Breakdown of Scale Invariance in the Coarsening of Phase-Separating Binary Fluids

Wagner, A. James; Yeomans, J. M.

doi:10.1103/physrevlett.80.1429

Cited by 148 publications

(178 citation statements)

References 12 publications

Supporting

Mentioning

156

Contrasting

Order By: Relevance

“…In contrast, our aim in Secs. VIII A and VIII B is simply to reproduce behaviour seen earlier in the literature by lattice Boltzmann techniques [38,41,42]. The purpose of this comparative part of our study is threefold: First, and foremost, to develop confidence in our own algorithm and the code via which it is implemented; second, to demonstrate the method used here, which is potentially simpler and faster than lattice Boltzmann, to be equally capable of capturing the physics of demixing, in 2D at least; and third, to provide an independent check of some recent results concerning nonequilibrium steady states under shear [38].…”

Section: Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Role of inertia in nonequilibrium steady states of sheared binary fluids

Fielding

2008

Phys. Rev. E

View full text Add to dashboard Cite

We study numerically phase separation in a binary fluid subject to an applied shear flow in two dimensions, with full hydrodynamics. To do so, we introduce a mixed finite-differencing/spectral simulation technique, with a transformation to render trivial the implementation of Lees-Edwards sheared periodic boundary conditions. For systems with inertia, we reproduce the nonequilibrium steady states reported in a recent lattice Boltzmann study. The domain coarsening that would occur in zero shear is arrested by the applied shear flow, which restores a finite domain size set by the inverse shear rate. For inertialess systems, in contrast, we find no evidence of nonequilibrium steady states free of finite size effects: coarsening persists indefinitely until the typical domain size attains the system size, as in zero shear. We present an analytical argument that supports this observation, and that furthermore provides a possible explanation for a hitherto puzzling property of the nonequilibrium steady states with inertia.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

“…In contrast, our aim in Secs. VIII A and VIII B is simply to reproduce the behaviour seen in previous lattice Boltzmann studies [38,41,42], thereby gaining confidence in our own simulation method. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Role of inertia in nonequilibrium steady states of sheared binary fluids

Fielding

2008

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…Thermodynamic coarsening-first studied in the context of solid alloys [2,4]-can be fundamentally altered in fluid mixtures by means of hydrodynamic effects that lead to more complex dynamics. For instance, hydrodynamic coalescence due to curvature-induced pressure differences can enhance the coarsening rate [5,6]. Under uniform shear flow, a highly anisotropic layered phase ordering appears in the mixture [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…In previous studies of spinodal decomposition coupled to flow, fluid phase is inferred from composition, and not independently described [6,9,[12][13][14][15]. The free energy of such mixtures is formulated as a functional of molar fractions and their gradients and, in its simplest setting, the coarsening dynamics is described by a Cahn-Hilliard equation [29].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Cueto‐Felgueroso

Juanes

2016

Phys. Rev. E

View full text Add to dashboard Cite

We study the evolution of binary mixtures far from equilibrium, and show that the interplay between phase separation and hydrodynamic instability can arrest the Ostwald ripening process characteristic of nonflowing mixtures. We describe a model binary system in a Hele-Shaw cell using a phase-field approach with explicit dependence of both phase fraction and mass concentration. When the viscosity contrast between phases is large (as is the case for gas and liquid phases), an imposed background flow leads to viscous fingering, phase branching, and pinch off. This dynamic flow disorder limits phase growth and arrests thermodynamic coarsening. As a result, the system reaches a regime of statistical steady state in which the binary mixture is permanently driven away from equilibrium.

show abstract

“…(Without shear, subtle non-scaling effects arise in 2D from the formation of disconnected droplets [8], but shear seems to suppress these [9].) Performing simulations in 2D is therefore a fair compromise, especially given the extreme computational demands of the full 3D problem [3,10].…”

mentioning

confidence: 99%

Nonequilibrium Steady States in Sheared Binary Fluids

et al. 2006

View full text Add to dashboard Cite

We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths Lx,y in the directions (x, y) of velocity and velocity gradient. Apparent scaling exponents are estimated as Lx ∼γ −2/3 and Ly ∼γ −3/4 . We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.PACS numbers: 47.11.+jSystems that are not in thermal equilibrium play a central role in modern statistical physics, and arise in areas ranging from soap manufacture to subcellular biology [1]. Such systems include two important classes: those that are evolving towards Boltzmann equilibrium (e.g., by phase separation following a temperature quench), and those that are maintained in nonequilibrium by continuous driving (such as a shear flow). Of fundamental interest, and surprising physical subtlety, are systems combining both features -such as a binary fluid undergoing phase separation in the presence of shear. Here it is not known [2,3] whether coarsening continues indefinitely, as it does without shear, or whether a steady state is reached, in which the characteristic length scales L x,y,z of the fluid domain structure attain finiteγ-dependent values at late times. (We define the mean velocity as u x =γy so that x, y, z are velocity, velocity gradient and vorticity directions respectively;γ is the shear rate.) Experimentally, saturating length scales are reportedly reached after a period of anisotropic domain growth [2,4]. However, the extreme elongation of domains along the flow direction means that, even in experiments, finite size effects could play an essential role in such saturation [5]. Theories in which the velocity does not fluctuate, but does advect the diffusive fluctuations of the concentration field, predict instead indefinite coarsening, with length scales L y,z scaling asγ-independent powers of the time t since quench, and (typically) L x ∼γtL y [5]. In real fluids, however, the velocity fluctuates strongly in nonlinear response to the advected concentration field, and hydrodynamic scaling arguments, balancing either interfacial and viscous or interfacial and inertial forces, predict saturation (e.g., L ∼γ −1 or L ∼γ −2/3 ) [3,6,7]. Given these experimental and theoretical differences of opinion, computer simulations of sheared binary fluids, with full hydrodynamics, are of major interest.The aforementioned scaling arguments cannot really distinguish one Cartesian direction from another, but even in theories that can do so, a two dimensional (2D) representation, suppressing z, is expected to capture the main physics [5]. (Without shear, subtle non-scaling effects arise in 2D from the formation of disconnected droplets [8], but shear seems to suppress these [9].) Performing simulations in 2D is therefore a fair compromise, especially given the extreme computational demands of the full 3D problem [3,10]. But, apart from [9,11]...

show abstract

Breakdown of Scale Invariance in the Coarsening of Phase-Separating Binary Fluids

Cited by 148 publications

References 12 publications

Role of inertia in nonequilibrium steady states of sheared binary fluids

Role of inertia in nonequilibrium steady states of sheared binary fluids

Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Nonequilibrium Steady States in Sheared Binary Fluids

Contact Info

Product

Resources

About