference

μ:

Viscosity

α, β:

Fractional parameters

ψ:

Stream function

φ:

Porosity of porous medium

λ:

Wavelength

τ̃γ̇:

Shear stress, rate of shear strain

λ̅ 1 λ̅ 2 :

Material constants

ρ:

Fluid density

References

  1. Elman R. The danger of sudden deflation of acutely distended bowel in late low intestinal obstruction. The American Journal of Surgery, 1934, 26, 438–446.

    Article  Google Scholar 

  2. Grassi R, Romano S, D’Amario F, Giorgio Rossi A, Romano L, Pinto F, Di Mizio R. The relevance of free fluid between intestinal loops detected by sonography in the clinical assessment of small bowel obstruction in adults. European Journal of Radiology, 2004, 50, 5–14.

    Article  Google Scholar 

  3. Farrell J J. Methods in Disease: Investigating the Gastrointestinal Tract. Gastroenterology, 1999, 116, 1009–1010.

    Article  Google Scholar 

  4. Rommel N, Selleslagh M, Rosen R L, L Rodriguez, Kritas S, Scheerens C, Tack J F, Omari T, Nurko S. Esophageal pressure topography (ept) incorporating pressure flow analysis discriminates dysphagia due to weak peristalsis from dysphagia due to abnormal bolus flow resistance in children. Gastroenterology, 2013, 144, S170–S170.

    Article  Google Scholar 

  5. Kishi K, Yamada K. Sugiyama T. Gastric outlet obstruction caused by a large gallstone in the duodenum (Bouveret’s syndrome). Clinical Gastroenterology and Hepatology, 2008, 6, e11.

    Article  Google Scholar 

  6. Bég O A, Uddin M J, Khan W A. Bioconvective non-Newtonian nanofluid transport in porous media containing micro-organisms in a moving free stream. Journal of Mechanics Medicine Biology, 2015, 15, 1550071.

    Article  Google Scholar 

  7. Sukop M C, Van Dijk G J, Perfect E, Van Loon W K P. Percolation thresholds in 2-dimensional prefractal models of porous media. Transport in Porous Media, 2002, 48, 187–208.

    Article  Google Scholar 

  8. Frangi, A F, Lassila T, Vardakis J C, Ventikos Y. Multiscale modelling of transport phenomena in biological tissue. 4th International Conference on Computational and Mathematical Biomedical Engineering (CMBE 2015), France, 2015.

    Google Scholar 

  9. Zidi M, Tounsi A, Houari M S A, Bedia A A, Bég O A. Bending analysis of FGM plates under hgro-thermo-mechanical loading using a four variable refined plate theory. Aerospace Science and Technology, 2014, 34, 24–34.

    Article  Google Scholar 

  10. Rohan E. Modeling Large-deformation-induced microflow in soft biological tissues. Theoretical and Computational Fluid Dynamics, 2006, 20, 251–276.

    Article  MATH  Google Scholar 

  11. Kothandapani M, Srinivas S. Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium. Physics Letters A, 2008, 372, 1265–1276.

    Article  MATH  Google Scholar 

  12. Mekheimer K S, Abd Elmaboud Y. Peristaltic flow through a porous medium in an annulus: Application of an endoscope. Applied Mathematics & Information Sciences, 2008, 2, 103–121.

    MathSciNet  MATH  Google Scholar 

  13. El Shehawey F, Husseny S Z A. Effects of porous boundaries on peristaltic transport through a porous medium. Acta Mechanica, 2000, 143, 165–177.

    Article  MATH  Google Scholar 

  14. Mekheimer K S. Non-linear peristaltic transport through a porous medium in an inclined planar channel. Journal of Porous Media, 2003, 6, 189–201.

    Article  MATH  Google Scholar 

  15. Srinivas S, Gayathri R. Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium. Applied Mathematics and Computation, 2009, 215, 185–196.

    Article  MathSciNet  MATH  Google Scholar 

  16. Skalak R, Ozkaya N, Skalak T C. Biofluid Mechanics. Annual Review of Fluid Mechanics, 1989, 21, 167–200.

    Article  MathSciNet  MATH  Google Scholar 

  17. Radhakrishnamacharya G. Long wave length approximation to peristaltic motion of a power-law fluid. Rheologica Acta, 1982, 21, 30–35.

    Article  MATH  Google Scholar 

  18. Li W G, Luo X Y, Chin S B, Hill N A, Johnson A G, Bird N C. Non-Newtonian bile flow in elastic cystic duct: One- and three-dimensional modeling. Annals of Biomedical Engineering, 2008, 36, 1893–1908.

    Article  Google Scholar 

  19. Akbar N S, Nadeem S. Simulation of peristaltic flow of chyme in small intestine for couple stress fluid. Meccanica, 2013, 49, 325–334.

    Article  MathSciNet  MATH  Google Scholar 

  20. Muthu P, Ratish Kumar B V, Chandra P. Peristaltic motion of micropolar fluid in circular cylindrical tubes: Effect of wall properties. Applied Mathematical Modelling, 2008, 32, 2019–2033.

    Article  MathSciNet  MATH  Google Scholar 

  21. Vicente J D. Viscoelasticity–From Theory to Biological Applications, InTech, Virginia, USA, 2012.

    Book  Google Scholar 

  22. Norouzi M, Davoodi M, Bég O A, Joneidi A A. Analysis of the effect of normal stress differences on heat transfer in creeping viscoelastic Dean flow. International Journal of Thermal Sciences, 2013, 69, 61–69.

