Electroosmotic Slip Flow of Powell–Eyring Fluid in a Parallel-Plate Microchannel
Abstract
1. Introduction
- At low shear rates, it exhibits Newtonian characteristics; at high shear rates, its apparent viscosity diminishes in a manner akin to power-law fluids [41]. The hyperbolic sine function enables a natural transition of shear behavior without requiring piecewise modeling.
- Based on Eyring’s molecular activation energy theory, it treats flow as a transition process where molecules overcome energy barriers. This provides clear physical interpretation and makes it suitable for mechanistic studies (e.g., polymer chain dynamics).
- It simultaneously incorporates Newtonian viscosity, shear-thinning, and viscoelasticity, allowing comprehensive description of flow behavior.
- Without yield stress limitations, it applies to continuously varying flow behaviors such as those of biological fluids or polymer solutions.
2. Governing Equations
2.1. Assumptions
- The fluid is assumed to be incompressible.
- The flow is considered fully developed, resulting in time-independent velocity profiles.
- Gravitational effects on the EOF are negligible.
- The zeta potential exhibits a consistent distribution along the channel’s surface.
- The parallel-plate microchannel configuration is assumed to be homogeneous and symmetric.
- The applied external electric field strength remains within a range that justifies neglecting Joule heating effects.
2.2. Governing Equation
2.3. Electric Potential
2.4. Dimensionless Processing
3. Approximate and Numerical Solutions
3.1. Approximate Solution
3.2. Numerical Solution
4. Results and Discussion
5. Conclusions
- (1)
- The modified SLLM demonstrates significant superiority in terms of both the number of iterations and accuracy.
- (2)
- The pressure gradient-to-electric field ratio exhibits a nonlinear modulating effect on the EOF velocity.
- (3)
- A thicker EDL significantly constrains flow development, maintaining a parabolic velocity distribution. Conversely, a thinner EDL allows pressure-driven effects to dominate, leading to a velocity profile that approaches the ideal “plug flow” shape.
- (4)
- The shear-thinning characteristics of the Powell–Eyring fluid are particularly pronounced in the central region under high pressure gradients and in the boundary layer region when wall slip is present.
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
HPM | Homotopy perturbation method |
SLLM | Spectral local linearization method |
EOF | Electroosmotic flow |
EDL | Electric double layer |
MEMSs | Micro-Electro-Mechanical Systems |
MHD | Magnetohydrodynamic |
RMSEs | Root mean square errors |
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Symbol | Meaning |
---|---|
, | Length and width of microchannel (m) |
Height of microchannel (m) | |
Zeta potential (V) | |
External electric field strength (V/m) | |
Shear stress (Pa) | |
Net charge body density of the EDL (V/m) | |
Pressure (Pa) | |
, | Material parameters |
Dielectric constant | |
Volumetric concentration of ions (mol/m3) | |
Elementary electronic charge (C) | |
Valence of the ions | |
Boltzmann constant (J/K) | |
Absolute temperature (K) | |
EDL thickness (m) | |
Dimensionless electric width | |
Ratio of pressure gradient to electric field | |
Ratio of the inertial force to the viscous force | |
Material parameters of the Powell–Eyring fluid | |
Dimensionless parameter | |
Dimensionless parameter | |
Dimensionless parameter | |
Dimensionless parameter |
Parameter | Method | Numbers of Iterations | Residual |
---|---|---|---|
SLLM | 26 | ||
Modified SLLM () | 6 | ||
Finite Difference Method | 6 | ||
Finite Element Method | 4 | ||
SLLM | 20 | ||
Modified SLLM () | 4 | ||
Finite Difference Method | 2 | ||
Finite Element Method | 2 |
Parameter | ||||||||
---|---|---|---|---|---|---|---|---|
Method | HPM | Modified SLLM | HPM | Modified SLLM | HPM | Modified SLLM | HPM | Modified SLLM |
Residual errors (10−4) | 9.9298 | 1 | 38.385 | 2 | 85.67 | 6 | 152.18 | 24 |
RMSEs (10−4) | 8.4649 | 0 | 35.018 | 1 | 79.631 | 4 | 143.03 | 14 |
Time (s) | 0.025741 | 0.220497 | 0.014740 | 0.188548 | 0.014680 | 0.176582 | 0.015518 | 0.185754 |
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Jiang, Y. Electroosmotic Slip Flow of Powell–Eyring Fluid in a Parallel-Plate Microchannel. Symmetry 2025, 17, 1071. https://doi.org/10.3390/sym17071071
Jiang Y. Electroosmotic Slip Flow of Powell–Eyring Fluid in a Parallel-Plate Microchannel. Symmetry. 2025; 17(7):1071. https://doi.org/10.3390/sym17071071
Chicago/Turabian StyleJiang, Yuting. 2025. "Electroosmotic Slip Flow of Powell–Eyring Fluid in a Parallel-Plate Microchannel" Symmetry 17, no. 7: 1071. https://doi.org/10.3390/sym17071071
APA StyleJiang, Y. (2025). Electroosmotic Slip Flow of Powell–Eyring Fluid in a Parallel-Plate Microchannel. Symmetry, 17(7), 1071. https://doi.org/10.3390/sym17071071