Skip to main content
SpringerLink
Log in

Transient membrane kinematic model for viscoplastic fluids: periodic contraction in the microchannel

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

A linear viscoplastic fluid model is considered to analyze the viscoplastic effects in membrane-based pumping flow through the microchannel in mathematical framework. The pressure is generated by the time-dependent wall deformation due to membrane motion. This selective wall compression (expansion) approach drives fluid to unidirectional. The motivation behind this mathematical analysis is to derive the flow visualization of the concentrated and chemical composite (viscoplastic) fluid in the microchannel. The creeping nature of flow analysis in an inelastic microchannel has been modeled using lubrication theory and the long-wavelength approximation. The analytical solutions of dimensionless boundary value problem are obtained to derive the closed-form solutions. The computational results have shown the rheological effects on flow analysis and pumping characteristics. The streamlines of the velocity vector help to understand the flow visualization of viscoplastic fluid. It is observed that the pressure distribution for the viscoplastic fluid is extremely high which is 30.7% more as compared to Newtonian fluid. The magnitude of the volumetric flow rate is reduced by 18.5% as the width of plug flow region is increased from 0 to 0.05.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Y.-N. Wang, L.-M. Fu, Micropumps and biomedical applications–a review. Microelectron. Eng. 195, 121–138 (2018)

    Article  Google Scholar 

  2. L. Xu, A. Wang, X. Li, K.W. Oh, Passive micropumping in microfluidics for point-of-care testing. Biomicrofluidics 14(3), 031503 (2020)

    Article  Google Scholar 

  3. A. Bein, W. Shin, S. Jalili-Firoozinezhad, M.H. Park, A. Sontheimer-Phelps, A. Tovaglieri, A. Chalkiadaki, H.J. Kim, D.E. Ingber, Microfluidic organ-on-a-chip models of human intestine. Cell. Mol. Gastroenterol. Hepatol. 5(4), 659–668 (2018)

    Article  Google Scholar 

  4. A. Bandopadhyay, D. Tripathi, S. Chakraborty, Electroosmosis-modulated peristaltic transport in microfluidic channels. Phys. Fluids 28(5), 052002 (2016)

    Article  ADS  Google Scholar 

  5. V.K. Narla, T. Dharmendra, D.S. Bhandari, Thermal analysis of micropolar fluid flow driven by electroosmosis and peristalsis in microchannel. Int. J. Ambient Energy 2, 1–24 (2022)

    Google Scholar 

  6. L. Wang, C. Liu, J. Li, Z. Xu, L. Gan, T. Li, L. Zhou, Y. Ma, H. Zhang, K. Zhang, External-integrated biomimetic micropump for microfluidic system. J. Micro/Nanolithogr. MEMS MOEMS 13(3), 033008 (2014)

    Article  ADS  Google Scholar 

  7. J. Diaz, J.M. Lopera, A.M. Pernia, F. Nuno, J.A. Martinez, J.V. Comas, L. Galletti, A micropump for pulmonary blood flow regulation. IEEE Ind. Electron. Mag. 1(1), 39–44 (2007)

    Article  Google Scholar 

  8. J. Prakash, D. Tripathi, A.K. Tiwari, S.M. Sait, R. Ellahi, Peristaltic pumping of nanofluids through a tapered channel in a porous environment: applications in blood flow. Symmetry 11(7), 868 (2019)

    Article  ADS  Google Scholar 

  9. J.J. Socha, W.-K. Lee, J.F. Harrison, J.S. Waters, K. Fezzaa, M.W. Westneat, Correlated patterns of tracheal compression and convective gas exchange in a carabid beetle. J. Exp. Biol. 211(21), 3409–3420 (2008)

    Article  Google Scholar 

  10. L. Hanna, A. Popadić, A hemipteran insect reveals new genetic mechanisms and evolutionary insights into tracheal system development. Proc. Natl. Acad. Sci. 117(8), 4252–4261 (2020)

    Article  ADS  Google Scholar 

  11. S. Hagner-Holler, A. Schoen, W. Erker, J.H. Marden, R. Rupprecht, H. Decker, T. Burmester, A respiratory hemocyanin from an insect. Proc. Natl. Acad. Sci. 101(3), 871–874 (2004)

    Article  ADS  Google Scholar 

  12. Y. Aboelkassem, Insect-inspired micropump: flow in a tube with local contractions. Micromachines 6(8), 1143–1156 (2015)

