Transient stratification force on particles crossing a density interface

We perform a series of experiments to measure Lagrangian trajectories of settling and rising particles as they traverse a density interface of thickness $h$ using an index-matched water-salt-ethanol solution. The experiments confirm the substantial deceleration that particles experience as a result of the additional force exerted on the particle due to the sudden change in density. This stratification force is calculated from the measurement data for all particle trajectories. In the absence of suitable parameterizations in the literature, a simple phenomenological model is developed which relies on parameterizations of the effective wake volume and recovery time scale. The model accurately predicts the particle trajectories obtained in our experiments and those of \cite{Fernando1999}. Furthermore, the model demonstrates that the problem depends on four key parameters, namely the entrance Reynolds number $Re_1$, entrance Froude number $Fr$, particle to fluid density ratio $ρ_p/ρ_f$, and relative interface thickness $h/a$.