Critical properties and phase separation in lattice Boltzmann fluid mixtures

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.

Discovery of Dynamic Two-Phase Flow in Porous Media Using Two-Dimensional Multiphase Lattice Boltzmann Simulation

The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.

Mass-transfer driven spinodal decomposition in a ternary polymer solution

Nonsolvent induced phase separation (NIPS) is a widely occuring process used in industrial membrane production, nanotechnology and Nature to produce microstructured polymer materials. A variety of process-dependent morphologies are produced when a polymer solution is exposed to a nonsolvent that, following a period where mass is exchanged, precipitates and solidifies the polymer. Despite years of investigation, both experimental and theoretical, many questions surround the pathways to the microstructures that NIPS can produce. Here, we provide simulation results from a model that simultaneously captures both the processess of solvent/nonsolvent exchange and phase separation. We show that the time it takes the nonsolvent to diffuse to the bottom of the film is an important timescale, and that phase separation is possible at times both much smaller and much larger than this scale. Our results include both one-dimensional simulations of the mass transfer kinetics and two- and three-dimensional simulations of morphologies at both short and long times. We find good qualitative agreement with experimental heuristics, but we conclude that an additional model for the vitrification process will be key for fully explaining experimental observations of microstructure formation.

Marangoni Flows during Nonsolvent Induced Phase Separation

Motivated by the much discussed, yet unexplained, presence of macrovoids in polymer membranes, we explore the impact of Marangoni flows in the process of nonsolvent induced phase separation. Such flows have been hypothesized to be important to the formation of macrovoids, but little quantitative evidence has been produced to date. Using a recently developed multifluid phase field model, we find that roll cells indicative of a solutal Marangoni instability are manifest during solvent/nonsolvent exchange across a stable interface. However, these flows are weak and subsequently do not produce morphological features that might lead to macrovoid formation. By contrast, initial conditions that lead to an immediate precipitation of the polymer film coincide with large Marangoni flows that disturb the interface. The presence of such flows suggests a new experimental and theoretical direction in the search for a macrovoid formation mechanism.

Controlling film topography to form highly hydrophobic waterborne coatings

Coatings have a tremendous impact on economy as they reduce corrosion that has an estimated cost of 3% of the world's GDP. Hydrophobic coatings are particularly efficient for this purpose and the challenge is to produce cost effective and environmentally friendly, highly hydrophobic, cohesive and non-porous coatings applicable to large and irregular surfaces. This work shows that this goal can be achieved by forming wrinkles on the surface of waterborne coatings through fine-tuning of the film forming conditions. The proof of concept was demonstrated by using waterborne dispersions of copolymers of 1H,1H,2H,2H-perfluorodecyl acrylate and 2-ethylhexyl acrylate, and using the temperature and hardness of the copolymer as control variables during film formation. This allowed the formation of transparent films with a wrinkled surface that had a contact angle of 133°, which represents an increase of 20° with respect to the film cast under standard conditions.

Highly Hydrophobic Coatings from Waterborne Latexes

This work reports on the formation of highly hydrophobic coatings from waterborne latexes able to form films at ambient temperature. The contact angle of film forming copolymers of 2-ethylhexyl acrylate and perfluorodecyl acrylate (PFDA) was limited to 114° because flat surfaces were obtained. Attempts to increase the roughness of the film using blends of film-forming latexes with the latex of PFDA homopolymer (which is not film forming) were not successful under regular casting conditions because the PFDA particles accumulated at the film-substrate interface. Film formation engineering allowed modifying the morphology of the film obtaining a contact angle of 137°.

Capillary rupture of suspended polymer concentric rings

We present the first experimental study on the simultaneous capillary instability amongst viscous concentric rings suspended atop an immiscible medium. The rings ruptured upon annealing, with three types of phase correlation between neighboring rings. In the case of weak substrate confinement, the rings ruptured independently when they were sparsely distanced, but via an out-of-phase mode when packed closer. If the substrate confinement was strong, the rings would rupture via an in-phase mode, resulting in radially aligned droplets. The concentric ring geometry caused a competition between the phase correlation of neighboring rings and the kinetically favorable wavelength, yielding an intriguing, recursive surface pattern. This frustrated pattern formation behavior was accounted for by a scaling analysis.

