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Analytical Solutions of the Riccati Differential Equation: Particle Deposition in a Viscous Stagnant Fluid

Author

Listed:
  • Santiago Laín

    (PAI+, Department of Mechanical Engineering, Universidad Autónoma de Occidente, Cali 760030, Colombia)

  • Diego F. García

    (PAI+, Department of Mechanical Engineering, Universidad Autónoma de Occidente, Cali 760030, Colombia)

  • Mario A. Gandini

    (PAI+, Institute for Sustainability, Universidad Autónoma de Occidente, Cali 760030, Colombia)

Abstract

In this communication, the solution of the differential Riccati equation is shown to provide a closed analytical expression for the transient settling velocity of arbitrary non-spherical particles in a still, unbounded viscous fluid. Such a solution is verified against the numerical results of the integrated differential equation, establishing its accuracy, and validated against previous experimental, theoretical and numerical studies, illustrating the effect of particle sphericity. The developed closed analytical formulae are simple and applicable to general initial velocity conditions in the Stokes, transitional and Newtonian regimes, extending the range of application of former published analytical approximate solutions on this subject.

Suggested Citation

  • Santiago Laín & Diego F. García & Mario A. Gandini, 2023. "Analytical Solutions of the Riccati Differential Equation: Particle Deposition in a Viscous Stagnant Fluid," Mathematics, MDPI, vol. 11(15), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3262-:d:1201997
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    References listed on IDEAS

    as
    1. N. Lyotard & W. L. Shew & L. Bocquet & J.-F. Pinton, 2007. "Polymer and surface roughness effects on the drag crisis for falling spheres," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(4), pages 469-476, December.
    2. Zegao Yin & Zhenlu Wang & Bingchen Liang & Li Zhang, 2017. "Initial Velocity Effect on Acceleration Fall of a Spherical Particle through Still Fluid," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, February.
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