ORIGINAL PAPER
Complex cilia electroosmotic modulated flow analysis with rheology of fractional-order fluid model
Shagufta Ijaz,
Hina Sadaf,
Corresponding Author
Shagufta Ijaz
Department of Mathematics, Faculty of Sciences, Rawalpindi Women University, Rawalpindi, Pakistan
Correspondence
Shagufta Ijaz, Department of Mathematics, Faculty of Sciences, Rawalpindi Women University, Rawalpindi 44400, Pakistan.
Email: [email protected]
Search for more papers by this authorHina Sadaf
DBS&H, CEME, National University of Sciences and Technology, Islamabad, Pakistan
Search for more papers by this authorShagufta Ijaz,
Hina Sadaf,
Corresponding Author
Shagufta Ijaz
Department of Mathematics, Faculty of Sciences, Rawalpindi Women University, Rawalpindi, Pakistan
Correspondence
Shagufta Ijaz, Department of Mathematics, Faculty of Sciences, Rawalpindi Women University, Rawalpindi 44400, Pakistan.
Email: [email protected]
Search for more papers by this authorHina Sadaf
DBS&H, CEME, National University of Sciences and Technology, Islamabad, Pakistan
Search for more papers by this authorFirst published: 08 May 2025
Abstract
In this paper, we look at a fractional second order fluid model that simulates flow transfer in an electroosmotic channel caused by complex cilia. The effects of heat absorption and viscous dissipation with velocity and convective conditions are also studied. By using appropriate variables, the equations that drive the flow analysis have been converted into non-dimensional form, and the equations are simplified by using longer wavelengths and low Reynolds number concessions. For velocity and temperature distribution, exact solutions are established, and graphs for velocity, temperature, pressure rise, pressure gradient, and stream function are plotted and described for important physical parameters. The output of the current model has significant applications in biological transport processes, artificial cilia structure, and the operation of other mechanical components.
REFERENCES
- 1Christensen, S.T., Pedersen, L.B., Schneider, L., Satir, P.: Sensory cilia and integration of signal transduction in human health and disease. Traffic 8(2), 97–109 (2007)
- 2Eggenschwiler, J.T., Anderson, K.V.: Cilia and developmental signaling. Annu. Rev. Cell Dev. Biol. 23(1), 345–373 (2007)
- 3Ibanez-Tallon, I., Heintz, N., Omran, H.: To beat or not to beat: Roles of cilia in development and disease. Hum. Mol. Genet. 12(l_1), R27–R35.
- 4Davis, E.E., Brueckner, M., Katsanis, N.: The emerging complexity of the vertebrate cilium: New functional roles for an ancient organelle. Dev. Cell. 11(1), 9–19 (2006)
- 5Shapiro, O.H., Fernandez, V.I., Garren, M., Guasto, J.S., Debaillon-Vesque, F.P., Kramarsky-Winter, E., Vardi, A., Stocker, R.: Vortical ciliary flows actively enhance mass transport in reef corals. Proc. Natl. Acad. Sci. 111, 13391–13396 (2014)
- 6Ben, S., Yao, J.J., Ning, Y.Z., Zhao, Z.H., Zha, J.L., Tian, D.L., Liu, K.S., Jiang, L.: A bioinspired magnetic responsive cilia array surface for microspheres underwater directional transport. Sci. China-Chem 63, 347–353 (2020)
- 7Lim, D., Lahooti, M., Kim, D.: Inertia-driven flow symmetry breaking by oscillating plates. AIP Adv. 9, 105119 (2019)
- 8Chateau, S., Favier, J., Poncet, S., D'Ortona, U.: Why antiplectic metachronal cilia waves are optimal to transport bronchial mucus. Phys. Rev. E 100, 042405 (2019)
- 9Sahadevan, V., Panigrahi, B., Chen, C.Y.: Microfluidic applications of artificial cilia: Recent progress, demonstration, and future perspectives. Micromachines 13(5), 735 (2022)
- 10Khaderi, S.N., den Toonder, J.M., Onck, P.R.: Magnetic artificial cilia for microfluidic propulsion. Appl. Mech. 48, 1–78 (2015)
