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

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.

Keywords

• Riccati differential equation
• closed analytical solution
• non-spherical particle
• unbounded viscous fluid
• settling velocity