Kinetics of nucleation and growth in a near-critical binary liquid mixture at rest and under a shear flow

Role of hydrodynamics in liquid-liquid transition of a single-component substance

Liquid-liquid transition (LLT) is an unconventional transition between two liquid states in a single-component system. This phenomenon has recently attracted considerable attention not only because of its counterintuitive nature but also since it is crucial for our fundamental understanding of the liquid state. However, its physical understanding has remained elusive, particularly of the critical dynamics and phase-ordering kinetics. So far, the hydrodynamic degree of freedom, which is the most intrinsic kinetic feature of liquids, has been neglected in its theoretical description. Here we develop a Ginzburg-Landau-type kinetic theory of LLT taking it into account, based on a two-order parameter model. We examine slow critical fluctuations of the nonconserved order parameter coupled to the hydrodynamic degree of freedom in equilibrium. We also study the nonequilibrium process of LLT. We show both analytically and numerically that domain growth becomes faster (slower), depending upon the density decrease (increase) upon the transition, as a consequence of hydrodynamic flow induced by the density change. The coupling between nonconserved order parameter and hydrodynamic interaction results in anomalous domain growth in both nucleation-growth-type and spinodal-decomposition-type LLT. Our study highlights the characteristic features of hydrodynamic fluctuations and phase ordering during LLT under complex interplay among conserved and nonconserved order parameters and the hydrodynamic transport intrinsic to the liquid state.

Emulsification in binary liquids containing colloidal particles: a structure-factor analysis

We present a quantitative confocal-microscopy study of the transient and final microstructure of particle-stabilized emulsions formed via demixing in a binary liquid. To this end, we have developed an image-analysis method that relies on structure factors obtained from discrete Fourier transforms of individual frames in confocal image sequences. Radially averaging the squared modulus of these Fourier transforms before peak fitting allows extraction of dominant length scales over the entire temperature range of the quench. Our procedure even yields information just after droplet nucleation, when the (fluorescence) contrast between the two separating phases is scarcely discernible in the images. We find that our emulsions are stabilized on experimental timescales by interfacial particles and that they are likely to have bimodal droplet-size distributions. We attribute the latter to coalescence together with creaming being the main coarsening mechanism during the late stages of emulsification and we support this claim with (direct) confocal-microscopy observations. In addition, our results imply that the observed droplets emerge from particle-promoted nucleation, possibly followed by a free-growth regime. Finally, we argue that creaming strongly affects droplet growth during the early stages of emulsification. Future investigations could clarify the link between quench conditions and resulting microstructure, paving the way for tailor-made particle-stabilized emulsions from binary liquids.

Growth of monodisperse mesoscopic metal-oxide colloids under constant monomer supply

In closed systems, control over the size of monodisperse metal-oxide colloids is generally limited to submicrometric dimensions. To overcome this difficulty, we explore the formation and growth of silica particles under constant monomer supply. The monomer source is externally driven by the progressive addition into the system of one of the precursors. Monodisperse spherical particles are produced up to a mesoscopic size. We analyze their growth versus the monomer addition rate at different temperatures. Our results show that in the presence of a continuous monomer addition, growth is limited by diffusion over the investigated temporal window. Using the temperature variation of the growth rate, we prove that rescaling leads to a data reduction onto a single master curve. Contrary to the growth process, the final particle's size reached after the end of the reagent supply strongly depends on the addition rate. The variation of the final particle size versus addition rate can be deduced from an analogy with crystal formation in jet precipitation. Within this framework, and using the temperature dependences of both the particle growth law and the final size, we determine the value of the molecular heat of dissolution associated to the silica solubility. These observations support the fact that classical theories of phase-ordering dynamics can be extended to the synthesis of inorganic particles. The emergence of a master behavior in the presence of continuous monomer addition also suggests the extension of these theories to open systems.

