Two-dimensional Vesicle dynamics under shear flow: effect of confinement

Dynamics of a single vesicle under shear flow between two parallel plates is studied using two-dimensional 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 non-monotonous dependence on the reduced volume and the effective viscosity shows a nonlinear behavior.Comment: 12 pages, 8 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

Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows

The pseudo-potential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudo-potential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudo-potential LB model. Firstly, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme and the exact-difference-method (EDM) forcing scheme. The nature of these two schemes and their recovered macroscopic equations will be shown. Secondly, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudo-potential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach for achieving thermodynamic consistency in the pseudo-potential LB model.Comment: 7 figure

Developing Benthic Class Specific, Chlorophyll-a Retrieving Algorithms for Optically-ShallowWater Using SeaWiFS

This study evaluated the ability to improve Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) chl-a retrieval from optically shallow coastal waters by applying algorithms specific to the pixels’ benthic class. The form of the Ocean Color (OC) algorithm was assumed for this study. The operational atmospheric correction producing Level 2 SeaWiFS data was retained since the focus of this study was on establishing the benefit from the alternative specification of the bio-optical algorithm. Benthic class was determined through satellite image-based classification methods. Accuracy of the chl-a algorithms evaluated was determined through comparison with coincident in situ measurements of chl-a. The regionally-tuned models that were allowed to vary by benthic class produced more accurate estimates of chl-a than the single, unified regionally-tuned model. Mean absolute percent difference was approximately 70% for the regionally-tuned, benthic class-specific algorithms. Evaluation of the residuals indicated the potential for further improvement to chl-a estimation through finer characterization of benthic environments. Atmospheric correction procedures specialized to coastal environments were recognized as areas for future improvement as these procedures would improve both classification and algorithm tuning

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

On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as porous media or microfluidic devices. The possibility to specify the exact position of the boundary, independent of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow to freely specify the direction of the flux, and it should be straight forward 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 is capable to accurately model the velocity field up to second order and does not contain any numerical slip.Comment: 13 pages, 4 figures, revised versio

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

During the last decade, lattice-Boltzmann (LB) 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 setup. We present a detailed discussion of possible simulation setups 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.Comment: 14 pages, 11 figure

Improved axisymmetric lattice Boltzmann scheme

This paper proposes an improved lattice Boltzmann scheme for incompressible axisymmetric flows. The scheme has the following features. First, it is still within the framework of the standard lattice Boltzmann method using the single-particle density distribution function and consistent with the philosophy of the lattice Boltzmann method. Second, the source term of the scheme is simple and contains no velocity gradient terms. Owing to this feature, the scheme is easy to implement. In addition, the singularity problem at the axis can be appropriately handled without affecting an important advantage of the lattice Boltzmann method: the easy treatment of boundary conditions. The scheme is tested by simulating Hagen-Poiseuille flow, three-dimensional Womersley flow, Wheeler benchmark problem in crystal growth, and lid-driven rotational flow in cylindrical cavities. It is found that the numerical results agree well with the analytical solutions and/or the results reported in previous studies.Comment: 31 pages, 7 figures

Pore-Scale Behavior of Darcy Flow in Static and Dynamic Porous Media

Lattice-Boltzmann numerical simulations are conducted to explore the pore-scale flow behavior inside modeled porous media over the Darcy regime. We use static (fixed) and dynamic (rotating) particles to form the porous media. The pore flow behavior (tortuosity) is found to be constant in the static medium within the Darcy range. However, the study reveals distinctively different flow structures in the dynamic case depending on the macroscopic Darcy flow rate and the level of internal energy imposed to the system (via the angular velocity of particles). With small Darcy flow rates, tortuous flow develops with vortices occupying a large portion of the pore space but contributing little to the net flow. The formation of the vortices is linked to spatial fluctuations of local pore fluid pressure. As the Darcy flow rate (and, hence, the global fluid pressure gradient across the medium) increases, the effect of local pressure fluctuations diminishes, and the flow becomes more channelized. Despite the large variations of the pore-scale flow characteristics in the dynamic porous media, the macroscopic flow satisfies Darcy's law with an invariant permeability. The applicability of Darcy's law is proven for an internally disturbed flow through porous media. The results raise questions concerning the generality of the models describing the Darcy flow as being channelized with constant (structure-dependent) tortuosity and how the internal sources of energy imposed to the porous media flow are considered