Contact Line Dynamics in Liquid-Vapor Flows Using Lattice Boltzmann Method

2006 ◽  
Author(s):  
Shi-Ming Li ◽  
Danesh K. Tafti
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Lattice Boltzmann ◽  
Solid Wall ◽  
Hydrodynamic Theory ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method ◽  
Contact Line Dynamics

A mean-field free-energy lattice Boltzmann method (LBM) is applied to simulate moving contact line dynamics. It is found that the common bounceback boundary condition leads to an unphysical velocity at the solid wall in the presence of surface forces. The magnitude of the unphysical velocity is shown proportional to the local force term. The velocity-pressure boundary condition is generalized to solve the problem of the unphysical velocity. The simulation results are compared with three different theories for moving contact lines, including a hydrodynamic theory, a molecular kinetic theory, and a linear cosine law of moving contact angle versus capillary number. It is shown that the current LBM can be used to replace the three theories in handling moving contact line problems.

A phase-field-based lattice Boltzmann method for moving contact line problems on curved stationary boundaries in two dimensions

2019 ◽  
Vol 30 (06) ◽  
pp. 1950044
Author(s):  
Weifeng Zhao
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Two Dimensions ◽  
Curved Boundaries ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method

In this work, we propose a phase-field-based lattice Boltzmann method to simulate moving contact line (MCL) problems on curved boundaries. The key point of this method is to implement the boundary conditions on curved solid boundaries. Specifically, we use our recently proposed single-node scheme for the no-slip boundary condition and a new scheme is constructed to deal with the wetting boundary conditions (WBCs). In particular, three kinds of WBCs are implemented: two wetting conditions derived from the wall free energy and a characteristic MCL model based on geometry considerations. The method is validated with several MCL problems and numerical results show that the proposed method has utility for all the three WBCs on both straight and curved boundaries.

A HYBRID PHASE-FIELD BASED LATTICE BOLTZMANN METHOD FOR CONTACT LINE DYNAMICS

2012 ◽  
Vol 19 ◽  
pp. 50-61
Author(s):  
JIANG YAN SHAO ◽  
CHANG SHU ◽  
YONG TIAN CHEW
Keyword(s):  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Solution Process ◽  
Droplet Spreading ◽  
Interface Evolution ◽  
Cahn Hilliard Equation ◽  
Boltzmann Method ◽  
Contact Line Dynamics

A hybrid phase-field based lattice Boltzmann method (LBM) is proposed in this paper to simulate the contact line dynamics. The flow field is obtained through the lattice Boltzmann equation (LBE). Concurrently, the interface capturing is accomplished by directly solving Cahn-Hilliard equation, which is the governing equation of interface evolution. A symmetric spatial discretization scheme is adopted to enhance the stability. Compared with the conventional algorithms which solve two sets of LBEs, the present method has several advantages such as reduction of the number of variables in the solution process, decoupling the mobility with relaxation time and enabling a more direct manner to implement wetting boundary conditions. The proposed algorithm is first validated through recovering the analytical profile of a surface layer. It is then applied to simulate droplet spreading on surfaces with different wettability.

A Unified Wall-Boundary Condition for the Lattice Boltzmann Method and its Application to Force Evaluation

2014 ◽  
Vol 31 (1) ◽  
pp. 55-68 ◽  
Author(s):  
S.-Y. Lin ◽  
Y.-H. Chin ◽  
F.-L. Yang ◽  
J.-F. Lin ◽  
J.-J. Hu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Solid Wall ◽  
Immersed Boundary ◽  
Equilibrium Pressure ◽  
Good Convergence ◽  
Wall Boundary Condition ◽  
Wall Boundary ◽  
Boltzmann Method

AbstractA unified wall-boundary condition for the pressure-based lattice Boltzmann method (LBM) is proposed. The present approach is developed from the direct-forcing technique in the immersed boundary method and is derived from the equilibrium pressure distribution function. The proposed method can handle many kinds of wall boundaries, such as fixed wall and moving wall boundaries, in the same way. It is found that the new method has the following advantages: (1) simple in concept and easy to implement, (2) higher-order accuracy, (3) mass conservation, and (4) a stable and good convergence rate. Based on this wall-boundary condition, if a solid wall is immersed in a fluid, then by applying Gauss's theorem, the formulas for computing the force and torque acting on the solid wall from fluid flow are derived from the volume integrals over the solid volume instead of from the surface integrals over the solid surface. Based on the pressure-based LBM, inlet and outlet boundary conditions are also proposed. The order of accuracy of the proposed boundary condition is demonstrated with the errors of the velocity field, wall stress, and gradients of velocity and pressure. The steady flow past a circular cylinder is simulated to demonstrate the efficiency and capabilities of the proposed unified method.

A Study of Fluid Interfaces and Moving Contact Lines Using the Lattice Boltzmann Method

2013 ◽  
Vol 13 (3) ◽  
pp. 725-740 ◽  
Author(s):  
S. Srivastava ◽  
P. Perlekar ◽  
L. Biferale ◽  
M. Sbragaglia ◽  
J.H. M. ten Thije Boonkkamp ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Lattice Boltzmann ◽  
Dynamical Behavior ◽  
Pressure Jump ◽  
Multiphase Model ◽  
Moving Contact ◽  
Wall Boundary Conditions ◽  
Boltzmann Method

AbstractWe study the static and dynamical behavior of the contact line between two fluids and a solid plate by means of the Lattice Boltzmann method (LBM). The different fluid phases and their contact with the plate are simulated by means of standard Shan-Chen models. We investigate different regimes and compare the multicomponent vs. the multiphase LBM models near the contact line. A static interface profile is attained with the multiphase model just by balancing the hydrostatic pressure (due to gravity) with a pressure jump at the bottom. In order to study the same problem with the multicomponent case we propose and validate an idea of a body force acting only on one of the two fluid components. In order to reproduce results matching an infinite bath, boundary conditions at the bath side play a key role. We quantitatively compare open and wall boundary conditions and study their influence on the shape of the meniscus against static and lubrication theory solution.

HYDRODYNAMIC BOUNDARY CONDITION AT THE FLUID-SOLID INTERFACE

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4131-4143 ◽  
Author(s):  
PING SHENG ◽  
TIEZHENG QIAN ◽  
XIAOPING WANG
Keyword(s):  
Boundary Condition ◽  
Contact Line ◽  
Solid Wall ◽  
Equations Of Motion ◽  
Minimum Energy ◽  
Dissipative System ◽  
Two Phase ◽  
Moving Contact Line ◽  
Solid Interface ◽  
Moving Contact

While the no-slip boundary condition (no relative motion at the fluid-solid interface) has been universally accepted as a cornerstone of hydrodynamics, it was known for some time that it is incompatible with the moving contact line, defined as the motion of the line of intersection of the immiscible (two phase) fluid-fluid interface with the solid wall. By employing Onsager's principle of minimum energy dissipation, we show in this work that a continuum hydrodynamics, comprising the equations of motion as well as the relevant boundary conditions, can be obtained which resolves the moving contact line problem. Our derivation reveals that just as other dissipative system dynamics, the fluid-solid interfacial boundary condition should be consistent with the framework of linear response theory. Implications of our results are discussed.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

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