Numerical simulation for separation of multi-phase immiscible fluids in porous media

Based on a lattice Boltzmann method and general principles of porous flow, a numerical technique is presented for analysing the separation of multi-phase immiscible fluids in porous media. The total body force acting on fluid particles is modified by axiding relative permeability in Nithiarasu＇s expression with an axiditional surface tension term. As a test of this model, we simulate the phase separation for the case of two immiscible fluids. The numerical results show that the two coupling relative permeability coefficients K12 and K21 have the same magnitude, so the linear flux-forcing relationships satisfy Onsager reciprocity. Phase separation phenomenon is shown with the time evolution of density distribution and bears a strong similarity to the results obtained from other numerical models and the flows in sands. At the same time, the dynamical rules in this model are local, therefore it can be run on massively parallel computers with well computational efficiency.

Modeling of Coalescence and Separation of Liquid Droplets During Solidification of Immiscible Alloys

Directional solidification methods are being used f or in-situ production of metallic immiscible composites. A quantitative understa nding of the dynamic behavior and growth kinetics of the nucleated second phase during solidification is necessary to produce homogeneous dispersion in solidifi ed composites. This paper presents a mathematical model for describing the grow th of nucleated dispersed phase in the two-liquid phase region ahead of the sol idification front and the entrapment of these droplets by the moving solid-liqu id interface in vertical unidirectional solidification systems. The model has t wo components. A macro-heat transfer model for describing the temperature prof iles and the rate of advance of the solidification front. The dynamic behavior and coalescence and growth of nucleated droplets in the two-liquid phase region under the influence of effective gravity and thermocapillary forces were repres ented through the solution the droplet momentum and mass conservation equations in particle space. These two components of the models were coupled through a sp ecial algorithm for tracking the particle location and size with respect to movi ng solidification front in the solidification time scale. The model is used to study the particle size distribution in unidirectional solidified Zn-Bi hypermo notectic alloys at reduced gravity conditions. It has been found that the parti cle size and distribution in the solidified alloy depends on solidification rate and the ratio of effective gravity to thermocapillary forces. It was also foun d that uniform dispersion could only be obtained in a very narrow range of effec tive gravity values near zero gravity. The model predictions were compared agai nst experimental measurements obtained at different effective gravity conditions in a novel unidirectional solidification apparatus that uses electromagnetic fo rces to modulate gravitational forces. The model was found to reasonably predic t the experimentally measured particle size and distribution over the entire ran ge of effective gravity investigated as well as gravity conditions for settling and flotation of the second phase during solidification. The practical signific ance of these findings will be discussed.