- 11Sadaf, H., Ijaz, S.: Complex wave's impact on the cilia-generated flow in a vertical tube with an endoscope. Waves Random Complex Media 1–15 (2022). https://doi.org/10.1080/17455030.2022.2152902
- 12Sadaf, H., Asghar, Z., Iftikhar, N.: Cilia-driven flow analysis of cross fluid model in a horizontal channel. Comput. Part. Mech. 10, 943–950 (2023)
- 13Ijaz, S., Nasir, N., Sadaf, H., Mehmood, R.: Biomechanics of cilia-assisted flow with hybrid nanofluid phenomena impulses by convective conditions. Waves Random Complex Media 1–25 (2022). https://doi.org/10.1080/17455030.2022.2085344
- 14Sadaf, H., Nadeem, S.: Fluid flow analysis of cilia beating in a curved channel in the presence of magnetic field and heat transfer. Can. J. Phys. 98(2), 191–197 (2020)
- 15Kada, B., Pasha, A.A., Asghar, Z., Khan, M.W.S., Aris, I.B., Shaikh, M.S.: Carreau–Yasuda fluid flow generated via metachronal waves of cilia in a micro-channel. Phys. Fluids 35, 013110 (2023)
- 16Wu, A., Abbas, S.Z., Asghar, Z., Sun, H., Waqas, M., Khan, W.A.: A shear-rate-dependent flow generated via magnetically controlled metachronal motion of artificial cilia. Biomech. Model. Mechanobiol. 19, 1713–1724 (2020)
- 17Tanveer, A., Mahmood, S.: Electroosmosis peristaltic flow with the domination of internal and activation energies for non-Newtonian fluid. Waves Random Complex Media 1–13 (2022). https://doi.org/10.1080/17455030.2022.2088886
- 18Khan, A.A., Zahra, B., Ellahi, R., Sait, S.M.: Analytical solutions of peristalsis flow of non-Newtonian Williamson fluid in a curved micro-channel under the effects of electro-osmotic and entropy generation. Symmetry 15(4), 889 (2023)
- 19Ijaz, S., Abdullah, M., Sadaf, H., Nadeem, S.: Generalized complex cilia tip modeled flow through an electroosmotic region. J. Cent. South. Univ. 30(4), 1217–1230 (2023)
- 20Tripathi, D., Jhorar, R., Anwar Bég, O., Shaw, S.: Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: Mathematical model. Meccanica 53, 2079–2090 (2018)
- 21Jayavel, P., Jhorar, R., Tripathi, D., et al.: Electroosmotic flow of pseudoplastic nanoliquids via peristaltic pumping. J. Braz. Soc. Mech. Sci. Eng. 41(2), 61 (2019)
- 22Ramesh, K., Tripathi, D., Bhatti, M.M., Khalique, C.M.: Electro-osmotic flow of hydromagnetic dusty viscoelastic fluids in a microchannel propagated by peristalsis. J. Mol. Liq. 314, 113568 (2020)
- 23Ijaz, S., Sadaf, H.: Electro-osmotically generalized bio-rheological fluid flowing through a ciliated passage. Mater. Sci. Eng. B 290, 116340 (2023)
10.1016/j.mseb.2023.116340 Google Scholar
- 24Kumar, M., Mondal, P.K.: Electrically actuated peristaltic transport of viscoelastic fluid: A theoretical analysis. Microfluid. Nanofluid. 28, 49 (2024). https://doi.org/10.1007/s10404-024-02742-y
- 25Mehta, S.K., Bhushan, P., Mondal, P.K., Wongwises, S.: Insight into the electroosmotic vortex modulated reaction characteristics of viscoplastic fluids. Phys. Fluids 36, 073106 (2024)
- 26Kumar, M., Mondal, P.K.: Leveraging perturbation method for the analysis of field-driven microflow of Carreau fluid. Microfluid. Nanofluid. 27(8), 51 (2023)
- 27Balasubramanian, S., Kaushik, P., Mondal, P.K.: Dynamics of viscoelastic fluid in a rotating soft microchannel. Phys. Fluids 32, 112003 (2020)
- 28Goswami, P., Kumar Mondal, P., Dutta, S., Chakraborty, S.: Electroosmosis of Powell–Eyring fluids under interfacial slip. Electrophoresis 36(5), 703–711 (2015)
- 29Dutta, S., Mondal, P.K., Goswami, P.: Slipping hydrodynamics of Powell–Eyring fluid in a cylindrical microchannel under electrical double layer phenomenon. Phys. Scr. 94(2), 025002 (2019)
