Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel
In this investigation, the transient electroosmotic flow of multi-layer immiscible viscoelastic fluids in a slit microchannel is studied. Through an appropriate combination of the momentum equation with the rheological model for Maxwell fluids, an hyperbolic partial differential equation is obtained...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/11/8/757 |
| _version_ | 1797560269512114176 |
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| author | Juan Escandón David Torres Clara Hernández René Vargas |
| author_facet | Juan Escandón David Torres Clara Hernández René Vargas |
| author_sort | Juan Escandón |
| collection | DOAJ |
| description | In this investigation, the transient electroosmotic flow of multi-layer immiscible viscoelastic fluids in a slit microchannel is studied. Through an appropriate combination of the momentum equation with the rheological model for Maxwell fluids, an hyperbolic partial differential equation is obtained and semi-analytically solved by using the Laplace transform method to describe the velocity field. In the solution process, different electrostatic conditions and electro-viscous stresses have to be considered in the liquid-liquid interfaces due to the transported fluids content buffer solutions based on symmetrical electrolytes. By adopting a dimensionless mathematical model for the governing and constitutive equations, certain dimensionless parameters that control the start-up of electroosmotic flow appear, as the viscosity ratios, dielectric permittivity ratios, the density ratios, the relaxation times, the electrokinetic parameters and the potential differences. In the results, it is shown that the velocity exhibits an oscillatory behavior in the transient regime as a consequence of the competition between the viscous and elastic forces; also, the flow field is affected by the electrostatic conditions at the liquid-liquid interfaces, producing steep velocity gradients, and finally, the time to reach the steady-state is strongly dependent on the relaxation times, viscosity ratios and the number of fluid layers. |
| first_indexed | 2024-03-10T17:57:06Z |
| format | Article |
| id | doaj.art-87a828b6867045af92b5b6d31e91c3b8 |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-10T17:57:06Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-87a828b6867045af92b5b6d31e91c3b82023-11-20T09:09:01ZengMDPI AGMicromachines2072-666X2020-08-0111875710.3390/mi11080757Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit MicrochannelJuan Escandón0David Torres1Clara Hernández2René Vargas3Instituto Politécnico Nacional, SEPI-ESIME Azcapotzalco, Departamento de Termofluidos, Av. de las Granjas No. 682, Col. Santa Catarina, Alcaldía Azcapotzalco, Ciudad de México 02250, MexicoInstituto Politécnico Nacional, SEPI-ESIME Azcapotzalco, Departamento de Termofluidos, Av. de las Granjas No. 682, Col. Santa Catarina, Alcaldía Azcapotzalco, Ciudad de México 02250, MexicoUniversidad Tecnológica de México -UNITEC MÉXICO- Campus Marina-Cuitláhuac, Ciudad de México 02870, MexicoInstituto Politécnico Nacional, SEPI-ESIME Azcapotzalco, Departamento de Termofluidos, Av. de las Granjas No. 682, Col. Santa Catarina, Alcaldía Azcapotzalco, Ciudad de México 02250, MexicoIn this investigation, the transient electroosmotic flow of multi-layer immiscible viscoelastic fluids in a slit microchannel is studied. Through an appropriate combination of the momentum equation with the rheological model for Maxwell fluids, an hyperbolic partial differential equation is obtained and semi-analytically solved by using the Laplace transform method to describe the velocity field. In the solution process, different electrostatic conditions and electro-viscous stresses have to be considered in the liquid-liquid interfaces due to the transported fluids content buffer solutions based on symmetrical electrolytes. By adopting a dimensionless mathematical model for the governing and constitutive equations, certain dimensionless parameters that control the start-up of electroosmotic flow appear, as the viscosity ratios, dielectric permittivity ratios, the density ratios, the relaxation times, the electrokinetic parameters and the potential differences. In the results, it is shown that the velocity exhibits an oscillatory behavior in the transient regime as a consequence of the competition between the viscous and elastic forces; also, the flow field is affected by the electrostatic conditions at the liquid-liquid interfaces, producing steep velocity gradients, and finally, the time to reach the steady-state is strongly dependent on the relaxation times, viscosity ratios and the number of fluid layers.https://www.mdpi.com/2072-666X/11/8/757electroosmotic flowmicrochannelimmiscible fluidselectrostatic effectsinterfacial phenomenaMaxwell fluids |
| spellingShingle | Juan Escandón David Torres Clara Hernández René Vargas Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel Micromachines electroosmotic flow microchannel immiscible fluids electrostatic effects interfacial phenomena Maxwell fluids |
| title | Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel |
| title_full | Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel |
| title_fullStr | Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel |
| title_full_unstemmed | Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel |
| title_short | Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel |
| title_sort | start up electroosmotic flow of multi layer immiscible maxwell fluids in a slit microchannel |
| topic | electroosmotic flow microchannel immiscible fluids electrostatic effects interfacial phenomena Maxwell fluids |
| url | https://www.mdpi.com/2072-666X/11/8/757 |
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