  Agglomeration, adsorption, and extraction in dispersed multiphase systems are
ubiquitously encountered in biological systems, energy industry, and medical
science. In this work, a novel lattice model is extended to the three-component
complex systems and criterions based on the determinant \Delta_i=F_i-K_c,i are
accordingly proposed to predict the aforementioned behaviors based on a
Helmholtz free energy formulation. Here, three characteristic factors F_i's are
introduced to describe the internal energy effect, i.e.,F_1=A^11+A^22-2A^12
(agglomeration), F_2=A^22+A^13-A^12-A^23 (adsorption) and
F_3=A^22+2A^13-A^33-2A^12 (extraction), where A_ij denotes the conservative
potential coefficient between liquid particles in phase i and j, while the
entropy factors K_c,i's in the determinants depend on the local structure of
the liquid. To verify the theoretical criterions, many-body dissipative
particle dynamics (mDPD) are employed to simulate the phase transition
phenomena in various many-body dissipative systems, including agglomeration in
a binary system, adsorption on solid surfaces from the liquid phase, and
extraction-adsorption around an immiscible liquid-liquid interface. The
simulation results show the notable dependence of the dispersed phase
distribution transition on the quasi-order parameters \Delta_i's, which
indicates the great potential of our model to analyzing various dispersed
multiphase systems. The criterions are expected to be extended to study the
structure effect induced by the temperature and dispersed particle shape on the
phase transition phenomena in those complex systems.
