Exit time of a colloidal particle out of a sedimenting drop

We are interested in the exit time calculation for a colloidal particle present inside a sedimenting drop. This is of particular relevance to drops of saliva and mucous expelled by sneezing or coughing that could possibly contain virulent pathogens. The internal flow field of such a drop is given by the standard Hadamard-Rybczynski solution. Langevin simulations are used to calculate the mean exit time of the colloidal particle and characterize its variation with the Peclet number (Pe). In the limit of Pe<<1, the exit time is merely τ = R² / D. For the case of Pe>>1, an enhanced diffusivity is observed due to the rising prominence of the convective motion within the sedimenting drop and leads to a faster exit. We also validate the predictions from Langevin dynamics by solving a backward Kolmogorov equation for the exit-time associated with a colloidal particle in a flow field inside a sedimenting drop.