External concentration gradients can drive a propagating wave in a coherently layered system of nanosheets

We present a model for the dynamics observed recently by Sano et al. [Nat. Commun. 12, 6771 (2021)] in a coherently layered system made up of sheetlike colloidal particles (nanosheets) subjected to an external concentration gradient. Adding a new macroscopic variable characteristic for the nonequilibrium situation encountered in the experiments to the hydrodynamics of smectic A liquid crystals, we show that all salient dynamic features observed in the experiments can be accounted for. For this nonequilibrium phenomenon, we identify the symmetry of the underlying ground state as undulating smectic A-like layering and the applied concentration gradient applied in the layer planes as the nonequilibrium driving force. As a result of our analysis, we find a coherent motion of undulating layers generated by a Helfrich-Hurault type instability propagating at a fixed velocity in accordance with the observations. If the coherence of the layering is lost, there is no longer any coherent propagation to be expected-as is also observed.