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Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: mathematical model

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Abstract

A theoretical study is presented of peristaltic hydrodynamics of an aqueous electrolytic non-Newtonian Jeffrey bio-rheological fluid through an asymmetric microchannel under an applied axial electric field. An analytical approach is adopted to obtain the closed form solution for velocity, volumetric flow, pressure difference and stream function. The analysis is also restricted under the low Reynolds number assumption (Stokes flow) and lubrication theory approximations (large wavelength). Small ionic Peclét number and Debye–Hückel linearization (i.e. wall zeta potential ≤ 25 mV) are also considered to simplify the Nernst–Planck and Poisson–Boltzmann equations. Streamline plots are also presented for the different electro-osmotic parameter, varying magnitudes of the electric field (both aiding and opposing cases) and for different values of the ratio of relaxation to retardation time parameter. Comparisons are also included between the Newtonian and general non-Newtonian Jeffrey fluid cases. The results presented here may be of fundamental interest towards designing lab-on-a-chip devices for flow mixing, cell manipulation, micro-scale pumps etc. Trapping is shown to be more sensitive to an electric field (aiding, opposing and neutral) rather than the electro-osmotic parameter and viscoelastic relaxation to retardation ratio parameter. The results may also help towards the design of organ-on-a-chip like devices for better drug design.

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References

  1. Brasseur JG, Corrsin S, Lu NQ (1987) The influence of a peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids. J Fluid Mech 174:495–519

    Article  ADS  Google Scholar 

  2. Rao AR, Usha S (1995) Peristaltic transport of two immiscible viscous fluids in a circular tube. J Fluid Mech 298:271–285

    Article  ADS  MATH  Google Scholar 

  3. Misra J, Pandey S (1999) Peristaltic transport of a non-Newtonian fluid with a peripheral layer. Int J Eng Sci 37:1841–1858

    Article  MATH  Google Scholar 

  4. Takagi D, Balmforth N (2011) Peristaltic pumping of viscous fluid in an elastic tube. J Fluid Mech 672:196–218

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Aboelkassem Y, Staples AE (2013) Selective pumping in a network: insect-style microscale flow transport. Bioinspir Biomim 8:026004

    Article  ADS  Google Scholar 

  6. Herzburn PA, Irvine RL, Malinowski KC (1985) Biological treatment of hazardous waste in sequencing batch reactors. J Water Pollut Control Fed 57:1163–1167

    Google Scholar 

  7. DeFlaun MF, Condee CW (1997) Electrokinetic transport of bacteria. J Hazard Mater 55:263–277

    Article  Google Scholar 

  8. Jaffrin M, Shapiro A (1971) Peristaltic pumping. Ann Rev Fluid Mech 3:13–37

    Article  ADS  Google Scholar 

  9. Pozrikidis C (1987) A study of peristaltic flow. J Fluid Mech 180:515–527

    Article  ADS  Google Scholar 

  10. Hayat T, Ali N, Asghar S (2007) Hall effects on peristaltic flow of a Maxwell fluid in a porous medium. Phys Lett A 363:397–403

    Article  ADS  MATH  Google Scholar 

  11. Wang Y, Hayat T, Ali N, Oberlack M (2008) Magnetohydrodynamic peristaltic motion of a Sisko fluid in a symmetric or asymmetric channel. Phys A Stat Mech Appl 387:347–362

    Article  MathSciNet  Google Scholar 

  12. Hina S, Hayat T, Alsaedi A (2012) Heat and mass transfer effects on the peristaltic flow of Johnson-Segalman fluid in a curved channel with compliant walls. Int J Heat Mass Transf 55:3511–3521

    Article  Google Scholar 

  13. Mekheimer KS (2011) Non-linear peristaltic transport of a second-order fluid through a porous medium. Appl Math Model 35:2695–2710

    Article  MathSciNet  MATH  Google Scholar 

  14. Sutradhar A, Mondal JK, Murthy P, Gorla RSR (2016) Influence of starling’s hypothesis and joule heating on peristaltic flow of an electrically conducting Casson fluid in a permeable microvessel. J Fluids Eng 138:111106

    Article  Google Scholar 

  15. Tripathi D, Bég OA (2014) Peristaltic propulsion of generalized Burgers’ fluids through a non-uniform porous medium: a study of chyme dynamics through the diseased intestine. Math Biosci 248:67–77

    Article  MathSciNet  MATH  Google Scholar 

  16. Abd-Alla A, Abo-Dahab S (2015) Magnetic field and rotation effects on peristaltic transport of a Jeffrey fluid in an asymmetric channel. J Magn Magn Mater 374:680–689

    Article  ADS  Google Scholar 

  17. Tripathi D, Bég OA (2014) Mathematical modelling of peristaltic propulsion of viscoplastic bio-fluids. Proc Inst Mech Eng Part H J Eng Med 228:67–88

    Article  MATH  Google Scholar 

  18. Mekheimer KS (2002) Peristaltic transport of a couple stress fluid in a uniform and non-uniform channels. Biorheology 39:755–765

    Google Scholar 

  19. Chakraborty S (2006) Augmentation of peristaltic microflows through electro-osmotic mechanisms. J Phys D Appl Phys 39:5356

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Tripathi D, Bushan S, Beg O (2016) Analytical study of electroosmosis modulated capillary peristaltic hemodynamics. J Mech Med Biol (JMMB)

  22. Goswami P, Chakraborty J, Bandopadhyay A, Chakraborty S (2016) Electrokinetically modulated peristaltic transport of power-law fluids. Microvasc Res 103:41–54

