A note on the lattice Boltzmann method beyond the Chapman Enskog limits

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice Boltzmann method, can provide semi-quantitative results also in the non-hydrodynamic, finite-Knudsen regime, up to $Kn\sim {\cal O}(1)$. This may help the interpretation of recent Lattice Boltzmann simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.Comment: 7 PAGES, 1 FIGUR

Modeling the coupled mechanics, transport, and growth processes in collagen tissues.

The purpose of this project is to develop tools to model and simulate the processes of self-assembly and growth in biological systems from the molecular to the continuum length scales. The model biological system chosen for the study is the tendon fiber which is composed mainly of Type I collagen fibrils. The macroscopic processes of self-assembly and growth at the fiber scale arise from microscopic processes at the fibrillar and molecular length scales. At these nano-scopic length scales, we employed molecular modeling and simulation method to characterize the mechanical behavior and stability of the collagen triple helix and the collagen fibril. To obtain the physical parameters governing mass transport in the tendon fiber we performed direct numerical simulations of fluid flow and solute transport through an idealized fibrillar microstructure. At the continuum scale, we developed a mixture theory approach for modeling the coupled processes of mechanical deformation, transport, and species inter-conversion involved in growth. In the mixture theory approach, the microstructure of the tissue is represented by the species concentration and transport and material parameters, obtained from fibril and molecular scale calculations, while the mechanical deformation, transport, and growth processes are governed by balance laws and constitutive relations developed within a thermodynamically consistent framework

An improved hydrodynamics formulation for multiphase flow lattice-Boltzmann models

Summarization: Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.Παρουσιάστηκε στο: International Journal of Modern Physic

Droplet Spreading on Heterogeneous Surfaces Using a Three-Dimensional Lattice Boltzmann Model

We use a three-dimensional lattice Boltzmann model to investigate the spreading of mesoscale droplets on homogeneous and heterogeneous surfaces. On a homogeneous substrate the base radius of the droplet grows with time as $t^{0.28}$ for a range of viscosities and surface tensions. The time evolutions collapse onto a single curve as a function of a dimensionless time. On a surface comprising of alternate hydrophobic and hydrophilic stripes the wetting velocity is anisotropic and the equilibrium shape of the droplet reflects the wetting properties of the underlying substrate.Comment: 10 pages, Lattice Boltzmann workshop in ICCS03 conference, to be published in LNC

On moving contact lines simulated by the single-component two-phase lattice-Boltzmann method

We studied moving contact lines (MCLs) simulated by the single-component two-phase lattice-Boltzmann method (TP-LBM) based on the free-energy theory. In TP-LBM simulations CL moves by evaporation and condensation, and they do not involve an explicit slip length. How the CL motion compares with those by other methods using a slip model is not well understood yet. By comparing the results for a benchmark problem with established analytical solutions, we found an effective slip length proportional to the interface thickness in TP-LBM simulations. Besides, it was found that a recently proposed simple method originally in the framework of LBM for binary fluids can also be applied to TP-LBM to regulate the CL motion, and this method can greatly enhance its capability to simulate realistic two-phase flows with very small slip lengths