  We consider the Riemann problem of the dilute approximation equations with
spatiotemporally dependent volume fractions from the full model of suspension,
in which the particles settle to the solid substrate and the clear liquid film
flows over the sediment [Murisic et al., J. Fluid. Mech. {\bf{717}}, 203--231
(2013)]. We present a method to find shock waves, rarefaction waves for the
Riemann problem of this system. Our method is mainly based on [Smoller,
Springer-Verlag, New York, second edition, (1994)].