    Article  Google Scholar 

  23. Shit GC, Ranjit NK, Sinha A (2016) Electro-magnetohydrodynamic flow of biofluid induced by peristaltic wave: a non-newtonian model. J Bionic Eng 13:436–448

    Article  Google Scholar 

  24. Tripathi D, Bhushan S, Bég OA (2016) Transverse magnetic field driven modification in unsteady peristaltic transport with electrical double layer effects. Colloids Surf A Physicochem Eng Asp 506:32–39

    Article  Google Scholar 

  25. Tripathi D, Yadav A, Bég OA (2017) Electro-kinetically driven peristaltic transport of viscoelastic physiological fluids through a finite length capillary: mathematical modeling. Math Biosci 283:155–168

    Article  MathSciNet  MATH  Google Scholar 

  26. Afonso A, Alves M, Pinho F (2009) Analytical solution of mixed electro-osmotic/pressure driven flows of viscoelastic fluids in microchannels. J Nonnewton Fluid Mech 159:50–63

    Article  MATH  Google Scholar 

  27. Das S, Chakraborty S (2006) Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian bio-fluid. Anal Chim Acta 559:15–24

    Article  Google Scholar 

  28. Zhao C, Yang C (2011) An exact solution for electroosmosis of non-Newtonian fluids in microchannels. J Nonnewton Fluid Mech 166:1076–1079

    Article  MATH  Google Scholar 

  29. Zhao C, Yang C (2013) Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel. Electrophoresis 34:662–667

    Article  Google Scholar 

  30. Zhao C, Yang C (2013) Electrokinetics of non-Newtonian fluids: a review. Adv Colloid Interface Sci 201:94–108

    Article  ADS  Google Scholar 

  31. Zhao M, Wang S, Wei S (2013) Transient electro-osmotic flow of Oldroyd-B fluids in a straight pipe of circular cross section. J Nonnewton Fluid Mech 201:135–139

    Article  Google Scholar 

  32. Carpi F, Menon C, De Rossi D (2010) Electroactive elastomeric actuator for all-polymer linear peristaltic pumps. IEEE/ASME Trans Mechatron 15:460–470

    Article  Google Scholar 

  33. Wang C, Gao Y, Nguyen N-T, Wong TN, Yang C, Ooi KT (2005) Interface control of pressure-driven two-fluid flow in microchannels using electroosmosis. J Micromech Microeng 15:2289

    Article  Google Scholar 

  34. Polson NA, Hayes MA (2000) Electroosmotic flow control of fluids on a capillary electrophoresis microdevice using an applied external voltage. Anal Chem 72:1088–1092

    Article  Google Scholar 

  35. Ericson C, Holm J, Ericson T, Hjertén S (2000) Electroosmosis-and pressure-driven chromatography in chips using continuous beds. Anal Chem 72:81–87

    Article  Google Scholar 

  36. Dutta P, Beskok A, Warburton TC (2002) Numerical simulation of mixed electroosmotic/pressure driven microflows. Numer Heat Transf Part A Appl 41:131–148

    Article  ADS  Google Scholar 

  37. Gillespie D, Pennathur S (2013) Separation of ions in nanofluidic channels with combined pressure-driven and electro-osmotic flow. Anal Chem 85:2991–2998

    Article  Google Scholar 

  38. Kothandapani M, Srinivas S (2008) Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel. Int J Nonlinear Mech 43:915–924

    Article  Google Scholar 

  39. Tripathi D, Pandey S, Anwar Bég O (2013) Mathematical modelling of heat transfer effects on swallowing dynamics of viscoelastic food bolus through the human oesophagus. Int J Therm Sci 70:41–53

    Article  Google Scholar 

  40. Ellahi R, Bhatti MM, Pop I (2016) Effects of hall and ion slip on MHD peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct. Int J Numer Methods Heat Fluid Flow 26:1802–1820

    Article  MathSciNet  MATH  Google Scholar 

  41. Bhatti M, Ellahi R, Zeeshan A (2016) Study of variable magnetic field on the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct having compliant walls. J Mol Liq 222:101–108

    Article  Google Scholar 

  42. Afonso AM, Alves MA, Pinho FT (2013) Analytical solution of two-fluid electro-osmotic flows of viscoelastic fluids. J Colloid Interface Sci 395:277–286

    Article  ADS  Google Scholar 

  43. Afonso AM, Ferrás LL, Nóbrega JM, Alves MA, Pinho FT (2014) Pressure-driven electrokinetic slip flows of viscoelastic fluids in hydrophobic microchannels. Microfluid Nanofluidics 16(6):1131–1142

    Article  Google Scholar 

  44. Ferrás LL, Afonso AM, Alves MA, Nóbrega JM, Pinho FT (2014) Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids. J Colloid Interface Sci 420:152–157

    Article  ADS  Google Scholar 

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Authors and Affiliations

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

    Dharmendra Tripathi & Ravindra Jhorar

  2. Fluid Mechanics, Propulsion and Nanosystems, Department of Mechanical and Aeronautical Engineering, Salford University, Newton Building, Salford, M54WT, England, UK

    O. Anwar Bég

  3. Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana

    Sachin Shaw

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  1. Dharmendra Tripathi
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  2. Ravindra Jhorar
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  4. Sachin Shaw
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Correspondence to Dharmendra Tripathi.

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Tripathi, D., Jhorar, R., Anwar Bég, O. et al. Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: mathematical model. Meccanica 53, 2079–2090 (2018). https://doi.org/10.1007/s11012-017-0795-x

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  • DOI: https://doi.org/10.1007/s11012-017-0795-x

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