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

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 i...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 15; p. 3262
Main Authors Laín, Santiago, García, Diego F., Gandini, Mario A.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2023
Subjects
closed analytical solution
Control theory
Differential equations
Exact solutions
Fluidized bed reactors
Hypotheses
Methods
non-spherical particle
Ordinary differential equations
Particle deposition
Riccati differential equation
Riccati equation
Sedimentation & deposition
Settling velocity
unbounded viscous fluid
Velocity
Viscosity
Viscous fluids
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ISSN2227-7390
2227-7390
DOI10.3390/math11153262

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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11153262