Jens Harting

Multiphase lattice Boltzmann simulations for porous media applications

Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article, we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.

Simulation of claylike colloids.

We investigate the properties of dense suspensions and sediments of small spherical silt particles by means of a combined molecular dynamics and stochastic rotation dynamics (SRD) simulation. We include van der Waals and effective electrostatic interactions between the colloidal particles, as well as Brownian motion and hydrodynamic interactions which are calculated in the SRD part. We present the simulation technique and first results. We have measured velocity distributions, diffusion coefficients, sedimentation velocity, spatial correlation functions, and we have explored the phase diagram depending on the parameters of the potentials and on the volume fraction.

Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann simulations

On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as those of porous media or microfluidic devices. The possibility of specifying the exact position of the boundary, independently of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow one to freely specify the direction of the flux, and it should be straightforward to implement in three dimensions. Furthermore, especially for parallelized solvers, it is of great advantage if the boundary condition can be applied locally, involving only information available on the current lattice site. We meet this need by describing in detail how to transfer the approach suggested by Zou and He to a D3Q19 lattice. The boundary condition acts locally, is independent of the details of the relaxation process during collision and contains no artificial slip. In particular, the case of an on-site no-slip boundary condition is naturally included. We test the boundary condition in several setups and confirm that it can be used to accurately model the velocity field up to second order and does not contain any numerical slip.

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.

Classification of Phase Transitions in Small Systems

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transition in a finite system and to small Ar clusters.

Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations

During the last decade, lattice-Boltzmann simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, well-known improvements of the original algorithm are often not implemented. These include, for example, multirelaxation time schemes or improved boundary conditions, as well as different possibilities to impose a pressure gradient. This paper shows that a significant difference of the calculated permeabilities can be found unless one uses a carefully selected set-up. We present a detailed discussion of possible simulation set-ups and quantitative studies of the influence of simulation parameters. We illustrate our results by applying the algorithm to a Fontainebleau sandstone and by comparing our benchmark studies to other numerical permeability measurements in the literature.

Two-dimensional vesicle dynamics under shear flow: effect of confinement.

Dynamics of a single vesicle under shear flow between two parallel plates is studied in two-dimensions using lattice-Boltzmann simulations. We first present how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using an approach known from the immersed boundary method. The fluid flow is computed on an Eulerian regular fixed mesh while the location of the vesicle membrane is tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle equilibrium shapes in a fluid at rest are found and the dynamical behavior of a vesicle under simple shear flow is being reproduced. Further, we focus on investigating the effect of the confinement on the dynamics, a question that has received little attention so far. In particular, we study how the vesicle steady inclination angle in the tank-treading regime depends on the degree of confinement. The influence of the confinement on the effective viscosity of the composite fluid is also analyzed. At a given reduced volume (the swelling degree) of a vesicle we find that both the inclination angle, and the membrane tank-treading velocity decrease with increasing confinement. At sufficiently large degree of confinement the tank-treading velocity exhibits a nonmonotonous dependence on the reduced volume and the effective viscosity shows a nonlinear behavior.

Assembling Ellipsoidal Particles at Fluid Interfaces Using Switchable Dipolar Capillary Interactions

How to dynamically tune an assembly of anisotropic colloidal particles adsorbed at fluid-fluid interfaces using dipolar capillary interactions is demonstrated. A previously discovered first-order phase transition is exploited and it is shown how to spontaneously turn off these dipolar capillary interactions by exceeding a critical field strength, providing unprecedented control of the bottom-up fabrication of soft materials.

Large-scale grid-enabled lattice Boltzmann simulations of complex fluid flow in porous media and under shear.

Well–designed lattice Boltzmann codes exploit the essentially embarrassingly parallel features of the algorithm and so can be run with considerable efficiency on modern supercomputers. Such scalable codes permit us to simulate the behaviour of increasingly large quantities of complex condensed matter systems. In the present paper, we present some preliminary results on the large–scale three–dimensional lattice Boltzmann simulation of binary immiscible fluid flows through a porous medium, derived from digitized X–ray micro–tomographic data of Bentheimer sandstone, and from the study of the same fluids under shear. Simulations on such scales can benefit considerably from the use of computational steering, and we describe our implementation of steering within the lattice Boltzmann code, called LB3D, making use of the RealityGrid steering library. Our large–scale simulations benefit from the new concept of capability computing, designed to prioritize the execution of big jobs on major supercomputing resources. The advent of persistent computational grids promises to provide an optimal environment in which to deploy these mesoscale simulation methods, which can exploit the distributed nature of computer, visualization and storage resources to reach scientific results rapidly; we discuss our work on the grid–enablement of lattice Boltzmann methods in this context.

Tensorial slip of superhydrophobic channels.

We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip-length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the use of the tensor formalism we develop a semianalytical theory of an effective slip in a parallel-plate channel with one superhydrophobic striped and one hydrophilic surface. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. We then present results of lattice Boltzmann simulations to validate the analysis. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations.