Two-layer sedimentation with a compression shock

With upper concentration $a$ and lower concentration $2a$, the clearing, internal and deposit fronts have speeds $-u_s(1-a)$, $-u_s(1-3a)$ and $2u_{s}a$. If the lower two merge, the resulting deposit/upper-suspension front has speed $u_{s}a$. Final deposit thickness is $a(H+z_m)$ by mass conservation.

For initial concentrations $a$ above $z_m$ and $2a$ below it, all three straight shocks meet when $z_m=H(1-a)/(1+a)$. The common time is $H/[u_s(1+a)]$ and height is $2aH/(1+a)$. Afterwards only a stationary deposit/clear-fluid boundary remains.