Study of EDL phenomenon in Peristaltic pumping of a Phan-Thien-Tanner Fluid through asymmetric channel

J. Prakash; Dharmendra Tripathi

Korea-Australia Rheology Journal, Vol.32, No.4, 271-285, November, 2020

DOI10.1007/s13367-020-0026-1 Export Citation

Study of EDL phenomenon in Peristaltic pumping of a Phan-Thien-Tanner Fluid through asymmetric channel

J. Prakash, and Dharmendra Tripathi^{1, †}

Department of Mathematics, Avvaiyar Government College for Women, Karaikal-609 602, Pondicherry –U.T., India
¹Department of Mathematics, National Institute of Technology Uttarakhand, Srinagar -246174, India

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This paper is mainly attained to examine the electric double layer (EDL) phenomena and rheological effects on peristaltic pumping through asymmetric microchannel in presence of Lorentz force. To examine the electroosmosis mechanism, Poisson.Boltzmann equation is considered. To describe the rheological behavior of the fluids, a Phan-Thien-Tanner model is taken into account. The governing equations are simplified by using scaling analysis with low Reynolds number and large wavelength approximations. The set of non-linear partial differential equations are solved by regular perturbation technique to find out the series solutions for stream function, axial velocity and pressure gradient. Furthermore, the shear stress at the channel wall is derived. The graphical results for velocity, pressure gradient, stream lines and shear stress are illustrated using the in-house code written in Mathematica software. It is revealed that velocity field, shear stress and trapping phenomenon are strongly altered with EDL thickness, electric and magnetic fields. It is further concluded that rheological parameter i.e. Weissenberg number significantly affects the physical mechanisms. This model can be applicable in various complex systems where the rheological fluids can be transported by novel microfluidics peristaltic pumps.

Keywords:electroosmosis;peristaltic pumping;Phan-Thien-Tanner fluid;magnetic field;electric double layer;trapping

[References]

Aboubacar M, Matallah H, Webster MF, J. Non-Newton. Fluid Mech., 103(1), 65 (2002)
Afonso AM, Alves MA, Pinho FT, J. Eng. Math., 71, 15 (2011)
Akbar, Sher N, Nadeem S, Heat Transfer Asian Res., 41, 10 (2012)
Ali N, Hussain S, Ullah K, Phys. Fluids, 32, 023105 (2020)
Ali N, Hussain S, Ullah K, Beg OA, Eur. Phys. J. Plus, 134, 141 (2019)
Alves MA, Pinho FT, Oliveira PJ, J. Non-Newton. Fluid Mech., 101(1-3), 55 (2001)
Bohme G, Friedrich R, J. Fluid Mech., 128, 109 (1983)
Chaube MK, Yadav A, Tripathi D, J. Braz. Soc. Mech. Sci., 40, 423 (2018)
Chaube MK, Yadav A, Tripathi D, Beg OA, Korea-Aust. Rheol. J., 30, 89 (2018)
Cross MM, J. Colloid Sci., 20, 417 (1965)
Denn MM, Ann. Rev. Fluid Mech., 22, 13 (1990)
Dhinakaran S, Afonso AM, Alves MA, Pinho FT, J. Colloid Interface Sci., 344(2), 513 (2010)
Abd El Naby AEH, J. Appl. Mech., 76, 064504 (2009)
Escandon J, Santiago F, Bautista O, Mendez F, Int. J. Therm. Sci., 86, 246 (2014)
Ferras LL, Afonso AM, Alves MA, Nobrega JM, Pinho FT, Phys. Fluids, 28, 093102 (2016)
Ferras LL, Nobrega JM, Pinho FT, J. Non-Newton. Fluid Mech., 171, 97 (2012)
Ferry JD, Viscoelastic Properties of Polymers, Wiley NewYork 1980.
Ghosh U, Chakraborty S, Phys. Fluids, 27, 062004 (2015)
Glowinski R, Wachs A, In Handbook of Numerical Analysis 16, 483-717 2011.
Hayat T, Noreen S, Ali N, Abbasbanday S, Numer. Methods Partial Differ. Equ., 28, 737 (2012)
Hussain S, Ali N, Ullah K, Rheol. Acta, 58(9), 603 (2019)
Jayavel P, Jhorar R, Tripathi D, Azese MN, J. Braz. Soc. Mech. Sci. Eng., 41, 61 (2019)
Vajravelu K, Sreenadh S, Lakshminarayana P, Sucharitha G, Rashidi MM, J. Appl. Fluid Mech., 9, 1615 (2016)
Vajravelu K, Sreenadh S, Dhananjaya S, Lakshminarayana P, Int. J. of Appl. Mech. Eng., 21, 713 (2016)
Lauga E, Phys. Fluids, 19, 083104 (2007)
Mallick B, Misra JC, Eng. Sci. Technol., Int. J., 22, 266 2019.
Narla VK, Tripathi D, Microvasc. Res., 123, 25 (2019)
Narla VK, Tripathi D, Beg OA, J. Biomech. Eng., 141, 021003 (2019)
Oliveira PJ, Pinho FT, J. Fluid Mech., 387, 271 (1999)
Pinho FT, Oliveira PJ, Int. J. Heat Mass Transf., 43(13), 2273 (2000)
Steffe JF, Rheological methods in food process engineering, Freeman press, 1996.
Tanveer A, Khan M, Salahuddin T, Malik MY, Comput. Methods Programs Biomed., 180, 105005 (2019)
Teran J, Fauci L, Shelley M, Phys. Fluids, 20, 073101 (2008)
Tripathi D, Yadav A, Beg OA, Math. Biosci., 283, 155 (2017)
Tripathi D, Yadav A, Beg OA, Eur. Phys. J. Plus, 132, 173 (2017)
Tripathi D, Beg OA, Curiel-Sosa JL, Comput. Methods Biomech. Biomed. Engin., 17, 433 (2014)
Tripathi D, Pandey SK, Das S, Appl. Math. Comput., 215, 3645 (2010)
Waheed S, Noreen S, Tripathi D, Lu DC, J. Biol. Phys., 1-21 2020.
Yoon K, Jung HW, Chun MS, Korea-Aust. Rheol. J., 32(1), 61 (2020)
Zhao C, Yang C, Appl. Math. Comput., 211, 502 (2009)

