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A shear-rate-dependent flow generated via magnetically controlled metachronal motion of artificial cilia

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Abstract

Cilia beating is a naturally occurring phenomenon that can be utilized in fluid transport in designing several biomechanical devices. Inspired by the ubiquity of bio-fluids (which are non-Newtonian), we report the characteristics of shear-rate-dependent viscosities on fluid flow generated by the wavy propulsion of magnetic cilia. We assume that the metachronal waves of these cilia form a two-dimensional wavy channel, which is filled with generalized Newtonian Carreau liquid. Galilean transformation is employed to relate fixed and moving frames. The constitutive equations are reduced under the classical lubrication assumption. The resulting fourth-order nonlinear differential equations are solved via a perturbation approach using the stream function. The effects of four dominant fluid parameters (shear thinning/thickening, power-law index, and zero- and infinite-shear-rate viscosity), magnetic parameter (Hartmann number), and metachronal wave parameters on fluid velocity, pressure rise per wavelength, and trapping phenomenon are shown in graphical results and explained thoroughly. This study could play an advisory role in designing a magnetic micro-bot useful in the biomedical industry.

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Acknowledgements

This project is supported by Beijing Municipal Commission of Science (No. Z161100005016043)

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Correspondence to S. Z. Abbas or W. A. Khan.

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Wu, A., Abbas, S.Z., Asghar, Z. et al. A shear-rate-dependent flow generated via magnetically controlled metachronal motion of artificial cilia. Biomech Model Mechanobiol (2020). https://doi.org/10.1007/s10237-020-01301-y

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Keywords

  • Carreau fluid
  • Ciliated channel
  • Magnetic effect
  • Metachronal wave
  • Stream function
  • Perturbation technique