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Modeling and simulation of capillary ridges on the free surface dynamics of third-grade fluid

  • Sherin Jose T. EMAIL logo , Kiran Kumar Patra ORCID logo and Satyananda Panda
Published/Copyright: January 8, 2021
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 3

Abstract

Most of the viscoelastic fluids have deformation while flowing over a heated plate. A typical feature of a thin viscous or viscoelastic fluid is the formation of the capillary ridges over locally heated plates. The creation of such ridges in the thin-film surface can affect the smoothness of the coating. This work particularly concerned the flow of non-Newtonian third-grade fluid over an inclined heated plate and the formation of ridges. The conservation laws associated with free surface and wall boundary conditions model the two-dimensional fluid flow. The long wave approximation of the model results in an equation of evolution to explain the structure of free surfaces. The resulting equation is discretized implicitly using the finite volume method. The obtained results are discussed for different flow parameters that affect capillary ridge emergence on the free surface. Variation in the height of capillary ridges of third-grade fluid is compared with the second-grade fluid and Newtonian fluid flow. We observe, the ridge size gets smaller for the third-grade fluid compared to the Newtonian and the second-grade fluid. Our analysis investigates how the third-grade viscoelastic parameters affect the dynamics of the free surface and the size of the capillary ridge concerning temperature changes and other phenomena of interest.

Keywords: capillary ridge; finite volume method; inclined flow; long wave approximation; thin film flow; third-grade fluid
MSC 2010: MSC[2020]76A10; 76A20; 76M12
Corresponding author: Satyananda Panda, Department of Mathematics, NIT Calicut, Calicut 673601, India, E-mail:

Funding source: DST, Government of India 10.13039/501100001409

Award Identifier / Grant number: SR/FST/MS-I/2019/40

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The authors (Sherin Jose T and Satyananda Panda) would like to thank the DST, Government of India, for providing support to carry out this work under the scheme 'FIST' (No. SR/FST/MS-I/2019/40).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-08-13
Accepted: 2020-11-29
Published Online: 2021-01-08
Published in Print: 2021-03-26

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2020-0225
Keywords for this article
capillary ridge; finite volume method; inclined flow; long wave approximation; thin film flow; third-grade fluid

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Remarks on axion-electrodynamics
  4. Dynamical Systems & Nonlinear Phenomena
  5. Interaction of waves in one-dimensional dusty gas flow
  6. On the ferrofluid lubricated exponential squeeze film-bearings
  7. Modeling and simulation of capillary ridges on the free surface dynamics of third-grade fluid
  8. Hydrodynamics
  9. Ternary-hybrid nanofluids: significance of suction and dual-stretching on three-dimensional flow of water conveying nanoparticles with various shapes and densities
  10. Solid State Physics & Materials Science
  11. Electronic and magnetic properties of Fe-doped GaN: first-principle calculations
  12. Genetic evolutionary approach for surface roughness prediction of laser sintered Ti–6Al–4V in EDM
  13. Thermodynamics & Statistical Physics
  14. Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field
  15. A mathematical model for thermography on viscous fluid based on damped thermal flux
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