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A numerical solution to the one dimensional Allen-Cahn equation. The Allen–Cahn equation (after John W. Cahn and Sam Allen) is a reaction–diffusion equation of mathematical physics which describes the process of phase separation in multi-component alloy systems, including order-disorder transitions.
The Cahn–Hilliard equation (after John W. Cahn and John E. Hilliard) [1] is an equation of mathematical physics which describes the process of phase separation, spinodal decomposition, by which the two components of a binary fluid spontaneously separate and form domains pure in each component.
The most common type of phase separation is between two immiscible liquids, such as oil and water. This type of phase separation is known as liquid-liquid equilibrium. Colloids are formed by phase separation, though not all phase separations forms colloids - for example oil and water can form separated layers under gravity rather than remaining ...
WB Hardy linked formation of biological colloids with phase separation in his study of globulins, stating that: "The globulin is dispersed in the solvent as particles which are the colloid particles and which are so large as to form an internal phase", [6] and further contributed to the basic physical description of oil-water phase separation. [7]
Polymerization-induced phase separation (PIPS) is the occurrence of phase separation in a multicomponent mixture induced by the polymerization of one or more components. [1] [2] The increase in molecular weight of the reactive component renders one or more components to be mutually immiscible in one another, resulting in spontaneous phase segregation.
Microstructural evolution under the Cahn–Hilliard equation, demonstrating distinctive coarsening and phase separation. Spinodal decomposition is a mechanism by which a single thermodynamic phase spontaneously separates into two phases (without nucleation). [1] Decomposition occurs when there is no thermodynamic barrier to phase separation. As ...
Liquid-liquid phase separation (LLPS) is well defined in the Biomolecular condensate page. LLPS databases cover different aspects of LLPS phenomena, ranging from cellular location of the Membraneless Organelles (MLOs) to the role of a particular protein/region forming the condensate state.
This phase separation can, however, be arrested by chemically-mediated inter-particle torques [24] or hydrodynamic interactions, [25] [26] which could explain the formation of finite-size clusters. Alternatively, clustering and phase-separation could be due to the presence of inter-particle attractive forces, as in equilibrium suspensions.