Analytical solution for electroosmotic flow of Casson fluid in varying microchannel with Zeta potential

Abstract

This study presents an analytical solution for the electroosmotic flow of Casson fluid in a microchannel with non-uniformly charged walls. Our objective is to determine analytical expressions for velocity and volumetric flow rates in both sheared and unsheared regions of the microchannel, as well as to describe the stress and temperature distributions in these regions. Using the lubrication approximation, we reduce the governing equations of Casson fluid flow to their dimensionless forms, which we then solve analytically. We express velocities and volumetric flow rates analytically in both sheared and unsheared regions using the cosine function. Graphical representations show stress distribution, velocity distributions, flow rate distributions, and temperature distributions in the sheared and unsheared regions. Our findings reveal that there are variations in volumetric flow rate with respect to rising pressure gradients due to the opposite response of pressure gradient and flow rate compared to other parameters. Furthermore, we present graphical representations of temperature distributions with wall shape amplitude and joule heating. This analytical solution has significant implications for the design and optimization of microfluidic devices that use Casson fluids in various applications.

Keywords

Casson fluid / electroosmosis / electric double layer / sheared region / unsheared region

References

[1] StoneH A, StroockA D, AjdariA. Engineering flows in small devices: Microfluidics toward a lab-on-a-chip [J]. Annual Review of Fluid Mechanics, 2004, 36: 381-411

[2] BurgreenD, NakacheF R. Electrokinetic flow in ultrafine capillary slits [J]. The Journal of Physical Chemistry, 1964, 68(5): 1084-1091

[3] TangG H, LiX F, HeY L, et al. . Electroosmotic flow of non-Newtonian fluid in microchannels [J]. Journal of Non-Newtonian Fluid Mechanics, 2009, 157(1–2): 133-137

[4] ZimmermanW B, ReesJ M, CravenT J. Rheometry of non-Newtonian electrokinetic flow in a microchannel T-junction [J]. Microfluidics and Nanofluidics, 2006, 2(6): 481-492

[5] ZhaoC, YangC. Electro-osmotic mobility of non-Newtonian fluids [J]. Biomicrofluidics, 2011, 5(1): 14110

[6] ZhaoC, YangC. An exact solution for electroosmosis of non-Newtonian fluids in microchannels [J]. Journal of Non-Newtonian Fluid Mechanics, 2011, 16617–181076-1079

[7] NAZEER M, HUSSAIN F, KHAN M I, et al. Theoretical analysis of electrical double layer effects on the multiphase flow of Jeffrey fluid through a divergent channel with lubricated walls [J]. Waves in Random and Complex Media, 2022: 1–15. DOI: https://doi.org/10.1080/17455030.2022.2126025.

[8] ShahidM, JavedH M A, AhmadM I, et al. . A brief assessment on recent developments in efficient electrocatalytic nitrogen reduction with 2D non-metallic nanomaterials [J]. Nanomaterials (Basel, Switzerland), 2022, 12(19): 3413

[9] JawedA M, SharmaA, TrivediM, et al. . On the convective mass transfer and flow across spherical droplet falling in Casson fluids [J]. Materials Today: Proceedings, 2022, 57: 1761-1764

[10] WaqasH, OreijahM, GuedriK, et al. . Gyrotactic motile microorganisms impact on pseudoplastic nanofluid flow over a moving Riga surface with exponential heat flux [J]. Crystals, 2022, 12(9): 1308

[11] TANVEER A, MAHMOOD S. Electroosmosis peristaltic flow with the domination of internal and activation energies for non-Newtonian fluid [J]. Waves in Random and Complex Media, 2022: 1–13. DOI: https://doi.org/10.1080/17455030.2022.2088886.

