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The upper fluid is conducting, while the lower fluid is nonconducting. This analysis is performed under the Debye\u2013H\u00fcckel approximation, utilizing perturbation expansion and the separation of variables. The potential distribution, velocity field, and the dependence of average velocity on roughness are derived. It is observed that the velocity distribution w(x, y), is significantly influenced by the phase difference \u03b8 between the corrugations on the upper and lower walls. The velocity w(x, y) decreases with an increase in the viscosity ratio \u03bcr of the bottom to top fluid, and w(x, y) is directly proportional to the dimensionless pressure gradient G and the zeta potential ratio \u03b6. The variation of the average velocity increment (roughness function) u2m related to wall roughness tends to decrease with the increase of the corrugation wave number \u03bb, the electrokinetic width K, the depth ratio hr of the bottom to top fluid, the zeta potential ratio \u03b6 and the dimensionless pressure gradient G; and increases with the increase of the viscosity ratio \u03bcr of the bottom to top fluid. Furthermore, the effect of uI2m is smaller than that of uII2m.<\/jats:p>","DOI":"10.3390\/mi15111315","type":"journal-article","created":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T10:45:35Z","timestamp":1730198735000},"page":"1315","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Two-Layer Electroosmotic Flow in a Parallel Plate Microchannel with Sinusoidal Corrugation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-6851-8295","authenticated-orcid":false,"given":"Long","family":"Chang","sequence":"first","affiliation":[{"name":"School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010071, China"},{"name":"School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3106-0976","authenticated-orcid":false,"given":"Mandula","family":"Buren","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Inner Mongolia Normal University, Hohhot 010022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Geming","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanjun","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010071, China"},{"name":"School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongjun","family":"Jian","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Donghua University, Shanghai 201620, China"},{"name":"Institute for Nonlinear Science, Donghua University, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1146\/annurev.fluid.36.050802.122124","article-title":"Engineering flows in small devices: Microfluidics toward a lab-on-a-chip","volume":"36","author":"Stone","year":"2004","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1016\/j.ijheatmasstransfer.2005.11.007","article-title":"Characterization of liquid flows in microfluidic systems","volume":"49","author":"Bayraktar","year":"2006","journal-title":"Int. J. Heat Mass Tran."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"032013","DOI":"10.1063\/5.0080107","article-title":"Analytical study of two-layered mixed electro-osmotic and pressure-driven flow and heat transfer in a microchannel with hydrodynamic slippage and asymmetric wall heating","volume":"34","author":"Banerjee","year":"2022","journal-title":"Phys. Fluids"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"042001","DOI":"10.1063\/1.3358473","article-title":"Time periodic electro-osmotic flow through a microannulus","volume":"22","author":"Jian","year":"2010","journal-title":"Phys. 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Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1016\/j.jnnfm.2011.02.003","article-title":"Time periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates","volume":"166","author":"Liu","year":"2011","journal-title":"J. Non-Newton. Fluid Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"102001","DOI":"10.1063\/1.3640082","article-title":"Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel","volume":"23","author":"Liu","year":"2011","journal-title":"Phys. Fluids"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2895","DOI":"10.1039\/D3CP05184F","article-title":"Ion current rectification properties of non-Newtonian fluids in conical nanochannels","volume":"26","author":"Tang","year":"2024","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"11","DOI":"10.21303\/2461-4262.2024.003050","article-title":"A rheophysical study of the non-newtonian behavior of water flow in thin channels","volume":"1","author":"Veliyev","year":"2024","journal-title":"EUREKA Phys. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.jelechem.2009.09.015","article-title":"Modeling of electroosmotic pumping of nonconducting liquids and biofluids by a two-phase flow method","volume":"636","author":"Liu","year":"2009","journal-title":"J. Electroanal. Chem."},{"key":"ref_13","first-page":"190","article-title":"Electroosmotic pumping of nonconducting liquids by viscous drag from a secondary conducting liquid","volume":"1","author":"Brask","year":"2003","journal-title":"Tech. Proc. Nanotech."