Abstract
To simulate the mass separation or mixture for chemical or biological fluids with viscoelastic characteristics, the rotating electroosmotic flow (EOF) of two-layer fluid in a microchannel with parallel plates is studied. This system is composed of Newtonian fluid and Caputo fractional Oldroyd-B fluid. Maxwell stress is introduced to describe the interaction of two fluids at the interface as well as the shear stress. Based on L1 approximation, numerical solutions are obtained by the finite difference method. The results show that mainstream velocity will oscillate first and then reach a stable state as there is enough time. Due to the existence of centrifugal force, mainstream velocity will increase with the increasing rotating angular velocity. Furthermore, the minimum value of velocity does not lie at the middle of channel because of viscoelastic effects, and the position where reverse flow appears also is pushed to the right side of the center when the rotating angular velocity is large enough. Moreover, with the increase of the interfacial zeta potential difference, the velocity distributions of two-layer fluid have different trends.
Similar content being viewed by others
References
Alshammari FS, Akyildiz FT (2020) Pseudo spectral solution of extended Graetz problem for combined pressure-driven and electroosmotic flow in a triangular micro-duct. Comput Math Appl 80(5):990–1008
Bown MR, Meinhart CD (2006) AC electroosmotic flow in a DNA concentrator. Microfluid Nanofluid 2(6):513–523
Cao LM, Zhang PP, Li BT et al (2021) Numerical study of rotating electro-osmotic flow of double layers with a layer of fractional second-order fluid in a microchannel. Appl Math Lett 111:106633
Chang CC, Wang CY (2011) Rotating electro-osmotic flow over a plate or between two plates. Phys Rev E Statale 84(5 Pt 2):056320
Chaube MK, Yadav A, Tripathi D et al (2018) Electroosmotic flow of biorheological micropolar fluids through microfluidic channels. Korea-Austral Rheol J 30(2):89–98
Das S, Das T, Chakraborty S (2005) Analytical solutions for the rate of DNA hybridization in a microchannel in the presence of pressure-driven and electroosmotic flows. Sens Actuators B 114(2):957–963
Deng SY, Xiao T, Wu SM (2021) Two-layer combined electroosmotic and pressure-driven flow of power-law fluids in a circular microcapillary. Colloids Surf A 610:125727
Ermakov SV, Jacobson SC, Ramsey JM (1998) Ramsey, computer simulations of electrokinetic transport in microfabricated channel structures. Anal Chem 70(21):4494–4504
Fetecau C, Fetecau C, Kamran M et al (2009) Exact solutions for the flow of a generalized Oldroyd-B fluid induced by a constantly accelerating plate between two side walls perpendicular to the plate. J Nonnewton Fluid Mech 156(3):189–201
Gallardo BS, Gupta VK, Eagerton FD (1999) Electrochemical principles for active control of liquids on submillimeter scales. Science 283:57–60
Hoshyargar V, Talebi M, Ashrafzadeh SN et al (2018) Hydrodynamic dispersion by electroosmotic flow of viscoelastic fluids within a slit microchannel. Microfluid Nanofluid 22(1):1–15
Hu Y, Xuan X, Werner C et al (2007) Electroosmotic flow in microchannels with prismatic elements. Microfluid Nanofluid 3(2):151–160
Jian YJ, Su J, Chang L (2014) Transient electroosmotic flow of general Maxwell fluids through a slit microchannel. Z Angew Math Phys 65(3):435–447
Jiang Y, Qi H, Xu H et al (2017) Transient electroosmotic slip flow of fractional Oldroyd-B fluids. Microfluid Nanofluid 21(1):1–10
Kaushik P, Mondal PK, Chakraborty S (2017) Rotational electrohydrodynamics of a non-Newtonian fluid under electrical double-layer phenomenon: the role of lateral confnement. Microfluid Nanofluid 21(7):1–16
Kaushik P, Abhimanyu P, Mondal PK et al (2017) Confinement effects on the rotational microflows of a viscoelastic fluid under electrical double layer phenomenon. J Nonnewton Fluid Mech 244:123–137
