Relaxation drag history of shock accelerated microparticles

Experimental measurements of the displacements of shock accelerated microparticles from shortly after shock. interaction to the particle relaxation time show time-dependent drag coefficients (C-D) that are much higher than those predicted by quasi-steady and unsteady drag models. Nylon particles with mean diameter of 4 mu n, accelerated by one-dimensional normal shocks (Mach number M-s = 1.2, 1.3 and 1.4), have measured C-D values that follow a power-law behaviour. The drag is a function of the time-dependent Knudsen number, K-n* = M-s/Re-p, where the particle Reynolds number (Re-p) is calculated using the time-dependent slip velocity. Some portion of the drag can be attributed to quasi-steady forces, but the total drag cannot he predicted by current unsteady force models that are based on the Basset-Boussinesq-Oseen equation and pressure drag. The largest contribution to the total drag is the unsteady component (C-D,C-us) until the particle attains K-n* approximate to 0.5-1.0, then the unsteady contribution decays. The quasi-steady component (C-D,C-qs,) increases almost linearly with K-n*, intersects the CD at K-n* approximate to 2 and becomes the primary contributor to the drag towards the end of the relaxation zone as Re-p, -> 0. There are currently no analytical models that arc able to predict the nonlinear behaviour of the shock accelerated particles during the relaxation phase of the flow.