8th Liquid Matter Conference September 6-10, 2011 Wien, Austria ...

P7.124Thu 811:10-14:00Dissolution behaviour of binary mixtures in capillarytubes. Phase-field modelAnatoliy Vorobev 1 and Andrea Boghi 11 University of Southampton, University Road, SO17 1BJ, Southampton, United KingdomWe develop a hydrodynamic model for multiphase systems with undergoing phase transformations;in particular, our current focus is equilibration of binary systems. The phase-field approach isutilised to capture evolution of diffusive interfacial boundaries and to define dynamic changes ofinterfacial properties, such as surface tension. It is known that the behaviour of such systems isdefined by the Cahn-Hilliard-Navier-Stokes (CHNS) equations. Owing to dependence of mixturedensity on concentration, the full CHNS equations are quasi-compressible, which makes theirnumerical solution unfeasible. Recently, on the basis of the multiple scale method, the full set ofthe CHNS equations was simplified by splitting out the fast quasi-acoustic processes (similar tothe derivation of the low-Mach-number approximation). The resultant incompressible equationsrepresent the Boussinesq approximation of the CHNS equations and define the slow dissolutiondynamics of binary mixtures. The analysis of the obtained equations shows that the evolution ofbinary systems is accompanied by hydrodynamic flows generated by surface energy or gravitymechanisms; the rate of mass transfer through interfacial boundaries is also influenced by thesurface energy and gravity (barrodiffusion) terms. The resultant equations are utilised to studythe equilibrium states and phase transformations of binary systems occupying capillary tubes. 1Dand 2D numerical solutions are currently analysed and compared with the experiments and othernumerical simulations. In particular, we examine the spontaneous imbibition of water into a solutefilledcapillary tube horizontally placed into water bath. We also consider the equilibrium statesand the rate of dissolution of a solute droplet immersed in a tube quickly spinning around its axis.We found that a special attention should be given to the choice of the free energy function neededto define the phase-field model, which will be also discussed.124