    Article  Google Scholar 

  13. K. Chatterjee, A. Staples, Slip flow in a microchannel driven by rhythmic wall contractions. Acta Mech. 229(10), 4113–4129 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  14. Y. Aboelkassem, A.E. Staples, A three-dimensional model for flow pumping in a microchannel inspired by insect respiration. Acta Mech. 225(2), 493–507 (2014)

    Article  MathSciNet  Google Scholar 

  15. Y. Aboelkassem, Pumping flow model in a microchannel with propagative rhythmic membrane contraction. Phys. Fluids 31(5), 051902 (2019)

    Article  ADS  Google Scholar 

  16. D. Tripathi, V. Narla, Y. Aboelkassem, Electrokinetic membrane pumping flow model in a microchannel. Phys. Fluids 32(8), 082004 (2020)

    Article  ADS  Google Scholar 

  17. D.S. Bhandari, D. Tripathi, V.K. Narla, Magnetohydrodynamics-based pumping flow model with propagative rhythmic membrane contraction. Eur. Phys. J. Plus 135(11), 1–19 (2020)

    Article  Google Scholar 

  18. B.T. Sebastian, P. Nagarani, On convection-diffusion in non-Newtonian fluid flow in an annulus with wall oscillations. Eur. Phys. J. Special Top. 228(12), 2729–2752 (2019)

    Article  ADS  Google Scholar 

  19. A. Magesh, M. Kothandapani, Heat and mass transfer analysis on non-Newtonian fluid motion driven by peristaltic pumping in an asymmetric curved channel. Eur. Phys. J. Special Top. 230(5), 1447–1464 (2021)

    Article  ADS  Google Scholar 

  20. P. Jayavel, R. Jhorar, D. Tripathi, M.N. Azese, Electroosmotic flow of pseudoplastic nanoliquids via peristaltic pumping. J. Braz. Soc. Mech. Sci. Eng. 41(2), 61 (2019)

    Article  Google Scholar 

  21. S. Pandey, M. Chaube, D. Tripathi, Peristaltic transport of multilayered power-law fluids with distinct viscosities: a mathematical model for intestinal flows. J. Theor. Biol. 278(1), 11–19 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. K.F. Liu, C.C. Mei, Slow spreading of a sheet of Bingham fluid on an inclined plane. J. Fluid Mech. 207, 505–529 (1989)

    Article  ADS  MATH  Google Scholar 

  23. D. Tripathi, A. Yadav, O.A. Bég, R. Kumar, Study of microvascular non-Newtonian blood flow modulated by electroosmosis. Microvasc. Res. 117, 28–36 (2018)

    Article  Google Scholar 

  24. X. Huang, M.H. Garcia, A perturbation solution for Bingham-plastic mudflows. J. Hydraul. Eng. 123(11), 986–994 (1997)

    Article  Google Scholar 

  25. C. Dorier, J. Tichy, Behavior of a Bingham-like viscous fluid in lubrication flows. J. Nonnewton. Fluid Mech. 45(3), 291–310 (1992)

    Article  MATH  Google Scholar 

  26. D. Tripathi, O.A. Bég, Mathematical modelling of peristaltic propulsion of viscoplastic bio-fluids. Proc. Inst. Mech. Eng. [H] 228(1), 67–88 (2014)

    Article  MATH  Google Scholar 

  27. N. Khabazi, S. Taghavi, K. Sadeghy, Peristaltic flow of Bingham fluids at large Reynolds numbers: A numerical study. J. Nonnewton. Fluid Mech. 227, 30–44 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Uttarakhand, Srinagar, 246174, India

    D. S. Bhandari, Dharmendra Tripathi & V. K. Narla

  2. Department of Mathematics, GITAM Deemed to be University, Hyderabad, 502329, India

    D. S. Bhandari, Dharmendra Tripathi & V. K. Narla

Authors
  1. D. S. Bhandari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dharmendra Tripathi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. K. Narla
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dharmendra Tripathi.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bhandari, D.S., Tripathi, D. & Narla, V.K. Transient membrane kinematic model for viscoplastic fluids: periodic contraction in the microchannel. Eur. Phys. J. Spec. Top. 232, 817–826 (2023). https://doi.org/10.1140/epjs/s11734-022-00655-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-022-00655-x

Search

Navigation