Mean-field free-energy approach to the lattice Boltzmann method for liquid-vapor and solid-fluid interfaces

2004 ◽  
Vol 69 (3) ◽  
Author(s):  
Junfeng Zhang ◽  
Baoming Li ◽  
Daniel Y. Kwok
Keyword(s):  
Free Energy ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Mean Field ◽  
Energy Approach ◽  
Fluid Interfaces ◽  
Boltzmann Method ◽  
Liquid Vapor

A Mean-Field Free-Energy Approach to Lattice Boltzmann Method for Liquid-Vapor and Solid-Fluid Interfaces in Micro and Nanofluidics

2004 ◽  
Author(s):  
Junfeng Zhang ◽  
Baoming Li ◽  
Daniel Y. Kwok
Keyword(s):  
Free Energy ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Mean Field ◽  
Contact Angles ◽  
Energy Approach ◽  
Fluid Interfaces ◽  
Field Representation ◽  
Fluid Systems ◽  
Boltzmann Method

We presented a lattice Boltzmann method (LBM) using a mean-field representation of the free energy for fluid systems. This free-energy approach provides more realistic contact angles and fluid density profiles near the vicinity of an impenetrable wall, which cannot be easily obtained by other LBM schemes. Our method was tested against various criteria and the results are in good agreement with those from thermodynamics and molecular dynamics considerations. This mean-field approach to LBM can have important implication on studies where the solid-fluid interactions are crucial to fluidic behaviors.

scholarly journals Research on Human Erythrocyte’s Threshold Free Energy for Hemolysis and Damage from Coupling Effect of Shear and Impact Based on Immersed Boundary-Lattice Boltzmann Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zhong Yun ◽  
Chuang Xiang ◽  
Liang Wang
Keyword(s):  
Free Energy ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Coupling Effect ◽  
Threshold Value ◽  
Blood Pump ◽  
Immersed Boundary ◽  
Threshold Limit ◽  
Spring Network Model ◽  
Boltzmann Method

Researches on the principle of human red blood cell’s (RBC) injuring and judgment basis play an important role in decreasing the hemolysis in a blood pump. In the current study, the judgment of hemolysis in a blood pump study was through some experiment data and empirical formula. The paper forms a criterion of RBC’s mechanical injury in the aspect of RBC’s free energy. First, the paper introduces the nonlinear spring network model of RBC in the frame of immersed boundary-lattice Boltzmann method (IB-LBM). Then, the shape, free energy, and time needed for erythrocyte to be shorn in different shear flow and impacted in different impact flow are simulated. Combining existing research on RBC’s threshold limit for hemolysis in shear and impact flow with this paper’s, the RBC’s free energy of the threshold limit for hemolysis is found to be 3.46 × 10 − 15  J. The threshold impact velocity of RBC for hemolysis is 8.68 m/s. The threshold value of RBC can be used for judgment of RBC’s damage when the RBC is having a complicated flow of blood pumps such as coupling effect of shear and impact flow. According to the change law of RBC’s free energy in the process of being shorn and impacted, this paper proposed a judging criterion for hemolysis when the RBC is under the coupling effect of shear and impact based on the increased free energy of RBC.

scholarly journals Simulating liquid-vapor phase separation under shear with lattice Boltzmann method

2009 ◽  
Vol 52 (9) ◽  
pp. 1337-1344 ◽  
Author(s):  
Ce Wang ◽  
AiGuo Xu ◽  
GuangCai Zhang ◽  
YingJun Li
Keyword(s):  
Phase Separation ◽  
Lattice Boltzmann Method ◽  
Vapor Phase ◽  
Lattice Boltzmann ◽  
Boltzmann Method ◽  
Liquid Vapor

A Mean-Field Pressure Formulation for Liquid-Vapor Flows

2006 ◽  
Vol 129 (7) ◽  
pp. 894-901 ◽  
Author(s):  
Shi-Ming Li ◽  
Danesh K. Tafti
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Capillary Waves ◽  
Wave Number ◽  
Density Profiles ◽  
Pressure Formulation ◽  
Boltzmann Method ◽  
Relationship Of ◽  
The Relationship ◽  
Liquid Vapor

A nonlocal pressure equation is derived from mean-field free energy theory for calculating liquid-vapor systems. The proposed equation is validated analytically by showing that it reduces to van der Waals’ square-gradient approximation under the assumption of slow density variations. The proposed nonlocal pressure is implemented in the mean-field free energy lattice Boltzmann method (LBM). The LBM is applied to simulate equilibrium liquid-vapor interface properties and interface dynamics of capillary waves and oscillating droplets in vapor. Computed results are validated with Maxwell constructions of liquid-vapor coexistence densities, theoretical relationship of variation of surface tension with temperature, theoretical planar interface density profiles, Laplace’s law of capillarity, dispersion relationship between frequency and wave number of capillary waves, and the relationship between radius and the oscillating frequency of droplets in vapor. It is shown that the nonlocal pressure formulation gives excellent agreement with theory.

MEAN-FIELD AND FLUCTUATION ANALYSIS OF A FORCED TURBULENCE SIMULATED BY THE LATTICE BOLTZMANN METHOD

2004 ◽  
Vol 18 (12n13) ◽  
pp. 583-596 ◽  
Author(s):  
WATARU SAKIKAWA ◽  
OSAMU NARIKIYO
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Exit Time ◽  
Mean Field ◽  
Fluctuation Analysis ◽  
Taylor’S Hypothesis ◽  
New Findings ◽  
Forced Turbulence ◽  
Boltzmann Method ◽  
Non Equilibrium

On the basis of the lattice Boltzmann method for the Navier–Stokes equation, we have done a numerical experiment of a forced turbulence in real space and time. Our new findings are summarized into two points. Firstly, in the analysis of the mean-field behavior of the velocity field using the exit-time statistics, we have verified Kolmogorov's scaling and Taylor's hypothesis at the same time. Secondly, in the analysis of the intermittent velocity fluctuations using a non-equilibrium probability distribution function and the wavelet denoising, we have clarified that the coherent vortices sustain the power-law velocity correlation in the non-equilibrium state.

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