A lattice mesoscopic model of dynamically heterogeneous fluids

We introduce a mesoscopic three-dimensional Lattice Boltzmann Model which attempts to mimick the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard Lattice Boltzmann dynamics with self-consistent constraints based on the non-local density of the surrounding fluid. The resulting dynamics exhibits typical features of dynamic heterogeneous fluids, such as non-Gaussian density distributions and long-time relaxation. Due to its intrinsically parallel dynamics, and absence of statistical noise, the method is expected to compute significantly faster than molecular dynamics, Monte Carlo and lattice glass models.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let

Volumetric formulation of lattice Boltzmann models with energy conservation

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum and energy. Issues related to boundary condition problems and improvements based on grid refinement are also investigated.Comment: 8 figure

Diel variations in cell division and biomass production of Emiliania huxleyi — Consequences for the calculation of physiological cell parameters

Cell division of the coccolithophore Emiliania huxleyi and other phytoplankton typically becomes entrained to diel light/dark cycles under laboratory conditions, with division occurring primarily during dark phases and production occurring during light phases. Under these conditions, increases in cell and biomass concentrations deviate from exponential functions on time scales < 24 h. These deviations lead to significant diel variations in common measurements of phytoplankton physiology such as cellular quotas of particulate organic and inorganic carbon (POC, PIC) and their production rates. Being time-dependent, only the temporal mean of the various values during the day are comparable between experiments. Deviations from exponential growth furthermore imply that increases in cell and biomass concentrations cannot be expressed by the daily growth rate μ24 h (typically determined from daily increments in cell concentrations). Consequently, conventional calculations of production as the product of a cellular quota (e.g., POC quota) and μ24 h are mathematically incorrect. To account for this, we here describe short-term changes in cell and biomass concentrations of fast -dividing, dilute-batch cultures of E. huxleyi grown under a diel light/dark cycle using linear regression. Based on the derived models, we present calculations for daily means of cellular quotas and production rates. Conventional (time-specific) measurements of cellular quotas and production differ from daily means by up to 65% in our example and, under some circumstances, cause false “effects” of treatments. Intending to reduce errors in ecophysiological studies, we recommend determining daily means—mathematically or by adjusting the experimental setup or sampling times appropriately

Herschel-Bulkley rheology from lattice kinetic theory of soft-glassy materials

We provide a clear evidence that a two species mesoscopic Lattice Boltzmann (LB) model with competing short-range attractive and mid-range repulsive interactions supports emergent Herschel-Bulkley (HB) rheology, i.e. a power-law dependence of the shear-stress as a function of the strain rate, beyond a given yield-stress threshold. This kinetic formulation supports a seamless transition from flowing to non-flowing behaviour, through a smooth tuning of the parameters governing the mesoscopic interactions between the two species. The present model may become a valuable computational tool for the investigation of the rheology of soft-glassy materials on scales of experimental interest.Comment: 5 figure

Lattice Boltzmann models for non-ideal fluids with arrested phase-separation

The effects of mid-range repulsion in Lattice Boltzmann models on the coalescence/breakup behaviour of single-component, non-ideal fluids are investigated. It is found that mid-range repulsive interactions allow the formation of spray-like, multi-droplet configurations, with droplet size directly related to the strength of the repulsive interaction. The simulations show that just a tiny ten-percent of mid-range repulsive pseudo-energy can boost the surface/volume ratio of the phase- separated fluid by nearly two orders of magnitude. Drawing upon a formal analogy with magnetic Ising systems, a pseudo-potential energy is defined, which is found to behave like a quasi-conserved quantity for most of the time-evolution. This offers a useful quantitative indicator of the stability of the various configurations, thus helping the task of their interpretation and classification. The present approach appears to be a promising tool for the computational modelling of complex flow phenomena, such as atomization, spray formation and micro-emulsions, break-up phenomena and possibly glassy-like systems as well.Comment: 12 pages, 9 figure

Impalement transitions in droplets impacting microstructured superhydrophobic surfaces

Liquid droplets impacting a superhydrophobic surface decorated with micro-scale posts often bounce off the surface. However, by decreasing the impact velocity droplets may land on the surface in a fakir state, and by increasing it posts may impale droplets that are then stuck on the surface. We use a two-phase lattice-Boltzmann model to simulate droplet impact on superhydrophobic surfaces, and show that it may result in a fakir state also for reasonable high impact velocities. This happens more easily if the surface is made more hydrophobic or the post height is increased, thereby making the impaled state energetically less favourable.Comment: 8 pages, 4 figures, to appear in Europhysics Letter

Numerical simulations of compressible Rayleigh-Taylor turbulence in stratified fluids

We present results from numerical simulations of Rayleigh-Taylor turbulence, performed using a recently proposed lattice Boltzmann method able to describe consistently a thermal compressible flow subject to an external forcing. The method allowed us to study the system both in the nearly-Boussinesq and strongly compressible regimes. Moreover, we show that when the stratification is important, the presence of the adiabatic gradient causes the arrest of the mixing process.Comment: 15 pages, 11 figures. Proceedings of II Conference on Turbulent Mixing and Beyond (TMB-2009

Investigation of a lattice Boltzmann model with a variable speed of sound

A lattice Boltzmann model is considered in which the speed of sound can be varied independently of the other parameters. The range over which the speed of sound can be varied is investigated and good agreement is found between simulations and theory. The onset of nonlinear effects due to variations in the speed of sound is also investigated and good agreement is again found with theory. It is also shown that the fluid viscosity is not altered by changing the speed of sound

Modelling thermal flow in a transition regime using a lattice Boltzmann approach

Lattice Boltzmann models are already able to capture important rarefied flow phenomena, such as velocity-slip and temperature jump, provided the effects of the Knudsen layer are minimal. However, both conventional hydrodynamics, as exemplified by the Navier-Stokes-Fourier equations, and the lattice Boltzmann method fail to predict the nonlinear velocity and temperature variations in the Knudsen layer that have been observed in kinetic theory. In the present paper, we propose an extension to the lattice Boltzmann method that will enable the simulation of thermal flows in the transition regime where Knudsen layer effects are significant. A correction function is introduced that accounts for the reduction in the mean free path near a wall. This new approach is compared with direct simulation Monte Carlo data for Fourier flow and good qualitative agreement is obtained for Knudsen numbers up to 1.58