Modeling the granule formation mechanism from single drop impact on a powder bed

Granule formation from drop impact on a powder bed can occur by either Tunneling or Spreading/Crater Formation. The governing regime can be specified by the experimentally determined modified Bond number (Bo(g)*), which is a ratio of the capillary force to the gravitational force acting on a particle. It was hypothesized that Tunneling would occur when the capillary and surface tension forces exceeded the weight of a powder aggregate in contact with the drop. To confirm this hypothesis, force balances were derived for a drop in contact with a single particle and separately for a drop in contact with an aggregate to predict when a particle or aggregate will be sucked into the drop. The force ratios derived for each case were compared to the Bo(g)* force ratio used in a previously published regime map that separates Tunneling from Spreading/Crater Formation. The force balance model correctly predicts the trends of the impact of powder and liquid properties on the governing regime. However, the single particle model does not quantitatively predict the critical Bond number for regime change in Tunneling. The aggregate model gave a better prediction of the Tunneling boundary than the single particle model, but it still under predicts the experimentally determined Tunneling criterion given by the Bond number. Potential reasons for this discrepancy are discussed.