Numerical simulation of flocculation and transport of suspended particles: Application to metered-dose inhalers

• Flocculation and transport of particles in an MDI canister is simulated.
• Particle size domain is discretized using orthogonal collocation on finite elements.
• The particle size distribution is determined as a function of time and position.
• The method is capable of predicting the dynamic behavior of the suspension.

This study investigates the dynamics of flocculation and transport of solid particles suspended in a liquid propellant. Polydisperse particles with lognormal size distribution are considered. Collision of particles is presumed to be controlled by upward velocity differential and Brownian motion. These mechanisms are enhanced by the van der Waals force. Flocculation of the particles is described using the continuous form of the Smoluchowski equation. Upward transport of the particles is specified via a convection term. The general dynamics of the system is governed by a nonlinear transient partial integro-differential equation which is solved numerically. The technique employed is based on discretizing the size distribution function using orthogonal collocation on finite elements. This is combined with a finite difference discretization of the physical domain, and an explicit Runge–Kutta–Fehlberg time marching scheme. The numerical analysis is validated by comparing with a closed form analytical solution. The simulation results represent the particle size distribution as a function of time and position. The method allows prediction of the effects of the initial conditions and physical properties of the suspension on its dynamic behavior and phase separation.