Aerosol Flow Through a Converging-Diverging Micro-Nozzle

Abstract

Cold spray is a material deposition process used to deposit metallic features for use in applications such as corrosion prevention, dimensional correction and repair, and wear resistant coatings. Micro Cold Spray Direct Write (MCS-DW) is a variant of the cold spray process in which metal particles are accelerated and focused to print fine features on flexible and rigid substrates with no postprocessing required. This paper presents results of numerical studies on the flow of 2 µm and 6 µm diameter silver particles through a converging-diverging micro nozzle with helium gas. The flow of helium was simulated by solving Navier Stokes equation using commercial software. The trajectory and velocity of the aerosol particles were determined using a Lagrangian particle tracking algorithm with a combination of Stokes drag force and Saffman lift force acting on the particles. A comparison of the effect of different corrections applied to Stokes and Saffman forces as well as the effect of Magnus force on the trajectory and velocity of aerosol particles is studied. The effect of particle rotation creating Magnus force is found negligibly small compared to Saffman force for particles of 2 µm diameter, however, the effect is found to be significant for particles of 6 µm diameter. A proposed converging-diverging nozzle is shown capable of accelerating silver particles to velocities as high as 600 m/s and enables aerosol beam widths as thin as 50 µm.

Numerical simulation of aerodynamic focusing of particles in supersonic micronozzles

“…It is worth noting that in the paper (Bhattacharya et al, 2013) they found that the Saffmann force causes an increase in focusing of the particles.…”

“…See, e.g., paper by Ling et al (2011), in which the situation where the unsteady contribution of force can be significant is considered in details. However, if the density of the carrier phase is considerably lower than that of the dispersed phase and particles do not interact with shock waves but gradually gain speed due to the accelerating carrier flow, then all of the forces except for drag and, possibly, the Saffman force become negligibly small (see, in particular, an analysis performed in (Bhattacharya et al, 2013)).…”

“…The possibility of creating collimated beams of relatively high-speed (up to 100 m/s) particles in a convergent subsonic nozzle was demonstrated both experimentally and numerically by Akhatov et al (2009) and Lutfurakhmanov et al (2010). Later, Bhattacharya et al (2013) investigated numerically the particle-laden flow in a converging-diverging (conical) nozzle and demonstrated, for two different particle diameters, that even higher-speed collimated beams can be obtained using such nozzles. However, the flow conditions considered in their work are restricted by the case when the gas accelerates in the diverging part of the nozzle only for a short distance and the maximum Mach number does not exceed 1.3.…”

“…In (Bhattacharya et al, 2013) an analysis of comparative importance of different forces acting on a particle in a micronozzle was performed and it was shown that such contributions as the Basset force, the virtual mass force, the pressure gradient force and the buoyancy (gravity) force are negligibly small while the Magnus lifting force is noticeable only for large (6 µm diameter) particles.…”

Micro Cold Spray printed top metallization layer for solar cells

“…The MCS system was developed similar to our work with CAB-DW where we utilized a model for fluid-particle interaction combining Stokes, Saffman, and when appropriate Magnus forces to design optimum flow conditions and nozzle geometries for specific processes. [7][8][9] In our recent work, we have shown the ability to print copper traces on glass substrates with near-bulk conductivity without postprocessing, and line widths below 50 µm with MCS. [7] In this paper, we will describe to you the most recent results with printing copper and silver for applications as the top metallization layer of silicon heterojunction solar cells.…”