Khan M, Farooq A, Khan WA et al (2016) Exact solution of an electroosmotic flow for generalized Burgers fluid in cylindrical domain. Results Phys 6(C):933–939
Li SX, Jian YJ, Xie ZY et al (2015) Rotating electro-osmotic flow of third grade fluids between two microparallel plates. Colloids Surf A 470:240–247
Liang PC, Wang SW, Zhao ML (2020) Numerical study of rotating electroosmotic flow of Oldroyd-B fluid in a microchannel with slip boundary condition. Chin J Phys 65:459–471
Liu F, Zhuang P, Anh V et al (2006) Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. Appl Math Comput 191(1):12–20
Mahmood A, Fetecau C, Fetecau C et al (2008) Some exact solutions for the helical flow of a generalized Oldroyd-B fluid in a circular cylinder. Comput Math Appl 56(12):3096–3108
Martínez L, Bautista O, Escandón J et al (2016) Electroosmotic flow of a Phan-Thien-Tanner fluid in a wavy-wall microchannel. Colloids Surf A 498:7–19
Ngoma GD, Erchiqui F, Sinha A et al (2006) Pressure gradient and electroosmotic effects on two immiscible fluids in a microchannel between two parallel plates. J Micromech Microeng 16:83–91
Patel M, Kruthiventi S, Kaushik P (2020) Rotating electroosmotic flow of power-law fluid through polyelectrolyte grafted microchannel. Colloids Surf B 193:111058
Patel M, Kruthiventi S, Kaushik P (2021) Polyelectrolyte layer grafting effect on the rotational electroosmotic flow of viscoplastic material. Microfluid Nanofluid 25(2):1–20
Qi C, Ng CO (2017) Rotating electroosmotic flow of viscoplastic material between two parallel plates. Colloids Surf A 513:355–366
Qi C, Ng CO (2018) Rotating electroosmotic flow in a non-uniform microchannel. Meccanica 53:2105–2120
Qi HT, Xu MY (2007) Stokes’ first problem for a viscoelastic fluid with the generalized Oldroyd-B model. Acta Mech Sin 23(05):463–469
Ren Y, Leung WF (2013) Flow and mixing in rotating zigzag microchannel. Chem Eng J 215–216:561–578
Shit GC, Mondal A, Sinha A et al (2016) Two-layer electro-osmotic flow and heat transfer in a hydrophobic micro-channel with fluid-solid interfacial slip and zeta potential difference. Colloids Surf A 506:535–549
Shit GC, Mondal A, Sinha A et al (2016) Two-layer electro-osmotic flow and heat transfer in a hydrophobic micro-channel with fluid-solid interfacial slip and zeta potential difference. Colloids Surf A 506:535–549
Singhal V, Garimella SV, Raman A (2004) Microscale pumping technologies for microchannel cooling systems. Appl Mech Rev 57(3):191–221
Stone HA, Stroock AD, Ajdari A (2004) Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu Rev Fluid Mech 36:381–411
Su J, Jian YJ, Chang L et al (2013) Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel. Acta Mech Sin 29(4):534–542
Tong DK, Zhang XM, Zhang XH (2009) Unsteady helical flows of a generalized Oldroyd-B fluid. J Nonnewton Fluid Mech 156(1–2):75–83
Wang X, Qi H, Yu B et al (2017) Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids. Commun Nonlinear Sci Numer Simul 50:77–87
Wang XP, Xu HY, Qi HT (2020) Numerical analysis for rotating electro-osmotic flow of fractional Maxwell fluids. Appl Math Lett 103:106179
Xie ZY, Jian YJ (2014) Rotating electroosmotic flow of power-law fluids at high zeta potentials. Colloids Surf A 461:231–239
Zheng JX, Jian YJ (2018) Rotating electroosmotic flow of two-layer fluids through a microparallel channel. Int J Mech Sci 136:293–302
Acknowledgements
This work is supported by National Natural Science Foundation of China (No. 12072024).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Cao, L., Zhang, P. & Si, X. Electroosmotic flow of two-layer fluid containing Oldroyd-B fluid with fractional derivative in a rotating microparallel channel. Microfluid Nanofluid 26, 34 (2022). https://doi.org/10.1007/s10404-022-02539-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10404-022-02539-x