Chondrule destruction in nebular shocks

Chondrules are millimeter-sized silicate spherules ubiquitous in primitive meteorites, but whose origin remains mysterious. One of the main proposed mechanisms for producing them is melting of solids in shock waves in the gaseous protoplanetary disk. However, evidence is mounting that chondrule-forming regions were enriched in solids well above solar abundances. Given the high velocities involved in shock models destructive collisions would be expected between differently sized grains after passage of the shock front as a result of differential drag. We investigate the probability and outcome of collisions of particles behind a 1D shock using analytic methods as well as a full integration of the coupled mass, momentum, energy and radiation equations. Destruction of protochondrules seems unavoidable for solid/gas ratios $\epsilon \gtrsim 0.1$, and possibly even for solar abundances because of "sandblasting" by finer dust. A flow with $\epsilon \gtrsim 10$ requires much smaller shock velocities ($\sim 2$ vs 8 km s$^{-1}$) in order to achieve chondrule-melting temperatures, and radiation trapping allows slow cooling of the shocked fragments. Initial destruction would still be extensive; although re-assembly of mm-sized particles would naturally occur by grain sticking afterward, the compositional heterogeneity of chondrules may be difficult to reproduce. We finally note that solids passing through small-scale bow shocks around few-km-sized planetesimals might experience partial melting and yet escape fragmentation.