Influence of substrate confinement on the phase-correlation in the capillary breakup of arrays of patterned polymer stripes

We investigated the influence of substrate confinement on the capillary breakup of parallel nonaxisymmetric polymer stripes suspended on top of, or confined between, another immiscible polymer pattern. When the residual layer thickness of the pattern was reasonably large, the PS (or PMMA) stripes confined within PMMA (or PS) trenches broke up, either nucleated, out-of-phase, or without clear phase correlation depending on the geometry and viscosity ratio between the two polymers. In stark contrast, for the two extreme cases of viscosity ratios we studied, in-phase breakup of confined polymer stripes was always observed when the alternating PS/PMMA stripes were formed, that is, without residual layer, regardless of the specific geometry.

Simulation of static critical phenomena in nonideal fluids with the lattice Boltzmann method

A fluctuating nonideal fluid at its critical point is simulated with the lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order parameter.

Progess in superhydrophobic surface development

Research into extreme water-repellent surfaces began many decades ago, although it was only relatively recently that the term superhydrophobicity appeared in literature. Here we review the work on the preparation of superhydrophobic surfaces, with focus on the different techniques used and how they have developed over the years, with particular focus on the last two years. We discuss the origins of water-repellent surfaces, examining how size and shape of surface features are used to control surface characteristics, in particular how techniques have progressed to form multi-scaled roughness to mimic the lotus leaf effect. There are notable differences in the terminology used to describe the varying properties of water-repellent surfaces, so we suggest some key definitions.

Recent advances in computational simulation of macro-, meso-, and micro-scale biomimetics related fluid flow problems

Over the last decade, computational methods have been intensively applied to a variety of scientific researches and engineering designs. Although the computational fluid dynamics (CFD) method has played a dominant role in studying and simulating transport phenomena involving fluid flow and heat and mass transfers, in recent years, other numerical methods for the simulations at meso- and micro-scales have also been actively applied to solve the physics of complex flow and fluid-interface interactions. This paper presents a review of recent advances in multi-scale computational simulation of biomimetics related fluid flow problems. The state-of-the-art numerical techniques, such as lattice Boltzmann method (LBM), molecular dynamics (MD), and conventional CFD, applied to different problems such as fish flow, electro-osmosis effect of earthworm motion, and self-cleaning hydrophobic surface, and the numerical approaches are introduced. The new challenging of modelling biomimetics problems in developing the physical conditions of self-clean hydrophobic surfaces is discussed.

Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models

We show that the spurious current present near a curved interface in a class of multiphase lattice Boltzmann (LB) models is due to the insufficient isotropy of the discrete gradient operator. A method of obtaining highly isotropic gradient operators on a lattice is given. Numerical simulations show that both the magnitude and the spatial extent of the spurious current are significantly reduced as gradient operators of increasingly higher order of isotropy is adopted in multiphase LB models.

Dynamic self-consistent field theory for unentangled homopolymer fluids

We present a lattice formulation of a dynamic self-consistent field (DSCF) theory that is capable of resolving interfacial structure, dynamics, and rheology in inhomogeneous, compressible melts and blends of unentangled homopolymer chains. The joint probability distribution of all the Kuhn segments in the fluid, interacting with adjacent segments and walls, is approximated by a product of one-body probabilities for free segments interacting solely with an external potential field that is determined self-consistently. The effect of flow on ideal chain conformations is modeled with finitely extensible, nonlinearly elastic dumbbells in the Peterlin approximation, and related to stepping probabilities in a random walk. Free segment and stepping probabilities generate statistical weights for chain conformations in a self-consistent field, and determine local volume fractions of chain segments. Flux balance across unit lattice cells yields mean field transport equations for the evolution of free segment probabilities and of momentum densities on the Kuhn length scale. Diffusive and viscous contributions to the fluxes arise from segmental hops modeled as a Markov process, with transition rates reflecting changes in segmental interaction, kinetic energy, and entropic contributions to the free energy under flow. We apply the DSCF equations to study both transient and steady-state interfacial structure, flow, and rheology in a sheared planar channel containing either a one-component melt or a phase-separated, two-component blend.

