Convective Cahn-Hilliard models: From coarsening to roughening

In this paper we demonstrate that convective Cahn-Hilliard models, describi ng phase separation of driven systems (e.g., faceting of growing thermodyna mically unstable crystal surfaces), exhibit, with the increase of the drivi ng force, a transition from the usual coarsening regime to a chaotic behavi or without coarsening via a pattern-forming state characterized by the form ation of various stationary and traveling periodic structures as well as st ructures with localized oscillations. Relation of this phenomenon to a. kin etic roughening of thermodynamically unstable surfaces is discussed.