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This study uses the level contour reconstruction method to numerically investigate the maximum spreading due to droplet collision with a dry, stationary, spherical particle. We consider a broad range of impact conditions: Weber number 30–90, Ohnesorge number 0.0013–0.7869, and droplet-to-particle size ratio 1/10–1/2, and quantitatively and systematically analyze 120 collision cases to understand how liquid viscosity and surface curvature affect the maximum spreading. The maximum spreading increases on the smaller particles for both the capillary and viscous regimes, but the underlying physics clearly differ. The increase in maximum spreading is governed mainly by the surface deformation of the rim for the capillary regime and viscous dissipation for the viscous regime. An empirical correlation that can be applied to the droplet impact on both a particle and a flat surface is also presented. The model shows good agreement with existing experimental data as well as our simulation results within a deviation range of ±15%.

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In the present study, the maximum spreading diameter of a droplet impacting with a spherical particle is numerically studied for a wide range of impact conditions: Weber number (We) 0-110, Ohnesorge number (Oh) 0.0013-0.7869, equilibrium contact angle ( θeqi) 20{degree sign}-160{degree sign}, and droplet-to-particle size ratio (Ω) 1/10-1/2. A total of 2600 collision cases are simulated to enable a systematic analysis and prepare a large dataset for training of a data-driven prediction model. The effects of four impact parameters (We, Oh, θeqi, and Ω) on the maximum spreading diameter ( β*max) are comprehensively analyzed, and particular attention is paid to the difference of β*max between the low and high Weber number regimes. A universal model for prediction of β*max, as a function of We, Oh, θeqi, and Ω, is also proposed based on a deep neural network. It is shown that our data-driven model can predict the maximum spreading diameter well, showing an excellent agreement with the existing experimental results as well as our simulation dataset within a deviation range of {plus minus} 10%.