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.jcis.2012.12.013","article-title":"Analytical solution of two-fluid electro-osmotic flows of viscoelastic fluids","volume":"395","author":"Afonso","year":"2013","journal-title":"J. Colloid Interf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.electacta.2012.09.021","article-title":"Experimental validation of induced-charge electrokinetic motion of electrically conducting particles","volume":"87","author":"Daghighi","year":"2013","journal-title":"Electrochim. Acta"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"012011","DOI":"10.1063\/1.5134878","article-title":"Electrokinetic transport of a non-conducting liquid droplet in a polyelectrolyte medium","volume":"32","author":"Barman","year":"2020","journal-title":"Phys. Fluids"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.jcis.2004.10.011","article-title":"Two-fluid electroosmotic flow in microchannels","volume":"284","author":"Gao","year":"2005","journal-title":"J. Colloid Interf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1088\/0960-1317\/17\/2\/023","article-title":"Electro-osmotic control of the interface position of two-liquid flow through a microchannel","volume":"17","author":"Gao","year":"2007","journal-title":"J. Micromech. Microeng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Alyousef, H.A., Yasmin, H., Shah, R., Shah, N.A., El-Sherif, L.S., and El-Tantawy, S.A. (2023). Mathematical Modeling and Analysis of the Steady Electro-Osmotic Flow of Two Immiscible Fluids: A Biomedical Application. Coatings, 13.","DOI":"10.3390\/coatings13010115"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1007\/s40430-019-1702-2","article-title":"AC two-immiscible-fluid EOF in a microcapillary","volume":"41","author":"Moghadam","year":"2019","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1002\/elps.201500457","article-title":"Electroosmotic transport of immiscible binary system with a layer of non-conducting fluid under interfacial slip: The role applied pressure gradient","volume":"37","author":"Gaikwad","year":"2016","journal-title":"Electrophoresis"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Deng, S., and Xiao, T. (2022). Transient Two-Layer Electroosmotic Flow and Heat Transfer of Power-Law Nanofluids in a Microchannel. Micromachines, 13.","DOI":"10.3390\/mi13030405"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1115\/1.3424575","article-title":"On Stokes flow between corrugated plates","volume":"46","author":"Wang","year":"1979","journal-title":"J. Appl. Mech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1088\/0022-3727\/33\/6\/307","article-title":"Slip flow in an annulus with corrugated walls","volume":"33","author":"Chu","year":"2000","journal-title":"J. Phys. D-Appl. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s10404-008-0290-8","article-title":"Electroosmotically driven creeping flows in a wavy microchannel","volume":"6","author":"Xia","year":"2009","journal-title":"Microfluid. Nanofluidics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.jnnfm.2012.01.012","article-title":"Electrokinetically-driven non-Newtonian fluid flow in rough microchannel with complex-wavy surface","volume":"173","author":"Cho","year":"2012","journal-title":"J. Non-Newton. Fluid Mech."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.ijthermalsci.2012.06.008","article-title":"Characteristics of combined electroosmotic flow and pressure-driven flow in microchannels with complex-wavy surfaces","volume":"61","author":"Cho","year":"2012","journal-title":"Int. J. Therm. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"021301","DOI":"10.1115\/1.4023441","article-title":"Characteristics of transient electroosmotic flow in microchannels with complex-wavy surface and periodic time-varying electric field","volume":"135","author":"Cho","year":"2013","journal-title":"J. Fluids Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.compfluid.2015.05.001","article-title":"Analysis of electro-osmotic flow in a microchannel with undulated surfaces","volume":"124","author":"Yoshida","year":"2016","journal-title":"Comput. Fluids"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"082001","DOI":"10.1063\/1.3467035","article-title":"Electro-osmotic flow in a wavy microchannel: Coherence between the electric potential and the wall shape function","volume":"22","author":"Shu","year":"2010","journal-title":"Phys. Fluids"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.molliq.2016.04.054","article-title":"Electroosmotic flow through a microtube with sinusoidal roughness","volume":"220","author":"Chang","year":"2016","journal-title":"J. Mol. Liq."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.ijheatmasstransfer.2015.08.089","article-title":"Analytical solutions for thermo-fluidic transport in electroosmotic flow through rough microtubes","volume":"92","author":"Keramati","year":"2016","journal-title":"Int. J. Heat Mass Tran."