Numerical simulation of aerodynamic focusing of particles in supersonic micronozzles

Particle-laden flows in plane, axisymmetric and 3D supersonic micronozzles are investigated numerically using a one-way coupled Eulerian/Lagrangian approach. The carrier gas flow is calculated by solving the Navier-Stokes equations. Rarefaction effects are taken into account by imposing the velocity slip and temperature jump boundary conditions on the nozzle walls. The parameters of the flow around particles are varied in a wide range including hydrodynamic, transitional and free-molecular regimes. It is shown that a collimated beam of particles can be produced using the effect of aerodynamic focusing due to converging flow streamlines in the subsonic part of the nozzle. The collimation is preserved in the supersonic part where the flow is divergent because the rapid drop in the gas density decreases significantly the force acting on the particle. An interesting and unexpected feature of aerodynamic focusing is that the beam collimation is observed in two different ranges of particle sizes. In the first range, for relatively large particles, the collimated beam consists only of particles seeded close to the nozzle axis. In the second range, for smaller particles, the beam includes also a great portion of peripheral particles. The numerical simulation also shows that aerodynamic focusing in a supersonic, convergent-divergent, nozzle enables one to increase significantly the velocity of the collimated beams compared to previously reported results for convergent subsonic nozzles. It may be helpful for technological applications where the aerodynamic scheme of particle focusing can be used (microthrusters, needle-free drug injection, microfabrication, etc.)