Smart control of monodisperse Stöber silica particles: effect of reactant addition rate on growth process

Control over the synthesis of monodisperse silica particles up to mesoscopic scale is generally made difficult due to intrinsic limitation to submicrometric dimensions and secondary nucleation in seeded experiments. To investigate this issue and overcome these difficulties, we have implemented single step processing by quantifying the effects of the progressive addition of a diluted tetraethyl orthosilicate solution in ethanol on the size and monodispersity of silica particles. Contrary to particles grown in seeded polymerization, monodisperse particles with size up to 2 microm were synthesized. Moreover, the particles exhibit a final diameter (d(f)), which varies with V(-1/3) over more than 2 orders of magnitude in rate of addition (V). On the basis of a kinetic study in the presence of addition showing that particle growth is limited by the diffusion of monomer species, we developed a diffusion-limited growth model to theoretically explain the observed d(f)(V) behavior and quantitatively retrieve the measured amplitude and exponent. Using a single parameter procedure, we can therefore predict and generate in the room temperature range, monodisperse particles of a targeted size by simply adjusting the rate of addition.

Viscoelastic phase separation in shear flow

We numerically investigate viscoelastic phase separation in polymer solutions under shear using a time-dependent Ginzburg-Landau model. The gross variables in our model are the polymer volume fraction and a conformation tensor. The latter represents chain deformations and relaxes slowly on the rheological time giving rise to a large viscoelastic stress. The polymer and the solvent obey two-fluid dynamics in which the viscoelastic stress acts asymmetrically on the polymer and, as a result, the stress and the diffusion are dynamically coupled. Below the coexistence curve, interfaces appear with increasing the quench depth and the solvent regions act as a lubricant. In these cases the composition heterogeneity causes more enhanced viscoelastic heterogeneity and the macroscopic stress is decreased at fixed applied shear rate. We find steady two-phase states composed of the polymer-rich and solvent-rich regions, where the characteristic domain size is inversely proportional to the average shear stress for various shear rates. The deviatoric stress components exhibit large temporal fluctuations. The normal stress difference can take negative values transiently at weak shear.

Early sedimentation and crossover kinetics in an off-critical phase-separating liquid mixture

Early sedimentation in a liquid mixture off-critically quenched in its miscibility gap was investigated with a light attenuation technique. The time evolution of the droplet distribution is characteristic of an emulsion coalescing by gravitational collisions. This sedimentation behavior gave access to the phase-separating kinetics, and a crossover on the way toward equilibrium was observed, which separates free growth from conserved order-parameter coarsening with a crossover time fitting well with theoretical predictions.

Late stage kinetics of a phase separation induced by a cw laser wave in binary liquid mixtures

cw laser waves can be used to locally induce phase transitions. We investigate experimentally and theoretically a laser-driven liquid-liquid phase separation in a micellar phase of microemulsion and analyze its late stage kinetics. The medium is optically quenched in composition in the metastable region of the phase diagram. Two processes can lead to these concentration variations: electrostriction and thermodiffusion. The first originates from induced dipolar couplings in a field gradient. The second corresponds to a variation in concentration driven by a small thermal gradient. Since the nucleated droplets are optically trapped by the beam, we show that it becomes possible to experimentally analyze an academic situation, i.e., the diffusion-driven growth of a single droplet in compensated gravity. The late stage of this kinetics can be divided into two parts, a bulk behavior and a regime controlled by the finite transverse size of the beam. The bulk regime is totally analogous to that observed in classical situations (R proportional, variant t(1/3), where R is the droplet radius and t the time), and the scaling of the amplitudes in terms of reduced length and time scales is in total agreement with the expected behaviors for fluids belonging to the same Ising universality class. Moreover, the Gaussian beam behaves as an optical bottle with "soft walls" in which the absence of rigid boundaries, and thus of wetting couplings, allows an intrinsic description of the influence of finite-size effects on the kinetics. The beam size breaks the dynamic universality when the growing domains start to feel it. We experimentally investigate the resulting slowing down, and a diffusion-driven model of the growth inside a laser wave is built for comparison. The good agreement observed for the bulk regime and during its modification induced by finite-size effects opens a promising field for the development of this new application of laser waves to control out-of-equilibrium liquid mixtures.