Optimal nonlinear dynamics of particles in convective plumes
A problem of optimum (in a specified sense) particle trajectories in convective flows is considered. The problem is investigated using Lagrangian formulation for the droplet dynamics. Definition of optimality is motivated by a practical application, and is formulated in terms of location of critical points on the trajectory. Analysis of the equation of motion reveals that it belongs to the special case of Abel Equations of the Second Kind where exact solution is not known. Proposed approximate method allows reasonably accurate estimation of optimum droplet diameters (i.e. diameters delivering optimum trajectory) to be made. Results are presented for particles of both constant and variable diameters, and are compared with those obtained by numerical integration of the Lagrangian equation of motion.