[Referenced By]

[1] Aboubacar M, Matallah H, Webster MF, J. Non-Newton. Fluid Mech., 103(1), 65 (2002)

[2] Afonso AM, Alves MA, Pinho FT, J. Eng. Math., 71, 15 (2011)

[3] Akbar, Sher N, Nadeem S, Heat Transfer Asian Res., 41, 10 (2012)

[4] Ali N, Hussain S, Ullah K, Phys. Fluids, 32, 023105 (2020)

[5] Ali N, Hussain S, Ullah K, Beg OA, Eur. Phys. J. Plus, 134, 141 (2019)

[6] Alves MA, Pinho FT, Oliveira PJ, J. Non-Newton. Fluid Mech., 101(1-3), 55 (2001)

[7] Bohme G, Friedrich R, J. Fluid Mech., 128, 109 (1983)

[8] Chaube MK, Yadav A, Tripathi D, J. Braz. Soc. Mech. Sci., 40, 423 (2018)

[9] Chaube MK, Yadav A, Tripathi D, Beg OA, Korea-Aust. Rheol. J., 30, 89 (2018)

[10] Cross MM, J. Colloid Sci., 20, 417 (1965)

[11] Denn MM, Ann. Rev. Fluid Mech., 22, 13 (1990)

[12] Dhinakaran S, Afonso AM, Alves MA, Pinho FT, J. Colloid Interface Sci., 344(2), 513 (2010)

[13] Abd El Naby AEH, J. Appl. Mech., 76, 064504 (2009)

[14] Escandon J, Santiago F, Bautista O, Mendez F, Int. J. Therm. Sci., 86, 246 (2014)

[15] Ferras LL, Afonso AM, Alves MA, Nobrega JM, Pinho FT, Phys. Fluids, 28, 093102 (2016)

[16] Ferras LL, Nobrega JM, Pinho FT, J. Non-Newton. Fluid Mech., 171, 97 (2012)

[17] Ferry JD, Viscoelastic Properties of Polymers, Wiley NewYork 1980.

[18] Ghosh U, Chakraborty S, Phys. Fluids, 27, 062004 (2015)

[19] Glowinski R, Wachs A, In Handbook of Numerical Analysis 16, 483-717 2011.

[20] Hayat T, Noreen S, Ali N, Abbasbanday S, Numer. Methods Partial Differ. Equ., 28, 737 (2012)

[21] Hussain S, Ali N, Ullah K, Rheol. Acta, 58(9), 603 (2019)

[22] Jayavel P, Jhorar R, Tripathi D, Azese MN, J. Braz. Soc. Mech. Sci. Eng., 41, 61 (2019)

[23] Vajravelu K, Sreenadh S, Lakshminarayana P, Sucharitha G, Rashidi MM, J. Appl. Fluid Mech., 9, 1615 (2016)

[24] Vajravelu K, Sreenadh S, Dhananjaya S, Lakshminarayana P, Int. J. of Appl. Mech. Eng., 21, 713 (2016)

[25] Lauga E, Phys. Fluids, 19, 083104 (2007)

[26] Mallick B, Misra JC, Eng. Sci. Technol., Int. J., 22, 266 2019.

[27] Narla VK, Tripathi D, Microvasc. Res., 123, 25 (2019)

[28] Narla VK, Tripathi D, Beg OA, J. Biomech. Eng., 141, 021003 (2019)

[29] Oliveira PJ, Pinho FT, J. Fluid Mech., 387, 271 (1999)

[30] Pinho FT, Oliveira PJ, Int. J. Heat Mass Transf., 43(13), 2273 (2000)

[31] Steffe JF, Rheological methods in food process engineering, Freeman press, 1996.

[32] Tanveer A, Khan M, Salahuddin T, Malik MY, Comput. Methods Programs Biomed., 180, 105005 (2019)

[33] Teran J, Fauci L, Shelley M, Phys. Fluids, 20, 073101 (2008)

[34] Tripathi D, Yadav A, Beg OA, Math. Biosci., 283, 155 (2017)

[35] Tripathi D, Yadav A, Beg OA, Eur. Phys. J. Plus, 132, 173 (2017)

[36] Tripathi D, Beg OA, Curiel-Sosa JL, Comput. Methods Biomech. Biomed. Engin., 17, 433 (2014)

[37] Tripathi D, Pandey SK, Das S, Appl. Math. Comput., 215, 3645 (2010)

[38] Waheed S, Noreen S, Tripathi D, Lu DC, J. Biol. Phys., 1-21 2020.

[39] Yoon K, Jung HW, Chun MS, Korea-Aust. Rheol. J., 32(1), 61 (2020)

[40] Zhao C, Yang C, Appl. Math. Comput., 211, 502 (2009)