Vibrational convection in a heterogeneous binary mixture. Part 1. Time-averaged equations. (14th May 2019)

• Record Type: Journal Article
• Authors: Vorobev, Anatoliy; Lyubimova, Tatyana
• Is Part Of: Journal of fluid mechanics. Volume 870(2019)
• Page Start: 543
• Page End: 562
• Publication Date: 2019-05-14
• Subjects: multiphase flow; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2019.282
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : High-frequency vibrations of a container filled with a fluid generate pulsation flows that however are barely visible with the naked eye, and induce the slow but large-amplitude averaged flows that are important for various practical applications. In this work we derive a theoretical model that gives the averaged description of the influence of uniform high-frequency vibrations on an isothermal mixture of two slowly miscible liquids. The miscible multiphase system is described within the framework of the phase-field approach. The full Cahn–Hillard–Navier–Stokes equations are split into the separate systems for the quasi-acoustic, pulsating and averaged flow fields, eliminating the need for the resolution of the short time scale pulsation motion and thus making the analysis of the long-term evolution much more efficient. The resultant averaged model includes the effects of concentration diffusion and barodiffusion, the dynamic interfacial stresses and the generation of the hydrodynamic flows by non-homogeneities of the concentration field (when they are combined with the effects of gravity and vibrations). The resultant model for the vibrational convection in a heterogeneous mixture of two fluids separated by diffusive boundaries could be used for the description of processes of mixing/de-mixing, solidification/melting, polymerisation, etc. in the presence of vibrations.