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The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe
Zhili Wang1, Yanjun Sun1,2, Yongjun Jian1
1School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China.
Micromachines
|November 25, 2023
Summary
Random roughness significantly impacts electromagnetic flow in micropipes. Sinusoidal corrugations show a greater effect on flow rate than triangular ones, especially at higher wave numbers and lower Hartmann numbers.
Area of Science:
- Fluid dynamics
- Electromagnetism
- Microfluidics
Background:
- Electromagnetic flow in confined geometries is crucial in various applications.
- Understanding the effect of surface roughness on fluid flow is essential for accurate modeling.
- Micropipes present unique challenges due to their small dimensions.
Purpose of the Study:
- To investigate the impact of random roughness on electromagnetic flow in cylindrical micropipes.
- To develop an analytical solution for flow rate considering surface corrugations.
- To quantify the influence of roughness parameters on flow behavior.
Main Methods:
- Utilized stationary random processes and small parameter expansion.
- Employed perturbation method to achieve analytical solutions up to second-order velocity.
- Integrated spectral density to derive the analytical expression for the roughness function.
- Analyzed sinusoidal and triangular corrugations.
Main Results:
- The roughness function (ζ) quantifies the deviation in flow rate due to roughness.
- Roughness function magnitude increases with wave number (λ) and decreases with Hartmann number (Ha).
- Sinusoidal corrugations exhibit a stronger influence on flow rate compared to triangular corrugations.
- Maximum roughness effect observed at λ=15, Ha=0 (ζ=27.5 for sinusoidal, ζ=18.7 for triangular).
Conclusions:
- Surface roughness significantly alters electromagnetic flow in micropipes.
- The choice of corrugation type (sinusoidal vs. triangular) affects flow rate modulation.
- The study provides a quantitative framework for predicting roughness effects in microfluidic devices.
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