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"144503","DOI":"10.1103\/PhysRevLett.105.144503","article-title":"Suppression of electro-osmotic flow by surface roughness","volume":"105","author":"Messinger","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1007\/s11012-020-01257-4","article-title":"Numerical analysis of the effects of roughness on the electro-osmotic laminar flow between two parallel plates","volume":"56","author":"Fakhari","year":"2021","journal-title":"Meccanica"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Chang, L., Zhao, G., Buren, M., Sun, Y., and Jian, Y. (2024). Alternating Current Electroosmotic Flow of Maxwell Fluid in a Parallel Plate Microchannel with Sinusoidal Roughness. Micromachines, 15.","DOI":"10.3390\/mi15111315"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Mehta, S.K., Padhi, P., Wongwises, S., and Mondal, P.K. (2024). Second law analysis: Electrically actuated flow of non-Newtonian fluids in wavy microchannels. Microsyst. Technol.","DOI":"10.1007\/s00542-024-05744-6"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"114979","DOI":"10.1016\/j.applthermaleng.2020.114979","article-title":"Mixing and heat transfer in micro\/nano-channel due to charged corrugated surfaces","volume":"170","author":"Nayak","year":"2020","journal-title":"Appl. Therm. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"092016","DOI":"10.1063\/5.0226494","article-title":"Electrokinetic flow and energy conversion induced by streaming potential in nanochannels with symmetric corrugated walls","volume":"36","author":"Xie","year":"2024","journal-title":"Phys. Fluids"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Maher, M., Mekheimer, K.S., Al-Wahsh, H., and Zaher, A. (2024). Hydrodynamic impact of dusty fluid-suspended solid particles in a single-walled corrugated channel for water-curing infrastructure networks. Chin. J. Phys.","DOI":"10.1016\/j.cjph.2024.08.014"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"100412","DOI":"10.1016\/j.ceja.2022.100412","article-title":"EDL impact on mixed magneto-convection in a vertical channel using ternary hybrid nanofluid","volume":"12","author":"Das","year":"2022","journal-title":"Chem. Eng. J. Adv."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Ma, N., Sun, Y., and Jian, Y. (2023). Electromagnetohydrodynamic (EMHD) flow in a microchannel with random surface roughness. Micromachines, 14.","DOI":"10.3390\/mi14081617"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Wang, Z., Sun, Y., and Jian, Y. (2023). The effect of random roughness on the electromagnetic flow in a micropipe. Micromachines, 14.","DOI":"10.3390\/mi14112054"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"106106","DOI":"10.1016\/j.icheatmasstransfer.2022.106106","article-title":"Heat transfer enhancement for microchannel heat sink by strengthening fluids mixing with backward right-angled trapezoidal grooves in channel side walls","volume":"135","author":"Zhu","year":"2022","journal-title":"Int. Commun. Heat Mass Tran."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1080\/10407782.2022.2083840","article-title":"Performance improvement of rectangular microchannel heat sinks using nanofluids and wavy channels","volume":"82","author":"Mohammadi","year":"2022","journal-title":"Numer. Heat Tr. A-Appl."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Qing, Y., Wang, J., and Li, F. (2024). Electro-Osmotic Flow and Mass Transfer through a Rough Microchannel with a Modulated Charged Surface. Micromachines, 15.","DOI":"10.3390\/mi15070882"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/0377-0257(95)01347-X","article-title":"An experimental investigation of the flow of dilute polymer solutions through corrugated channels","volume":"58","author":"Yalamanchili","year":"1995","journal-title":"J. Non-Newton. Fluid Mech."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1016\/S0017-9310(98)00264-6","article-title":"An experimental study of flow and heat transfer in sinusoidal wavy passages","volume":"42","author":"Rush","year":"1999","journal-title":"Int. J. Heat Mass Tran."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"065018","DOI":"10.1088\/0960-1317\/24\/6\/065018","article-title":"Experimental and CFD modeling of fluid mixing in sinusoidal microchannels with different phase shift between side walls","volume":"24","author":"Parsa","year":"2014","journal-title":"J.Micromech Microeng."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"055003","DOI":"10.1088\/1361-6439\/aaad46","article-title":"An experimental study on flow friction and heat transfer of water in sinusoidal wavy silicon microchannels","volume":"28","author":"Huang","year":"2018","journal-title":"J. Micromech. Microeng."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Hiemenz, P.C., and Rajagopalan, R. (2016). Principles of Colloid and Surface Chemistry, Revised and Expanded, CRC Press.","DOI":"10.1201\/9781315274287"}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/15\/11\/1315\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:23:20Z","timestamp":1760113400000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/15\/11\/1315"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,29]]},"references-count":50,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["mi15111315"],"URL":"https:\/\/doi.org\/10.3390\/mi15111315","relation":{},"ISSN":["2072-666X"],"issn-type":[{"value":"2072-666X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,29]]}}}