Double-diffusive and Rayleigh-Taylor instabilities in particle-laden water stratified over salt water in a Hele-Shaw cell*

An experimental and computational investigation is performed for double-diffusive (DD) and Rayleigh-Taylor (RT) instabilities in particle-laden fresh water initially stably-stratified over salt water in a Hele-Shaw cell. \textit{Computationally}, Darcy's Law coupled with an advection-diffusion equation for salt and an advection-diffusion equation for particle concentration that includes a settling velocity is solved for two-dimensional stratified fluids in the presence of particle-loading. The flows are parametrized in terms of a stability ratio, a gravity parameter, and a dimensionless settling velocity. Results are analyzed in terms of relative dimensions of concentration profiles of sediment and salt. \textit{Experimentally}, Schlieren imaging is used to image fresh water containing 3-6 $\mu $m glass microparticles layered above salt water both containing glycerol to slow dynamics. Dimensionless wavelength and time and distance until onset of instability are measured. Results are interpreted in terms of a ``nose'' region of increased density at the interface.