[12] BafakeehO T, RaghunathK, AliF, et al. . Hall current and soret effects on unsteady MHD rotating flow of second-grade fluid through porous media under the influences of thermal radiation and chemical reactions [J]. Catalysts, 2022, 12101233

[13] AhmedM F, ZaibA, AliF, et al. . Numerical computation for gyrotactic microorganisms in MHD radiative Eyring-Powell nanomaterial flow by a static/moving wedge with darcy-forchheimer relation [J]. Micromachines, 2022, 13101768

[14] ShamshuddinM D, MaboodF, KhanW A, et al. . Exploration of thermal Péclet number, vortex viscosity, and Reynolds number on two-dimensional flow of micropolar fluid through a channel due to mixed convection [J]. Heat Transfer, 2023, 521854-873

[15] SHAHZAD F, JAMSHED W, EID M R, et al. Thermal amelioration in heat transfer rate using Oldroyd-B model hybrid nanofluid by CNTs-based kerosene oil flow in solar collectors applications [J]. Waves in Random and Complex Media, 2022: 1–31. DOI: https://doi.org/10.1080/17455030.2022.2157511.

[16] ParkH M, LeeW M. Effect of viscoelasticity on the flow pattern and the volumetric flow rate in electroosmotic flows through a microchannel [J]. Lab on a Chip, 2008, 8(7): 1163-1170

[17] ZhaoC, YangC. Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels [J]. Applied Mathematics and Computation, 2009, 211(2): 502-509

[18] PanasetiP, GeorgiouG C. Viscoplastic flow development in a channel with slip along one wall [J]. Journal of Non-Newtonian Fluid Mechanics, 2017, 2488-22

[19] DasS, ChakrabortyS. Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian biofluid [J]. Analytica Chimica Acta, 2006, 559(1): 15-24

[20] PhilippouM, KountouriotisZ, GeorgiouG C. Viscoplastic flow development in tubes and channels with wall slip [J]. Journal of Non-Newtonian Fluid Mechanics, 2016, 238: 44-56

[21] LevineS, MarriottJ R, NealeG, et al. . Theory of electrokinetic flow in fine cylindrical capillaries at high zeta-potentials [J]. Journal of Colloid and Interface Science, 1975, 52(1): 136-149

[22] MaghsoudiP, ShahriariG, RasamH, et al. . Flow and natural convection heat transfer characteristics of non-Newtonian nanofluid flow bounded by two infinite vertical flat plates in presence of magnetic field and thermal radiation using Galerkin method [J]. Journal of Central South University, 2019, 26(5): 1294-1305

[23] HuJ, ShiQ. Relationship between rheological behavior and flotation rate in slurry with different chalcopyrite and lizardite concentration [J]. Journal of Central South University, 2022, 29(5): 1479-1487

[24] ZhangL, WangH. Evaluation of thixotropic behaviors of tailings pastes as a function of solids concentration [J]. Journal of Central South University, 2023, 30(1): 142-155

[25] MansouriA, ValiA, KostiukL W. Electrokinetic power generation of non-Newtonian fluids in a finite length microchannel [J]. Microfluidics and Nanofluidics, 2016, 20(5): 71

[26] ChakrabortyS. Electroosmotically driven capillary transport of typical non-Newtonian biofluids in rectangular microchannels [J]. Analytica Chimica Acta, 2007, 6052175-184

[27] BoydJ, BuickJ M, GreenS. Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method [J]. Physics of Fluids, 2007, 19(9): 093103

[28] MukhopadhyayS, DeP R, BhattacharyyaK, et al. . Casson fluid flow over an unsteady stretching surface [J]. Ain Shams Engineering Journal, 2013, 44933-938

[29] NgC O. Combined pressure-driven and electroosmotic flow of Casson fluid through a slit microchannel [J]. Journal of Non-Newtonian Fluid Mechanics, 2013, 198: 1-9

[30] BabaieA, SadeghiA, SaidiM H. Combined electroosmotically and pressure driven flow of power-law fluids in a slit microchannel [J]. Journal of Non-Newtonian Fluid Mechanics, 2011, 166(14–15): 792-798

[31] EldabeN T M, SaddeekG, El-SayedA F. Heat transfer of MHD non-Newtonian Casson fluid flow between two rotating cylinders [J]. Mechanics and Mechanical Engineering, 2001, 5(2): 230-250

[32] Anantha KumarK, SugunammaV, SandeepN. Effect of thermal radiation on MHD Casson fluid flow over an exponentially stretching curved sheet [J]. Journal of Thermal Analysis and Calorimetry, 2020, 140(5): 2377-2385

