Tests of dynamical scaling in three-dimensional spinodal decomposition

Abstract

We simulate late-stage coarsening of a 3-D symmetric binary fluid. With reduced units l, t (with scales set by viscosity, density and surface tension) our data extends two decades in t beyond earlier work. Across at least four decades, our own and others' individual datasets (< 1 decade each) show viscous hydrodynamic scaling (l ∼ a + bt), but b is not constant between runs as this scaling demands. This betrays either the unexpected intrusion of a discretization (or molecular) lengthscale, or an exceptionally slow crossover between viscous and inertial regimes.PACS numbers: 64.75+g, 07.05. Tp, 82.20.Wt When an incompressible binary fluid mixture is quenched far below its spinodal temperature, it will phase separate into domains of different composition. For symmetric (or nearly symmetric) mixtures, these domains will, at late times, form a bicontinuous structure, with sharp, well-developed interfaces. The late-time evolution of this structure in three dimensions remains incompletely understood despite theoretical [1][2][3] experimental [4] and simulation [5][6][7][8] work over recent years.In the present work, we use the DPD (dissipative particle dynamics) simulation algorithm [9] to access length and time-scales far beyond those reached previously. (Details of the simulations will appear elsewhere [10].) When combined with other datasets [5][6][7] our results allow a severe test of the dynamical scaling ideas which underlie most theoretical treatments [1][2][3] and data analyses [4]. We conclude that dynamical scaling is in doubt, perhaps due to the intrusion of a molecular lengthscale through the physics of topological reconnection events. An alternative explanation of the results, based on a universal but extremely slow crossover, is also carefully examined.As emphasized by Siggia [1], the physics of spinodal decomposition involves capillary forces, viscous dissipation, and fluid inertia. Indeed, assuming that no other physics enters, then the parameters governing the behavior are the interfacial tension σ, fluid mass density ρ, and viscosity η. (We now specialize to 50/50 mixtures with complete symmetry of the two species. Any asymmetries in composition, thermodynamics or viscosity [11] provide additional control parameters.) From these three parameters can be constructed only one length, L 0 = η 2 /ρσ and one time T 0 = η 3 /ρσ 2 . We now define the lengthscale L(T ) of the domain structure at time T via the structure factor S(k) as [12] L = (2π) kS(k)dk/ S(k)dk −1 . The exclusion of other physics in late-stage growth then leads us to the dynamical scaling hypothesis [1,2]:where we define reduced time and length variables via l ≡ L/L 0 and t ≡ T /T 0 . Since dynamical scaling should hold only after interfaces have become sharp, and transport by molecular diffusion suppressed, we have allowed for a nonuniversal offset a in eq.1. Thereafter the scaling function f (t) should approach a universal form, the same for all (fully symmetric, deep-quenched, incompressible) binary fluid mixtures. It was argued furt...

Binary fluids under steady shear in three dimensions

“…(Note however that earlier studies accepted L < Λ/2 as sufficient, e.g. [21].) Accordingly we expect that the quantitative scaling of all our correlation length data with shear rate may still be affected by finite size corrections.…”

Spinodal decomposition of asymmetric binary fluids in a micro-Couette geometry simulated with molecular dynamics

“…12 The two earlier stages have also been studied in computer simulations by using dedicated Navier-Stokes solvers, such as LB and lattice gas automata, [13][14][15] and by off-lattice particle-based methods including molecular dynamics ͑MD͒ and dissipative particle dynamics ͑DPD͒. [16][17][18][19][20][21] Other spinodal decomposition processes are less well understood than the idealized situation outlined above, although the basic principles guiding the ongoing investigations remain the same. Dynamical asymmetry of the two mixed fluids, meaning that their viscosities differ significantly or that one component shows viscoelastic behavior, explains the complex phase separation processes and the "phase inversion" phenomenon observed in polymer-solvent mixtures and colloidal suspensions.…”

Dynamical geometry for multiscale dissipative particle dynamics

“…Each fluid particle interacts only with its nearest neighbour, thereby reducing the amount of communication. Previous standard dissipative particle methods [6,23] lacked this strong locality feature, interacting with many more neighbouring particles and severely limiting the parallel performance [24,25].…”