Spinodal decomposition under shear flow

Padilla, P.; Toxværd, Søren

doi:10.1063/1.473788

Cited by 38 publications

(40 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Despite previous experimental [4,5,6,7,8,9,10,11,12,13,14], numerical [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] and theoretical [18,19,20,21,29,32,33,34,35,36,37] work, this question remained open until the recent simulation studies of Stansell et al in Refs [38,39]. Using Lattice Boltzmann techniques, they gave convincing evidence for the formation of nonequilibrium steady states, with domains of a finite size set by the inverse shear rate, independent of the system size.…”

Section: Introductionmentioning

confidence: 98%

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: Introductionmentioning

confidence: 98%

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

“…The full problem with the Navier-Stokes and the convection-diffusion equations has been considered in Refs. [25,32,33,34,35,36] but also in this case reliable results for the growth exponents are not yet available. Actually, the true existence of an asymptotic growth regime in alternative with a stationary state with a finite transverse size is a question still to be clarified [37,25].…”

Section: Introductionmentioning

confidence: 99%

Phase-separating binary fluids under oscillatory shear

Gonnella

Lamura³

2003

Phys. Rev. E

View full text Add to dashboard Cite

We apply lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the convection-diffusion equations. The interplay between several time scales produces a rich and complex phenomenology. We investigate the effects of different oscillation frequencies and viscosities on the morphology of the phase separating domains. We find that at high frequencies the evolution is almost isotropic with growth exponents 2/3 and 1/3 in the inertial (low viscosity) and diffusive (high viscosity) regimes, respectively. When the period of the applied shear flow becomes of the same order of the relaxation time TR of the shear velocity profile, anisotropic effects are clearly observable. In correspondence with non-linear patterns for the velocity profiles, we find configurations where lamellar order close to the walls coexists with isotropic domains in the middle of the system. For particular values of frequency and viscosity it can also happen that the convective effects induced by the oscillations cause an interruption or a slowing of the segregation process, as found in some experiments. Finally, at very low frequencies, the morphology of domains is characterized by lamellar order everywhere in the system resembling what happens in the case with steady shear. 05.70.Ln, 47.20.Hw, 47.11.+j, 83.10.Tv

show abstract

“…Characteristic length scales in directions parallel and perpendicular to the flow increase as (t 5 / ln t) 1/4 and (t/ ln t) 1/4 respectively. The structure factor in the shear-flow plane exhibits two parallel ridges as observed in experiment.The dynamics of phase separation under shear has attracted considerable theoretical [1], experimental [2][3][4][5] and simulational [6][7][8] attention in recent years. In the absence of shear, the dynamics of phase separation is now quite well understood [9].…”

mentioning

confidence: 99%

Dynamics of Phase Separation under Shear: A Soluble Model

Rapapa

Bray

1999

Phys. Rev. Lett.

View full text Add to dashboard Cite

The dynamics of phase separation for a binary fluid subjected to a uniform shear are solved exactly for a model in which the order parameter is generalized to a n-component vector and the large-n limit taken. Characteristic length scales in directions parallel and perpendicular to the flow increase as (t 5 / ln t) 1/4 and (t/ ln t) 1/4 respectively. The structure factor in the shear-flow plane exhibits two parallel ridges as observed in experiment.The dynamics of phase separation under shear has attracted considerable theoretical [1], experimental [2][3][4][5] and simulational [6][7][8] attention in recent years. In the absence of shear, the dynamics of phase separation is now quite well understood [9]. Domains of the two equilibrium phases are formed, and coarsen with time in a manner well-described by a dynamical scaling phenomenology with a single growing length scale L(t) which generally grows as a power law in time, L(t) ∼ t a . The structure factor is spherically symmetric, with a maximum at wavevector k m ∼ L −1 . For binary fluids, the exponent a takes different values depending on the dynamical regime under study. In order of increasing time, there are 'diffusive' (a = 1/3), 'viscous hydrodynamic' (a = 1) and the 'inertial hydrodynamic' (a = 2/3) regimes [9][10][11]. The crossover between these regimes is determined by the fluid properties (viscosity, density). Here we will focus on the diffusive regime, in which hydrodynamic effects can be neglected. In the absence of shear, phase separation is described by the Cahn-Hilliard equation for the order-parameter field φ(r, t), namely [9]. If a uniform shear flow is imposed in the x-direction, with shear direction y, the flow velocity is v x = γy, where γ is the shear rate. For an incompressible fluid, the Cahn-Hilliard equation acquires an advective term v · ∇φ = γy∂ x φ on the left-hand side. Generalizing to an n-component vector order parameter, this givesFor a critical mixture quenched into the two-phase region from the homogeneous phase, an appropriate initial condition is a Gaussian random field with zero mean and short-range correlations:In this Letter we present the first exact solution for a system phase-separating under shear, by solving (1) in the limit n → ∞. We obtain characteristic length scales, andmz ∼ (t/ ln t) 1/4 . These are extracted from the structure factor, S(k, t) which has four maxima, located at k = ±(k mx , −k my , ±k mz ). Thus the rotational symmetry of the zero-shear limit is completely broken. In the k z = 0 plane there are two maxima terminating two long parallel ridges as observed in experiment [2]. The structure factor exhibits multiscaling [12], rather than simple scaling, but this is presumably an artifact of the large-n limit, as in the zero-shear case [13]. At the end of the paper we conjecture how the results will be modified for the scalar order parameter appropriate to binary mixtures.In the limit n → ∞, one can replace ( φ) 2 /n in (1) by its mean in the usual way, leading to a self-consistent linear equation. After ...

show abstract

Spinodal decomposition under shear flow

Cited by 38 publications

References 23 publications

Role of inertia in nonequilibrium steady states of sheared binary fluids

Role of inertia in nonequilibrium steady states of sheared binary fluids

Phase-separating binary fluids under oscillatory shear

Dynamics of Phase Separation under Shear: A Soluble Model

Contact Info

Product

Resources

About