Hydrodynamic coarsening of binary fluids

Colloidal phase separation of concentrated PNIPAm solutions

In the concentration range of 1-6 wt %, solutions of a thermosensitive polymer (poly-N-isopropylacrylamide (PNIPAm), Mw = 1.4 x 10(5) g.mol(-1)) are shown to phase separate in the form of dense stable colloids of nearly pure polymer. Diffuse wave spectroscopy and small-angle neutron scattering both provide consistent measurements of the colloidal size as a function of temperature. Results are in agreement with a Cahn regime of spinodal decomposition blocked at an early stage, prior to a growth that would lead to a macroscopic phase separation. [Early results of this work were presented at the 231st American Chemical Society National Meeting, Symposium on Amphiphilic Polymers, Atlanta, GA, 2006, March 26-30.].

Dynamics of a drop at a fluid interface under shear

We analyze the dynamics of a two-dimensional drop lying on a fluid interface, sometimes called a liquid lens, subjected to simple shear flow. The three fluids, the drop and the two external fluids, meet at a triple point (or a triple line in three dimensions). A requirement for steady drop shapes is that the triple points are stationary. This leads to a flow topology different than that of a freely suspended drop. Results are substantiated with numerical results using a level set method for interface evolution and treatment of triple points. Possible implications for new drop instabilities are also discussed.

Coarsening dynamics of phase-separating systems

When a system such as a binary liquid is cooled rapidly from a homogeneous phase into a two-phase region, domains of the two equilibrium phases form and grow ('coarsen') with time. In the absence of an external drive, such as gravity or an imposed shear flow, a dynamical-scaling regime emerges in which the domain morphology is statistically self-similar at different times, up to an overall length-scale (coarsening scale) that grows with time. In the first part of the paper, the scaling phenomenology will be reviewed and the time-dependence of the coarsening scale will be discussed in the context of a number of different physical systems and scaling regimes. In the second part, the influence of an external drive, in particular a shear flow, will be addressed and recent developments reviewed. Interesting open questions include the late-time behaviour under shear and whether the coarsening continues indefinitely or is ultimately arrested by the shear flow.

Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. The model is derivable from a continuous-time Boltzmann-BGK equation in the presence of an intercomponent body force. We find the average domain size grows with time as t(gamma), where gamma increases in the range 0.545+/-0.014<gamma<0.717+/-0.002, consistent with a crossover between diffusive t(1/3) and hydrodynamic viscous, t(1.0), behavior. We find good collapse onto a single scaling function, yet the domain growth exponents differ from previous results for similar values of the unique characteristic length L0 and time T0 that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. For Re=2.7 and small wave numbers q we also find a q(2)<-->q(4) crossover in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later stages (Re=37). This excludes noise as the cause for a q(2) behavior, as analytically derived from Yeung and proposed by Appert et al. and Love et al. on the basis of their lattice-gas simulations. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wave numbers less than a threshold value, in accordance with the diffusive Cahn-Hilliard Model B. However, this exponential growth is also present in regimes proscribed by that model. There is no evidence that regions of parameter space for which the scheme is numerically stable become unstable as the simulations proceed, in agreement with finite-difference relaxational models and in contradistinction with an unconditionally unstable lattice-BGK free-energy model previously reported. Those numerical instabilities that do arise in this model are the result of large intercomponent forces which turn the equilibrium distribution negative.

Hydrodynamics of binary fluid phase segregation

Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field u when the system is segregated into two phases (at low temperatures) with a sharp interface between them. u satisfies the incompressible Navier-Stokes equations together with a jump boundary condition for the pressure across the interface which, in turn, moves with a velocity given by the normal component of u. Numerical simulations of the Vlasov-Boltzmann equations for shear flows parallel and perpendicular to the interface in a phase segregated mixture support this analysis. We expect similar behavior in real fluid mixtures.

Three-dimensional hydrodynamic lattice-gas simulations of domain growth and self-assembly in binary immiscible and ternary amphiphilic fluids

We simulate the dynamics of phase assembly in binary immiscible fluids and ternary microemulsions using a three-dimensional hydrodynamic lattice-gas approach. For critical spinodal decomposition we perform the scaling analysis in reduced variables introduced by Jury et al. [Phys. Rev. E 59, R2535 (1999)] and by Bladon et al. [Phys. Rev. Lett. 83, 579 (1999)]. We find a late-stage scaling exponent consistent with the R approximately t(2/3) inertial regime. However, as observed with the previous lattice-gas model of Appert et al. [J. Stat. Phys. 81, 181 (1995)] our data do not fall in the same range of reduced length and time as those of Jury et al. and Bladon et al. For off-critical binary spinodal decomposition we observe a reduction of the effective exponent with decreasing volume fraction of the minority phase. However, the n=1 / 3 Lifshitz-Slyzov-Wagner droplet coalescence exponent is not observed. Adding a sufficient number of surfactant particles to a critical quench of binary immiscible fluids produces a ternary bicontinuous microemulsion. We observe a change in scaling behavior from algebraic to logarithmic growth for amphiphilic fluids in which the domain growth is not arrested. For formation of a microemulsion where the domain growth is halted we find that a stretched exponential growth law provides the best fit to the data.