A. Koponen

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media.

Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5

Lattice-Boltzmann hydrodynamics on parallel systems

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Lattice-Boltzmann Simulation of Capillary Rise Dynamics

m. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately, while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude. This finding confirms earlier qualitative predictions based on local porosity theory. Two numerical algorithms were used in these simulations. One is based on the lattice-Boltzmann method, and the other on conventional finite-difference techniques. The accuracy of these two methods is discussed and compared, also with experiment.

Spreading dynamics of three-dimensional droplets by the lattice-Boltzmann method ☆

Realistic lattice-Boltzmann simulations often require large amounts of computational resources and are therefore executed on parallel systems. Generally, parallelization is based on one- and two-dimensional decomposition of the computational grid in equal subvolumes, and load balancing is completely ignored for simplicity. Besides reviewing the existing parallelization strategies we report here a new approach based on the Orthogonal Recursive Bisection (ORB) method. To illustrate the different decomposition methods, two realistic applications were simulated, namely fluid flow in random fibre networks and flow in a centrifugal elutriation chamber. For heterogeneously distributed workloads, the ORB method is found to be 12 to 60% more efficient compared to traditional parallelization strategies. It is shown that high parallel efficiencies can be obtained for both homogeneously and heterogeneously distributed workloads, thus supporting efficient simulations of a variety of realistic systems.

Simulations of Single-Fluid Flow in Porous Media

We report results of extensive two-phase lattice-Boltzmann simulations of capillary rise dynamics. We demonstrate that the method can be used to model the hydrodynamic behaviour inside a capillary tube provided that the diameter of the tube is large enough, typically at least 30 lattice units. We also present results for the dependence of the cosine of the dynamic contact angle on the capillary number Ca. Its deviation from the static advancing contact angle has a power-law form, with the value of the exponent very close to 3/2 for capillary rise at zero gravity, while behaviour is more complex in the presence of gravity.

Evaluation of a lattice-Boltzmann method for mercury intrusion porosimetry simulations

Abstract We have simulated spreading of small droplets on smooth and rough solid surfaces using the three-dimensional lattice-Boltzmann method. We present results for the influence of the initial distance and shape of the drop from the surface on scaling of droplet radius R as a function of time. For relatively flat initial drop shapes our observations are consistent with Tanners law R ∼ t q , where q =1/10. For increasingly spherical initial shapes, the exponent q increases rapidly being above one half for spherical droplets initially just above the surface. As expected, surface roughness slows down spreading, decreases the final drop radius, and results in irregular droplet shape due to pinning of the droplet edge. Our results show that lattice-Boltzmann method can be a powerful tool in realistic simulations of droplet spreading.

Shear Stress in a Couette Flow of Liquid-Particle Suspensions

Several results of lattice-gas and lattice-Boltzmann simulations of single-fluid flow in 2D and 3D porous media are discussed. Simulation results for the tortuosity, effective porosity and permeability of a 2D random porous medium are reported. A modified Kozeny–Carman law is suggested, which includes the concept of effective porosity. This law is found to fit well the simulated 2D permeabilities. The results for fluid flow through large 3D random fibre webs are also presented. The simulated permeabilities of these webs are found to be in good agreement with experimental data. The simulations also confirm that, for this kind of materials, permeability depends exponentially on porosity over a large porosity range.

Simulations of non-spherical particles suspended in a shear flow

We have simulated intrusion of a non-wetting liquid into pores of varying shape and size. Simulations were based on the lattice-Boltzmann method and the Shan-Chen multiphase model. The liquid-solid contact angle for pores with circular cross-section was found to be equal to that for pores with square cross-section, and constant even for small pore sizes if the discretised shape of the circular cross-section was taken into account. For comparison, contact angle was also determined for a liquid column descending in a capillary tube, and the results were found to be consistent. Application of the method to mercury intrusion porosimetry is discussed.

Simulations of water flow through bordered pits of conifer xylem

The mechanisms of momentum transfer and shear stress of liquid-particle suspensions in two-dimensional Couette flow are studied using direct numerical simulation by lattice-Boltzmann techniques. The results obtained display complex flow phenomena that arise from the two-phase nature of the fluid including a nonlinear velocity profile, layering of particles, and apparent slip near the solid walls. The general rheological behaviour of the suspension is dilatant. A detailed study of the various momentum transfer mechanisms that contribute to the total shear stress indicates that the observed shear thickening is related to enhanced relative solid phase stress for increasing shear rates.

New insight into rheology and flow properties of complex fluids with Doppler optical coherence tomography

The lattice-Boltzmann method was used to investigate the effects of the shape and concentration of the particles on the rheological properties of non-Brownian suspensions for non-zero Reynolds numbers. Several case studies were analyzed and the methods used were found to give accurate predictions for these systems. The viscosity of suspensions of both spherical and non-spherical particles was determined as functions of shear rate and concentration of particles. It was shown that, for high shear rates, shear thickening appears. This phenomenon is particularly pronounced for particles of irregular shape.