Criteria of Distribution Transitions in Dispersed Multiphase Systems Based on an Extended Lattice Model

Dispersed multiphase systems are ubiquitous in biological systems, energy industries, and medical science. The distribution transition of the dispersed phase is critical to the properties and functions of the multiphase systems, among which the agglomeration, adsorption, and extraction processes are of most significance due to their impact on the colloidal stability, interface modification, and particle synthesis. To reveal fundamental correlations between the macroscopic particle distributions and the microscopic interactions, general thermodynamic models of the dispersed multiphase systems are needed. Here, based on Meyer's model, which is restricted to binary isotropic mixtures, we propose a novel extended lattice model that can be applied to multicomponent anisotropic mixtures with interfaces considered. For agglomeration, adsorption, and extraction processes, the approximate free energy differences between the initial distribution and the final distribution are obtained. Based on the minimum free energy principle, the above free energy differences are used to derive three criteria for the prediction of the preferable distribution of the system with given interparticle interaction potentials. While the quasi-uniform number density assumption is still required for all the previous lattice models, the long-range interactions neglected by previous lattice models are incorporated. The validity of our model and criteria is verified by many-body dissipative particle dynamics (mDPD) simulations. By tuning the interaction coefficients between mDPD particles, the simulated distribution transitions for all the agglomeration, adsorption, and extraction cases perfectly match the predictions from the three criteria. The good agreement between the theoretical predictions and the mDPD simulation results shows the great potential of our model for applications in various dispersed multiphase systems.