    Article  Google Scholar 

  23. Tripathi D. Numerical and analytical simulation of peristaltic flows of generalized Oldroyd-B fluids. International Journal for Numerical Methods in Fluids, 2011, 67, 1932–1943.

    Article  MathSciNet  MATH  Google Scholar 

  24. Yasmin H, Hayat T, Alsaedi A, Alsulami H H. Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary conditions. Applied Mathematics and Mechanics, 2014, 35, 697–716.

    Article  MathSciNet  MATH  Google Scholar 

  25. Tripathi D, Pandey S K, Bég O A. Mathematical modelling of heat transfer effects on swallowing dynamics of viscoe-lastic flood bolus through the human oesophagus. International Journal of Thermal Sciences, 2013, 70, 41–53.

    Article  Google Scholar 

  26. Tripathi D, Bég O A, Curiel-Sosa J L. Homotopy Semi-Numerical Simulation of Peristaltic flow of generalized Oldroyd-B fluids with slip effects. Computer Methods in Biomechanics and Biomedical Engineering, 2014, 17, 433–442.

    Article  Google Scholar 

  27. Alemayehu H, Radhakrishnamacharya G. The dispersion in peristaltic flow of micropolar fluid in a porous medium. Journal of Porous Media, 2012, 15, 1067–1077.

    Article  MATH  Google Scholar 

  28. Mekheimer K S. Non-linear peristaltic transport of a second-order fluid through a porous medium. Applied Mathematical Modelling, 2010, 35, 2695–2710.

    MathSciNet  MATH  Google Scholar 

  29. Tripathi D, Bég O A. A numerical study of oscillating peristaltic flow of generalized Maxwell viscoelastic fluids through a porous medium. Transport in Porous Media, 2012, 95, 337–348.

    Article  MathSciNet  Google Scholar 

  30. Alemayehu H, Radhakrishnamacharya G. Dispersion of a solute in peristaltic motion of a couple stress fluid through a porous medium. Tamkang Journal of Mathematics, 2012, 43, 541–555.

    MathSciNet  MATH  Google Scholar 

  31. Tripathi D. Peristaltic hemodynamic flow of couple-stress fluids through a porous medium with slip effect. Transport in Porous Media, 2012, 92, 559–572.

    Article  MathSciNet  Google Scholar 

  32. Oldroyd J G. On the formulation of rheological equations of state. Proceedings of the Royal Society of London A, 1950, 200, 523–541.

    Article  MathSciNet  MATH  Google Scholar 

  33. Qi H, Xu M. Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative. Applied Mathematical Modelling, 2009, 33, 4184–4191.

    Article  MathSciNet  MATH  Google Scholar 

  34. Nadeem S. General periodic flows of fractional Oldroyd-B fluid for an edge. Physics Letters A, 2007, 368, 181–187.

    Article  MATH  Google Scholar 

  35. Liu Y, Zheng L, Zhang X. Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative. Computers and Mathematics with Applications, 2011, 61, 443–450.

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhou J K. Differential Transformation and its Application for Electrical Circuits, Huazhong University Press, Wuhan, 1986.

    Google Scholar 

  37. Rashidi M M, Parsa A B, Bég O A, Shamekhi L, Sadri S M, Bég T A. Parametric analysis of entropy generation in magneto-hemodynamic flow in a semi-porous channel with OHAM and DTM. Applied Bionics and Biomechanics, 2014, 11, 1–2.

    Article  Google Scholar 

  38. Tan W C, Masuoka T. Stokes’ first problem for an Oldroyd-B fluid in a porous half space. Physics of Fluids, 2005, 17, 023101.

    Article  MathSciNet  MATH  Google Scholar 

  39. Xue C, Nie J. Exact solutions of Rayleigh-Stokes problem for heated generalized Maxwell fluid in a porous half-space. Mathematical Problems in Engineering, 2008, 2008, 641431.

    Article  MathSciNet  MATH  Google Scholar 

  40. Khan M, Hayat T, Asghar S. Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy’s law. International Journal of Engineering Sciences, 2006, 44, 333–339

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Manipal University Jaipur, Jaipur, 303007, India

    Dharmendra Tripathi

  2. Gort Engovation-Bio-Propulsion Research, Gabriel’s Wing House, Bradford, BD6 1FA, UK

    Osman Anwar Bég

  3. Department of Mathematics, National Institute of Technology Silchar, Silchar, 788010, India

    Praveen Kumar Gupta

  4. Department of Mathematics, National Institute of Technology, Warangal, 506004, India

    Ganjam Radhakrishnamacharya

  5. School of Electrical & Electronic Engineering, The University of Adelaide, Adelaide, SA, 5005, Australia

    Jagannath Mazumdar

Authors
  1. Dharmendra Tripathi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Osman Anwar Bég
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Praveen Kumar Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ganjam Radhakrishnamacharya
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jagannath Mazumdar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dharmendra Tripathi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tripathi, D., Bég, O.A., Gupta, P.K. et al. DTM Simulation of Peristaltic Viscoelastic Biofluid Flow in Asymmetric Porous Media: A Digestive Transport Model. J Bionic Eng 12, 643–655 (2015). https://doi.org/10.1016/S1672-6529(14)60154-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S1672-6529(14)60154-2

Keywords

Search

Navigation