Power-law coarsening in network-forming phase separation governed by mechanical relaxation

Abstract

A space-spanning network structure is a basic morphology in phase separation of soft and biomatter, alongside a droplet one. Despite its fundamental and industrial importance, the physical principle underlying such network-forming phase separation remains elusive. Here, we study the network coarsening during gas-liquid-type phase separation of colloidal suspensions and pure fluids, by hydrodynamic and molecular dynamics simulations, respectively. For both, the detailed analyses of the pore sizes and strain field reveal the self-similar network coarsening and the unconventional power-law growth more than a decade according to ℓ ∝ t1/2, where ℓ is the characteristic pore size and t is the elapsed time. We find that phase-separation dynamics is controlled by mechanical relaxation of the network-forming dense phase, whose limiting process is permeation flow of the solvent for colloidal suspensions and heat transport for pure fluids. This universal coarsening law would contribute to the fundamental physical understanding of network-forming phase separation.

Ice needles weave patterns of stones in freezing landscapes

“…Phase separation has in the past decades become a central physical principle for self-organized patterning in cell structure ( 21 , 22 ), gravitational fluid ( 23 , 24 ), active matter ( 18 , 25 – 28 ), and ecological systems ( 29 – 31 ). Herein, we suggest that the principle leads to insights into pattern formation in geomorphic systems.…”

Macroporosity Control by Phase Separation in Sol-Gel Derived Monoliths and Microspheres

“…In general, phase separation starts from a molecular length scale and proceeds with the growing of the characteristic size (mean dimension of a set of skeleton and pore) of phase-separated domains with time toward a macroscopic length scale. The dynamics of phase separation were studied intensively in the 20th century [ 8 , 9 ], notwithstanding the recent studies that have been devoted to this topic, namely the coarsening behavior of the network-forming phase separation of colloidal suspensions [ 10 , 11 ]. In particular, phase separation by spinodal decomposition occurs in the unstable region of the miscibility window in an equilibrium phase diagram.…”

Reincarnations of the phase separation problem

“…But this was regarded chiefly as a nuisance, something akin to trying to play sports during bad weather. These new papers show beautiful conceptual novelty 1 and practical utility 2 . When one speculates how these ideas may spread in the future, the latter is especially notable when one considers the high value that the era in which we live gives to having technology impact.…”

“…enter the statement of the problem 3 . Yet the paper by Tateno and Tanaka 1 demonstrates unconventional t 1/2 power-law growth of time (t)-dependent structure in liquid-liquid phase separation, shockingly faster than the t 1/3 dependence that normally follows from conventional analysis for the Lifshitz-Slyozov-Wagner mechanism, Brownian coagulation mechanism, and even nonequilibrium thermodynamics when energy-dissipating systems are mapped onto a formalism of equivalent free energy 6 . The engineering-oriented paper by Xi et al likewise demonstrates findings contrary to textbook expectations.…”

“…Then came a surprise-the identification of spinodal decomposition (dotted red line)4 . b In modern times, Tanaka and coworkers1,6 have demonstrated the novelty of thermal phase separation when the phase-separating components respond over drastically different response times, shown here schematically as viscoelasticity resulting from time-dependent elastic (red) interactions in the viscous (blue) liquid. c Other modern work toggles molecular interactions themselves during the course of phase separation, shown here schematically as modulation in time.…”