On shapes and forms: Population balance dynamics of corrugated stirred fronts

Publication date: Available online 22 October 2018Source: Comptes Rendus PhysiqueAuthor(s): Emmanuel VillermauxAbstractWe introduce a unified framework to discuss the emergence of corrugations on material interfaces transported by random media. Relating the shape of these interfaces to the stirring field giving birth to it, we formalize a population balance dynamics for the r-elements (segments of length r) needed to cover the interface contour in the course of its deformation. As long as corrugations grow kinematically, shapes change continuously, their fractal dimension df(r,t) is a non-monotonous function of the scale r, and increases in time t with no bounds. Interface creation and destruction balance, however, in self-propagating fronts like flames, and in fronts smearing by molecular diffusion, through a mixing induced overlap mechanism, leading to a stationary shape. These findings, which help reexamining old observations in a new perspective, also reconcile kinetics with geometry.RésuméNous introduisons un cadre unifié pour discuter l'émergence de corrugations sur les interfaces matérielles transportées dans des milieux agités aléatoirement. En reliant la forme de ces interfaces au champ d'agitation qui la crée, nous formalisons une dynamique de bilan de population pour les r-éléments (segments de longueur r) nécessaires pour couvrir le contour de l'interface au cours de sa déformation. Tant que les corrugations croissent cinématiquement, les formes chan...

Source: Comptes Rendus Physique - October 23, 2018 Category: Physics Source Type: research