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Capillary flows along microchannels in the presence of magnetic field

  • Kai Cui
  • Zhilong Zhao
  • Sen Chen
  • Jianjun Gao
  • Lufeng Wei
  • Jingying Guo
Original Paper

Abstract

To analytically determine liquid depth and velocity, we formulated a theoretical a capillary flow. The coupling effects of viscous force (Fv), capillary force (Fs), and electromagnetic force (Fm) were considered during the modeling process. Periodical electromagnetic force facilitates capillary flow in hydrophilic conditions, and velocity vibration synchronizes with electromagnetic force. A sufficiently high electromagnetic force was required for ensuring the upward movement of liquid front in hydrophobic conditions. Liquid depth was increased with the increase in magnetic field, damping factor, and angular frequency. The velocity peak was positively related to \(\mid \cos\theta \mid\) and magnified with the increase in damping factor and angular frequency in hydrophilic conditions. However, variations in velocity in hydrophobic conditions experienced an initial forward instantaneous peak and became consistent with that of hydrophilic conditions because of electromagnetic force.

Keywords

Capillary flow Circular microchannels Magnetic field Liquid depth Average velocity 

List of symbols

B

Magnetic induction intensity

B0

Peak of magnetic induction

F

Total force

Fs

Capillary force

Fv

Total viscous force

Fm

Electromagnetic force

h

Liquid depth

P

Pressure

R

Radius

t

Time

v

Flow velocity

\(\overline{v}\)

Average velocity

r, z

Coordinate directions

Greek symbol

γ

Viscous shearing force

θ

Contact angle

τ

Damping factor

σ

Surface tension

ω

Angular frequency

μ

Magnetic permeability

η

Dynamic viscosity

PACS Nos.

47.10.−g 47.10.A− 47.15.G− 47.55.dr 47.65.−d 

Notes

Acknowledgements

The work is supported by the National Natural Science Foundation of China (51374173) and Natural Science Basic Research Plan in Shanxi Province of China (2018JM5082).

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Copyright information

© Indian Association for the Cultivation of Science 2018

Authors and Affiliations

  • Kai Cui
    • 1
  • Zhilong Zhao
    • 1
  • Sen Chen
    • 1
  • Jianjun Gao
    • 1
  • Lufeng Wei
    • 1
  • Jingying Guo
    • 1
  1. 1.School of Mechanical EngineeringNorthwestern Polytechnical UniversityXi’anChina

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