Large-scale lattice Boltzmann simulations of complex fluids: advances through the advent of computational Grids

During the last 2.5 years, the RealityGrid project has allowed us to be one of the few scientific groups involved in the development of computational Grids. Since smoothly working production Grids are not yet available, we have been able to substantially influence the direction of software and Grid deployment within the project. In this paper, we review our results from large-scale three-dimensional lattice Boltzmann simulations performed over the last 2.5 years. We describe how the proactive use of computational steering, and advanced job migration and visualization techniques enabled us to do our scientific work more efficiently. The projects reported on in this paper are studies of complex fluid flows under shear or in porous media, as well as large-scale parameter searches, and studies of the self-organization of liquid cubic mesophases.

Breakup of a fluid thread in a confined geometry: droplet-plug transition, perturbation sensitivity, and kinetic stabilization with confinement

We investigate the influence of geometrical confinement on the breakup of long fluid threads in the absence of imposed flow using a lattice Boltzmann model. Our simulations primarily focus on the case of threads centered coaxially in a tube filled with another Newtonian fluid and subjected to both impulsive and random perturbations. We observe a significant slowing down of the rate of thread breakup ("kinetic stabilization") over a wide range of the confinement, Lambda= R(tube)/R(thread) < or =10 and find that the relative surface energies of the liquid components influence this effect. For Lambda<2.3, there is a transition in the late-stage morphology between spherical droplets and tube "plugs." Unstable distorted droplets ("capsules") form as transient structures for intermediate confinement (Lambda approximately equal 2.1-2.5). Surprisingly, the thread breakup process for more confined threads (Lambda< or =1.9 ) is found to be sensitive to the nature of the initial thread perturbation. Localized impulsive perturbations ("taps") cause a "bulging" of the fluid at the wall, followed by thread breakup through the propagation of a wave-like disturbance ("end-pinch instability") initiating from the thread rupture point. Random impulses along the thread, modeling thermal fluctuations, lead to a complex breakup process involving a competition between the Raleigh and end-pinch instabilities. We also briefly compare our tube simulations to threads confined between parallel plates and to multiple interacting threads under confinement.

Ultrafast laser-induced molecular and morphological changes during spinodal demixing of water/2-butoxyethanol/KCl

We initiated morphological and molecular level changes in the spinodal decomposition (SD) of H(2)O/2-butoxyethanol/KCl with a pulsed ir laser. Transient Raman spectra gave us a molecular level view of the early stage of this process that could be linked to later morphological events. Chemical changes during SD, such as reorganization of H bonds and forced hydrophobic interactions, ended after 1 micros; however, phase domains continued to grow with self-similarity after 30 micros. The growth of the phase domains satisfied the power law L(t) approximately t(0.55) and was consistent with the late stage of SD. The time scale for the onset of late stage SD is many orders of magnitude faster than previously reported in ionic and nonionic conditions.

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.

Lattice Boltzmann study of spinodal decomposition in two dimensions

A lattice Boltzmann model using the Shan-Chen prescription for a binary immiscible fluid is described, and the macroscopic equations obeyed by the model are derived. The model is used to quantitatively examine spinodal decomposition of a two-dimensional binary fluid. This model allows examination of the early-time period corresponding to interface formation, and shows agreement with analytical solutions of the linearized Cahn-Hilliard equation, despite the fact that the model contains no explicit free-energy functional. This regime has not, to the knowledge of the authors, been previously observed using any lattice Boltzmann method. In agreement with other models, a scaling law with the exponent 2/3 is observed for late-time domain growth. Breakdown of scaling is also observed for certain sets of simulation parameters.