An analytical model to describe the motion of a low concentration of spherical particles within a Newtonian fluid

• Published in: Chemical engineering science Vol. 102; pp. 76 - 86
• Main Authors: Wilms, J.M., Smit, G.J.F., Diedericks, G.P.J.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2013
• Subjects: Chemical engineering; Closure modelling; Collision dynamics; Derivation; Fluid–solid drag; FORTRAN; Low concentrations; Mathematical analysis; Mathematical models; mechanics; Newtonian fluids; Particle interaction; Settling-tube; Two-phase flow; Fluid–solid drag; Particle interaction; Settling-tube; Two-phase flow; Closure modelling
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2013.07.043

In this paper a particle–particle interaction term is derived and incorporated into the two-fluid analytical model of Smit et al. (2011). This model was developed for low concentration spherical particle motion in a Newtonian fluid and the inclusion of particle interactions is required for instances where particles collide. Moreover, such a modification serves as a first step towards the modelling of higher particle concentrations. A brief overview of the analytical derivation of the model by Smit et al. (2011) is included for clarity and a detailed derivation of the newly developed particle–particle interaction term is given. In this derivation, particle interaction is described using impulse mechanics with a collision sphere model in a centre of mass reference frame for collision detection. The updated model is included into an existing Fortran 95 program and validated with experimental data obtained by the authors from camera- and settling tube procedures. [Display omitted] •Closure of the fluid–solid drag with a Representative Unit Cell model (RUC).•Derivation of a particle viscosity term for modelling of particle–particle interaction.•Numerical and physical settling tube experiments for validation of the model.