Simulations of amphiphilic fluids using mesoscale lattice-Boltzmann and lattice-gas methods

We compare two recently developed mesoscale models of binary immiscible and ternary amphiphilic fluids. We describe and compare the algorithms in detail and discuss their stability properties. The simulation results for the cases of self-assembly of ternary droplet phases and binary water-amphiphile sponge phases are compared and discussed. Both models require parallel implementation and deployment on large scale parallel computing resources in order to achieve reasonable simulation times for three-dimensional models. The parallelisation strategies and performance on two distinct parallel architectures are compared and discussed. Large scale three dimensional simulations of multiphase fluids requires the extensive use of high performance visualisation techniques in order to enable the large quantities of complex data to be interpreted. We report on our experiences with two commercial visualisation products: AVS and VTK. We also discuss the application and use of novel computational steering techniques for the more efficient utilisation of high performance computing resources. We close the paper with some suggestions for the future development of both models.Comment: 30 pages, 9 figure

Numerical simulations of complex fluid-fluid interface dynamics

Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually deformable and their shapes are not known a priori. Since experiments do not provide access to all observables of interest, computer simulations pose attractive alternatives to gain insight into the physics of interfaces. In the present article, we restrict ourselves to systems with dimensions comparable to the lateral interface extensions. We provide a critical discussion of three numerical schemes coupled to the lattice Boltzmann method as a solver for the hydrodynamics of the problem: (a) the immersed boundary method for the simulation of vesicles and capsules, the Shan-Chen pseudopotential approach for multi-component fluids in combination with (b) an additional advection-diffusion component for surfactant modelling and (c) a molecular dynamics algorithm for the simulation of nanoparticles acting as emulsifiers.Comment: 24 pages, 12 figure

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. We find the average domain size growing with time as $t^\gamma$, where $\gamma$ increases in the range $0.545 < \gamma < 0.717$, consistent with a crossover between diffusive $t^{1/3}$ and hydrodynamic viscous, $t^{1.0}$, behaviour. We find good collapse onto a single scaling function, yet the domain growth exponents differ from others' works' for similar values of the unique characteristic length and time that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. At early times, we also find a crossover from $q^2$ to $q^4$ in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later times. This excludes noise as the cause for a $q^2$ behaviour, as proposed by others. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review

Optimization of chaotic micromixers using finite time Lyapunov exponents

In microfluidics mixing of different fluids is a highly non-trivial task due to the absence of turbulence. The dominant process allowing mixing at low Reynolds number is therefore diffusion, thus rendering mixing in plain channels very inefficient. Recently, passive chaotic micromixers such as the staggered herringbone mixer were developed, allowing efficient mixing of fluids by repeated stretching and folding of the fluid interfaces. The optimization of the geometrical parameters of such mixer devices is often performed by time consuming and expensive trial and error experiments. We demonstrate that the application of the lattice Boltzmann method to fluid flow in highly complex mixer geometries together with standard techniques from statistical physics and dynamical systems theory can lead to a highly efficient way to optimize micromixer geometries. The strategy applies massively parallel fluid flow simulations inside a mixer, where massless and noninteracting tracer particles are introduced. By following their trajectories we can calculate finite time Lyapunov exponents in order to quantify the degree of chaotic advection inside the mixer. The current report provides a review of our results published in [1] together with additional details on the simulation methodology

Self-assembly of the gyroid cubic mesophase: Lattice-Boltzmann simulations

We present the first simulations of the self-assembly kinetics of the gyroid cubic mesophase using a Boltzmann transport method. No macroscopic parameters are included in the model and three-dimensional hydrodynamics is emergent from the microscopic conservation laws. The self-assembly arises from local inter-particle interactions in an initially homogeneous, phase-segregating binary fluid with dispersed amphiphile. The mixture evolves in discrete time according to the dynamics of a set of coupled Boltzmann-BGK equations on a lattice. We observe a transient microemulsion phase during self-assembly, the structure function peaks and direct-space imaging unequivocally identifying the gyroid at later times. For larger lattices, highly ordered subdomains are separated by grain boundaries. Relaxation towards the ordered equilibrium structure is very slow compared to the diffusive and microemulsion-assembling transients, the structure function oscillating in time due to a combination of Marangoni effects and long-time-scale defect dynamics

Stress response and structural transitions in sheared gyroidal and lamellar amphiphilic mesophases: lattice-Boltzmann simulations

We report on the stress response of gyroidal and lamellar amphiphilic mesophases to steady shear simulated using a bottom-up lattice-Boltzmann model for amphiphilic fluids and sliding periodic (Lees-Edwards) boundary conditions. We study the gyroid per se (above the sponge-gyroid transition, of high crystallinity) and the molten gyroid (within such a transition, of shorter-range order). We find that both mesophases exhibit shear thinning, more pronounced and at lower strain rates for the molten gyroid. At late times after the onset of shear, the skeleton of the crystalline gyroid becomes a structure of interconnected irregular tubes and toroidal rings, mostly oriented along the velocity ramp imposed by the shear, in contradistinction with free-energy Langevin-diffusion studies which yield a much simpler structure of disentangled tubes. We also compare the shear stress and deformation of lamellar mesophases with and without amphiphile when subjected to the same shear flow applied normal to the lamellae. We find that the presence of amphiphile allows (a) the shear stress at late times to be higher than in the case without amphiphile, and (b) the formation of rich patterns on the sheared interface, characterized by alternating regions of high and low curvature. © 2006 The American Physical Societ

Receptor concentration and diffusivity control multivalent binding of Sv40 to membrane bilayers

Incoming Simian Virus 40 particles bind to their cellular receptor, the glycolipid GM1, in the plasma membrane and thereby induce membrane deformation beneath the virion leading to endocytosis and infection. Efficient membrane deformation depends on receptor lipid structure and the organization of binding sites on the internalizing particle. To determine the role of receptor diffusion, concentration and the number of receptors required for stable binding in this interaction, we analyze the binding of SV40 to GM1 in supported membrane bilayers by computational modeling based on experimental data. We measure the diffusion rates of SV40 virions in solution by fluorescence correlation spectroscopy and of the receptor in bilayers by single molecule tracking. Quartz-crystal microbalance with dissipation (QCM-D) is used to measure binding of SV40 virus-like particles to bilayers containing the viral receptor GM1. We develop a phenomenological stochastic dynamics model calibrated against this data, and use it to investigate the early events of virus attachment to lipid membranes. Our results indicate that SV40 requires at least 4 attached receptors to achieve stable binding. We moreover find that receptor diffusion is essential for the establishment of stable binding over the physiological range of receptor concentrations and that receptor concentration controls the mode of viral motion on the target membrane. Our results provide quantitative insight into the initial events of virus-host interaction at the nanoscopic level