Article
The Viscous Froth Model: steady states and the highvelocity limit
Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences (Impact Factor: 2). 06/2009; DOI: 10.1098/rspa.2009.0057
Source: OAI

Article: Rheology of aqueous foams
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ABSTRACT: Les mousses aqueuses sont des suspensions de bulles à l'intérieur de phases aqueuses. Leur caractère multiphasique conduit à un comportement rhéologique complexe qui est utile dans de nombreuses applications, depuis la récupération du pétrole jusqu'aux industries alimentaire et cosmétique. Leur structure est très similaire à celle des émulsions, de telle sorte que ces deux types de matériaux partagent des propriétés mécaniques communes. En particulier, la présence de surfactants aux interfaces gaz–liquide mène à des propriétés interfaciales et dissipatives particulières. La rhéologie des mousses constitue un champ de recherche actif et a déjà été évoquée dans plusieurs revues, la plupart d'entre elles couvrant des mesures rhéométriques à l'échelle de la mousse, couplées avec des interprétations à l'échelle locale des bulles et des interfaces. Nous commençons cette revue en suivant cette approche, puis nous tentons de couvrir les caractéristiques multiéchelles des écoulements de mousses liquides, en insistant sur les régimes où des échelles de longueur intermédiaires doivent être prises en compte, ou sur les régimes suffisamment rapides pour que l'écoulement sorte de la limite quasi statique.Comptes Rendus Physique 10/2014; · 1.64 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Numerical simulations of mass transfer are performed for a circulating liquid drop with applications in liquid–liquid extraction. Simulation parameters are chosen for a multicomponent ternary system acetone–methanol–benzene. The drop circulation pattern is estimated via a truncated Galerkin representation of the drop streamfunction. Fickian diffusivities for multicomponent mass transfer are obtained via Maxwell–Stefan theory with thermodynamic corrections. The advection–diffusion equations governing mass transfer are solved via two distinct numerical methods: a finite difference scheme (using the alternating direction implicit method) and a finite element scheme. Good agreement was obtained between both schemes. Simulation results are presented for a Reynolds number (Re=30) and for a selection of Peclet numbers (Pe=100, 1000 and 10 000, thereby giving insight into the effects of increasing Peclet number). The numerical simulations of the full advection–diffusion equations are compared against predictions of a rigid drop model (i.e. without circulation) and also against predictions of a semianalytical boundary layer model developed by UribeRamirez and Korchinsky. Results for bulk mass fractions reveal that the rigid drop model predictions evolve too slowly, while the boundary layer model predictions evolve much more quickly than the numerical simulations. Advection–diffusion simulation results for the evolution of mass fractions at selected individual locations in the drop show that points on streamlines nearest to the drop surface and/or drop axis evolve fastest, while those closest to the drop internal stagnation point evolve slowest. Corroborated by contour plots of component concentrations throughout the drop at selected times, this supports a picture whereby mass fractions become roughly uniform along individual streamlines, but mass is transferred diffusively from streamline to streamline.Chemical Engineering Science 05/2010; · 2.61 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The viscous froth model is used to study the evolution of a long and initially straight soap film which is sheared by movin its endpoint at a constant velocity in a direction perpendicular to the initial film orientation. Film elements are thereb set into motion as a result of the shear, and the film curves. The simple scenario described here enables an analysis of th transport of curvature along the film, which is important in foam rheology, in particular for energyrelaxing ‘topologica transformations’. Curvature is shown to be transported diffusively along films, with an effective diffusivity scaling as th ratio of film tension to the viscous froth drag coefficient. Computed (finitelength) film shapes at different times are foun to approximate well to the semiinfinite film and are observed to collapse with distances rescaled by the square root of time. The tangent to the film at the endpoint reorients so as to make a very small angle with the line along which the film endpoin is dragged, and this angle decays roughly exponentially in time. The computed results are described in terms of a simple asymptoti solution corresponding to an infinite film that initially contains a rightangled corner.Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 11/2013; 469(2159). · 2.00 Impact Factor
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