[33] RajaramV, VaradharajB, JayavelP. Impact of the electromagnetic flow of an MHD Casson fluid over an oscillating porous plate [J]. Heat Transfer, 2022, 51(5): 4053-4079

[34] Abd El-AzizM, AfifyA A. MHD casson fluid flow over a stretching sheet with entropy generation analysis and hall influence [J]. Entropy, 2019, 21(6): 592

[35] ReddyM G, KumariP V, PadmaP. Effect of thermal radiation on MHD casson nano fluid over a cylinder [J]. Journal of Nanofluids, 2018, 73428-438

[36] VermaV K, MondalS. A brief review of numerical methods for heat and mass transfer of Casson fluids [J]. Partial Differential Equations in Applied Mathematics, 2021, 3: 100034

[37] PONALAGUSAMY R, SANGEETHA J. Electroosmotic effect on two immiscible (conducting-non-conducting) fluids flowing in the porous channel under magnetic field [J]. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2022: 095440892211311. DOI: https://doi.org/10.1177/09544089221131157.

[38] SHAMSHUDDIN M, RAJPUT G R, MISHRA S R, et al. Radiative and exponentially space-based thermal generation effects on an inclined hydromagnetic aqueous nanofluid flow past thermal slippage saturated porous media [J]. International Journal of Modern Physics B, 2023. DOI: https://doi.org/10.1142/s0217979223502028.

[39] AsjadM I, KarimR, HussananA, et al. . Applications of fractional partial differential equations for MHD casson fluid flow with innovative ternary nanoparticles [J]. Processes, 2023, 11(1): 218

[40] FELICITA A, GIREESHA B J, NAGARAJA B, et al. Mixed convective flow of Casson nanofluid in the microchannel with the effect of couple stresses: Irreversibility analysis [J]. International Journal of Modelling and Simulation, 2023: 1–15. DOI: https://doi.org/10.1080/02286203.2022.2156974.

[41] CassonN. A flow equation for pigment-off suspensions of the printing ink type [J]. British Society of Rheology Bulletin, 1957, 525-6

[42] WeissmanM H. Rheology of the circulation [J]. Science, 1969, 163(3871): 1054

[43] ErrillE W. Rheology of blood [J]. Physiological Reviews, 1969, 494863-888

[44] RezaM, RanaA. Analysis of exact solutions of electromagnetohydrodynamic flow and heat transfer of non-Newtonian Casson fluid in microchannel with viscous dissipation and Joule heating [C]. Advances in Fluid Mechanics and Solid Mechanics, 2020, Singapore, Springer: 117-127

[45] SulochanaC, AparnaS R, SandeepN. Heat and mass transfer of magnetohydrodynamic Casson fluid flow over a wedge with thermal radiation and chemical reaction [J]. Heat Transfer, 2021, 50(4): 3704-3721

[46] HUMANE P P, PATIL V S, SHAMSHUDDIN M, et al. Role of bioconvection on the dynamics of chemically active Casson nanofluid flowing via an inclined porous stretching sheet with convective conditions [J]. International Journal of Modelling and Simulation, 2023: 1–20. DOI: https://doi.org/10.1080/02286203.2022.2164156.

[47] AbbasiA, FarooqW, Tag-EldinE S M, et al. . Heat transport exploration for hybrid nanoparticle (Cu, Fe₃O₄) - based blood flow via tapered complex wavy curved channel with slip features [J]. Micromachines, 2022, 13(9): 1415

[48] LiS, KhanM I, AlzahraniF, et al. . Heat and mass transport analysis in radiative time dependent flow in the presence of Ohmic heating and chemical reaction, viscous dissipation: An entropy modeling [J]. Case Studies in Thermal Engineering, 2023, 42102722

[49] PapanastasiouT C. Flows of materials with yield [J]. Journal of Rheology, 1987, 315385-404

[50] RanaA, RezaM, ShitG C. Electromagnetohydrodynamic thermo-fluidic transport in a porous microchannel with wall roughness [J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2022, 650129336