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Shock Dynamics in Particle-Laden Thin Films

We present theory and experiments for thin ﬁlm particle-laden ﬂow on an incline. At higher particle concentration and inclination angle, a new phenomenon is observed in which a large particle-rich ridge forms at the contact line. We derive a lubrication theory for this system which is qualitatively compared to preliminary experimental data. The ridge formation arises from the creation of two shocks due to the diﬀerential transport rates of ﬂuid and particles. This parallels recent ﬁndings of double shocks in thermal-gravity driven ﬂow [A. L. Bertozzi et. al. , PRL, 81 , 5169 (1998), J. Sur et. al. , PRL 90 , 126105 (2003), A. M¨unch, PRL 91 , 016105 (2003)]. However, here the emergence of the shocks arises from a new mechanism involving the settling rates of the species.