- 30Mehta, S.K., Mondal, P.K.: Vortex-assisted electroosmotic mixing of Carreau fluid in a microchannel. Electrophoresis 44(21–22), 1629–1636 (2023)
- 31Tabassum, R., Al-Zubaidi, A., Rana, S., Mehmood, R., Saleem, S.: Slanting transport of hybrid (MWCNTs-SWCNTs/H2O) nanofluid upon a Riga plate with temperature dependent viscosity and thermal jump condition. Int. Commun. Heat Mass Transf. 135, 106165 (2022)
- 32Sarma, R., Deka, N., Sarma, K., Mondal, P.K.: Electroosmotic flow of Phan-Thien–Tanner fluids at high zeta potentials: An exact analytical solution. Phys. Fluids 30, 062001 (2018)
- 33Siva, T., Kumbhakar, B., Jangili, S., Mondal, P.K.: Unsteady electro-osmotic flow of couple stress fluid in a rotating microchannel: An analytical solution. Phys. Fluids 32, 102013 (2020)
- 34Gaikwad, H.S., Baghel, P., Sarma, R., Mondal, P.K.: Transport of neutral solutes in a viscoelastic solvent through a porous microchannel. Phys. Fluids 31(2), 022006 (2019)
- 35Gaikwad, H.S., Mondal, P.K., Wongwises, S.: Softness induced enhancement in net throughput of non-linear bio-fluids in nanofluidic channel under EDL phenomenon. Sci. Rep. 8(1), 7893 (2018)
- 36Mondal, P.K., DasGupta, D., Chakraborty, S.: Rheology-modulated contact line dynamics of an immiscible binary system under electrical double layer phenomena. Soft Matter 11(33), 6692–6702 (2015)
- 37Wenchang, T., Wenxiao, P., Mingyu, X.: A note on unsteady flows of a viscoelastic fluid with the Maxwell model between two parallel plates. Int. J. Non Linear Mech. 38(5), 645–650 (2003)
10.1016/S0020-7462(01)00121-4 Google Scholar
- 38Arshad, S., Sohail, A., Maqbool, K.: Nonlinear shallow water waves: A fractional order approach. Alex. Eng. J. 55, 525–532 (2016)
- 39Yang, D.I., Zhu, K.Q.: Start-up flow of a viscoelastic fluid in a pipe with fractional Maxwell's model. Comput. Math. Appl. 60, 2231–2238 (2010)
- 40Maqbool, K., Beg, O.A., Sohail, A.: Analytical solutions for wall slip effects on magnetohydrodynamic oscillatory rotating plate and channel flows in porous media using a fractional Burgers' viscoelastic model. Eur. Phys. J. Plus 131, 140 (2016)
- 41Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)
- 42Maqbool, K., Mann, A.B., Siddiqui, A.M., Shaheen, S.: Fractional generalized Burgers' fluid flow due to metachronal waves of cilia in an inclined tube. Adv. Mech. Eng. 9(8), 1687814017715565 (2017)
- 43Momani, S., Odibat, Z.: Analytical solution of a time-fractional Navier–Stokes equation by Adomian decomposition method. Appl. Math. Comput. 177(2), 488–494 (2006)
- 44Akram, J., Mehmood, R.: Electroosmotically assisted peristaltic propulsion of blood-based hybrid nanofluid through an endoscope with activation energy. Int. Commun. Heat Mass Transf. 159, 108190 (2024)
- 45Ajmal, M., Mehmood, R., Akbar, N.S., Muhammad, T.: Electroosmotic base magnetic field study of peristaltic transport in a non-uniform wavy ciliated channel for Williamson fluid with enhancing nanoparticles. J. Appl. Math. Mech. 104(12), e202400296 (2024)
10.1002/zamm.202400296 Google Scholar
- 46Ajmal, M., Mehmood, R., Akbar, N.S., Muhammad, T.: Computational study on cilia transport of Prandtl nanofluid (blood-Fe3O4) enhancing convective heat transfer along microorganisms under electroosmotic effects in wavy capillaries. Int. J. Numer. Methods Heat Fluid Flow (2024). https://doi.org/10.1108/HFF-07-2024-0503
- 47Tripathi, D.: Peristaltic flow of a fractional second grade fluid through a cylindrical tube. Therm. Sci. 15, 167–173 (2011)
- 48Sadaf, H., Ijaz, S.: Complex wave's impact on the cilia-generated flow in a vertical tube with an endoscope. Waves Random Complex Media 1–15 (2022). http://doi.org/10.1080/17455030.2022.2152902
