Micro-Scale Aspects of Spray Deposition Processing: A Semi-Analytical Model for Droplet Spreading and Solidification at Off-Normal Impact Angles

Droplet impacts are rarely normal to the target substrate during thermal spray processing because of droplet dispersion in the spray cone or because the substrate is moving. A model for droplet spreading and solidification after off-normal impact on a cold substrate was developed. This model is based on Madejski’s energy conservation model but uses a three-dimensional velocity field, which satisfies the no slip condition at the solid front, the no shear condition at the free surface as well as the continuity equation. Furthermore, the present model assumes the shape of the spreading droplet to have a non-axisymmetric shape (limaçon perimeter and a uniform height). Stefan solidification is assumed. A mechanical energy balance is used to describe the deformation of the spreading droplet. The resulting integro-differential equation is solved numerically using a modified Euler predictor-corrector method. This model was validated by comparison with existing energy-conservation models in the case of normal impact. The results indicate both a decrease in the final splat diameter and a decrease in the expansion rate of the spreading droplet as the impact angle increases, as measured from the normal axis. The resulting impacts are therefore less efficient as the impact angle increases.