Early extinction of a settling rarefaction fan ($a_{\ast }=1-\sqrt{2/3}$)

For upper concentration $a$, lower $a/2$ and interface height $4H/5$, both curved fronts meet inside the fan only if $a\ge 1-\sqrt{2/3}$. At smaller $a$, the deposition front reaches the fan upper edge first, then advances through uniform concentration $a$. The clearing front remains straight and final time is $H(1-3a/5)/[u_s(1-a)]$.