Survey of morphologies formed in the wake of an enslaved phase-separation front in two dimensions

Transverse modulational dynamics of quenched patterns

We study the modulational dynamics of striped patterns formed in the wake of a planar directional quench. Such quenches, which move across a medium and nucleate pattern-forming instabilities in their wake, have been shown in numerous applications to control and select the wavenumber and orientation of striped phases. In the context of the prototypical complex Ginzburg-Landau and Swift-Hohenberg equations, we use a multiple-scale analysis to derive a one-dimensional viscous Burgers' equation, which describes the long-wavelength modulational and defect dynamics in the direction transverse to the quenching motion, that is, along the quenching line. We show that the wavenumber selecting properties of the quench determine the nonlinear flux parameter in the Burgers' modulation equation, while the viscosity parameter of the Burgers' equation is naturally determined by the transverse diffusivity of the pure stripe state. We use this approximation to accurately characterize the transverse dynamics of several types of defects formed in the wake, including grain boundaries and phase-slips.

Nonequilibrium Processes in Polymer Membrane Formation: Theory and Experiment

Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processes─evaporation, solvent-nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrest─that dictates the complex structure of the membrane on different scales.

Fluctuating lattice Boltzmann method for the diffusion equation

We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

Universal wave-number selection laws in apical growth

We study pattern-forming dissipative systems in growing domains. We characterize classes of boundary conditions that allow for defect-free growth and derive universal scaling laws for the wave number in the bulk of the domain. Scalings are based on a description of striped patterns in semibounded domains via strain-displacement relations. We compare predictions with direct simulations in the Swift-Hohenberg, the complex Ginzburg-Landau, the Cahn-Hilliard, and reaction-diffusion equations.

Phase separation and the 'coffee-ring' effect in polymer-nanocrystal mixtures

The coupling between the 'coffee-ring' effect and liquid-liquid phase separation is examined for ternary mixtures of solvent, polymer and semiconductor nanocrystal. Specifically, we study mixtures of toluene, polystyrene (PS) and colloidal silicon nanocrystals (SiNCs) using real-space imaging and spectroscopic techniques to resolve the kinetic morphology of the drying front for varied molecular weight of the PS. Our results demonstrate that the size of the polymer has a significant impact on both phase-separation and drying, and we relate these observations to simulations, measured and predicted binodal curves, and the observed shape of the flow field at the contact line. The results inform a deposition process that reduces the influence of drying instabilities for low-molecular-weight polymers while paving the way for more detailed and generic computational descriptions of drying instabilities in complex fluids.

Transition from rings to spots in a precipitation reaction–diffusion system

We report for the first time the transition from rings to spots with squared/hexagonal symmetry in a periodic precipitation system, which consists of sulfide/hydroxide ions diffusing into a gel matrix containing dissolved cadmium(ii) ions.

Probability of the emergence of helical precipitation patterns in the wake of reaction-diffusion fronts

Helical and helicoidal precipitation patterns emerging in the wake of reaction-diffusion fronts are studied. In our experiments, these chiral structures arise with well-defined probabilities P(H) controlled by conditions such as, e.g., the initial concentration of the reagents. We develop a model which describes the observed experimental trends. The results suggest that P(H) is determined by a delicate interplay among the time and length scales related to the front and to the unstable precipitation modes and, furthermore, that the noise amplitude also plays a quantifiable role.

Interfacial roughening in nonideal fluids: dynamic scaling in the weak- and strong-damping regime

Interfacial roughening denotes the nonequilibrium process by which an initially flat interface reaches its equilibrium state, characterized by the presence of thermally excited capillary waves. Roughening of fluid interfaces has been first analyzed by Flekkoy and Rothman [Phys. Rev. Lett. 75, 260 (1995)], where the dynamic scaling exponents in the weakly damped case in two dimensions were found to agree with the Kardar-Parisi-Zhang universality class. We extend this work by taking into account also the strong-damping regime and perform extensive fluctuating hydrodynamics simulations in two dimensions using the Lattice Boltzmann method. We show that the dynamic scaling behavior is different in the weakly and strongly damped case.

Marginal stability and traveling fronts in two-phase mixtures

Mixtures of materials that move relative to each other arise in a variety of applications, especially in biophysical problems where the mixture consists of materials with different material properties. The variety of applications leads to a bewildering array of multiphase models, each with slightly different behaviors and interpretations, depending on the application. Some of the behaviors include phase separation, traveling waves, and linear instabilities. Because of the variability of the predicted behaviors, there has been considerable attention paid to minimal models to determine the fundamental solutions, bifurcations, and instabilities. In this paper we describe a new solution for the simplest two-phase system where both phases are dominated by viscous forces, one-phase response to osmotic forces, and the phases interact through a drag term. The system develops a traveling front separating an unstable, uniform solution from a patterned, phase separated solution. We seek the velocity of the traveling front and show that, for large diffusion, marginal stability gives a simple and accurate prediction for the velocity. For smaller diffusion constants, the front is "pushed," and the linear prediction fails.