Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

Li, Qing; Luo, K.H.; Kang, Qinjun; He, Y.L.; Chen, Q.; Liu, Q.

doi:10.1016/j.pecs.2015.10.001

Title: Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

Abstract

We report that over the past few decades, tremendous progress has been made in the development of particle-based discrete simulation methods versus the conventional continuum-based methods. In particular, the lattice Boltzmann (LB) method has evolved from a theoretical novelty to a ubiquitous, versatile and powerful computational methodology for both fundamental research and engineering applications. It is a kinetic-based mesoscopic approach that bridges the microscales and macroscales, which offers distinctive advantages in simulation fidelity and computational efficiency. Applications of the LB method are now found in a wide range of disciplines including physics, chemistry, materials, biomedicine and various branches of engineering. The present work provides a comprehensive review of the LB method for thermofluids and energy applications, focusing on multiphase flows, thermal flows and thermal multiphase flows with phase change. The review first covers the theoretical framework of the LB method, revealing certain inconsistencies and defects as well as common features of multiphase and thermal LB models. Recent developments in improving the thermodynamic and hydrodynamic consistency, reducing spurious currents, enhancing the numerical stability, etc., are highlighted. These efforts have put the LB method on a firmer theoretical foundation with enhanced LB models that can achieve larger liquid-gas density ratio, higher Reynoldsmore »« less

Authors:

Li, Qing ^[1]; Luo, K.H. ^[2];

^[3]; He, Y.L. ^[4]; Chen, Q. ^[5]; Liu, Q. ^[4]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Central South University, Changsha (China)
University College London (United Kingdom)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Xi’an Jiaotong University (China)
Nanjing Forestry University (China)

Publication Date:: Tue Dec 01 00:00:00 EST 2015

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1457254

Alternate Identifier(s):: OSTI ID: 1396966

Report Number(s):: LA-UR-15-26103
Journal ID: ISSN 0360-1285

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Progress in Energy and Combustion Science

Additional Journal Information:: Journal Volume: 52; Journal Issue: C; Journal ID: ISSN 0360-1285

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Lattice Boltzmann method; Mesoscopic modeling; Multiphase flow; Heat transfer; Phase change

Citation Formats


                    Li, Qing, Luo, K.H., Kang, Qinjun, He, Y.L., Chen, Q., and Liu, Q. Lattice Boltzmann methods for multiphase flow and phase-change heat transfer.  United States: N. p., 2015. 
Web.  doi:10.1016/j.pecs.2015.10.001.

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                    Li, Qing, Luo, K.H., Kang, Qinjun, He, Y.L., Chen, Q., & Liu, Q. Lattice Boltzmann methods for multiphase flow and phase-change heat transfer.  United States.  https://doi.org/10.1016/j.pecs.2015.10.001

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                    Li, Qing, Luo, K.H., Kang, Qinjun, He, Y.L., Chen, Q., and Liu, Q. Tue .  
"Lattice Boltzmann methods for multiphase flow and phase-change heat transfer".  United States.  https://doi.org/10.1016/j.pecs.2015.10.001.  https://www.osti.gov/servlets/purl/1457254.

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@article{osti_1457254,

  title        = {Lattice Boltzmann methods for multiphase flow and phase-change heat transfer},

  author       = {Li, Qing and Luo, K.H. and Kang, Qinjun and He, Y.L. and Chen, Q. and Liu, Q.},

  abstractNote = {We report that over the past few decades, tremendous progress has been made in the development of particle-based discrete simulation methods versus the conventional continuum-based methods. In particular, the lattice Boltzmann (LB) method has evolved from a theoretical novelty to a ubiquitous, versatile and powerful computational methodology for both fundamental research and engineering applications. It is a kinetic-based mesoscopic approach that bridges the microscales and macroscales, which offers distinctive advantages in simulation fidelity and computational efficiency. Applications of the LB method are now found in a wide range of disciplines including physics, chemistry, materials, biomedicine and various branches of engineering. The present work provides a comprehensive review of the LB method for thermofluids and energy applications, focusing on multiphase flows, thermal flows and thermal multiphase flows with phase change. The review first covers the theoretical framework of the LB method, revealing certain inconsistencies and defects as well as common features of multiphase and thermal LB models. Recent developments in improving the thermodynamic and hydrodynamic consistency, reducing spurious currents, enhancing the numerical stability, etc., are highlighted. These efforts have put the LB method on a firmer theoretical foundation with enhanced LB models that can achieve larger liquid-gas density ratio, higher Reynolds number and flexible surface tension. Examples of applications are provided in fuel cells and batteries, droplet collision, boiling heat transfer and evaporation, and energy storage. Lastly, further developments and future prospect of the LB method are outlined for thermofluids and energy applications.},

  doi          = {10.1016/j.pecs.2015.10.001},

  journal      = {Progress in Energy and Combustion Science},

  number       = C,

  volume       = 52,

  place        = {United States},

  year         = {Tue Dec 01 00:00:00 EST 2015},

  month        = {Tue Dec 01 00:00:00 EST 2015}

}

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Abstract Fractures are conduits for fluid flow in low‐permeability geological formations. Multiphase flow properties of fractures are important in natural processes and in engineering applications such as the evaluation of the sealing capacity of caprocks and productivity of hydrocarbon‐bearing tight rocks. Investigations of flow and transport through fractures typically focus on the effects of fracture geometric and mechanical factors such as aperture, roughness, and compressibility. The wettability of the fracture surfaces and its influence on microscale interfacial phenomena and macroscale effective transport properties are seldom studied. Here, we investigated the effect of heterogeneous wetting properties on the displacement of watermore »« less
https://doi.org/10.1029/2020wr027943

Full Text Available
Three Dimensional Simulations of Multiphase Flows Using a Lattice Boltzmann Method Suitable for High Density Ratios - 12126

Conference Gokaltun, Seckin ; McDaniel, Dwayne ; Roelant, David

Multiphase flows involving gas and liquid phases can be observed in engineering operations at various Department of Energy sites, such as mixing of slurries using pulsed-air mixers and hydrogen gas generation in liquid waste tanks etc. The dynamics of the gas phase in the liquid domain play an important role in the mixing effectiveness of the pulsed-air mixers or in the level of gas pressure build-up in waste tanks. To understand such effects, computational fluid dynamics methods (CFD) can be utilized by developing a three-dimensional computerized multiphase flow model that can predict accurately the behavior of gas motion inside liquid-filledmore »« less
Three-dimensional multiphase segmentation of X-ray CT data of porous materials using a Bayesian Markov random field framework

Journal Article Kulkarni, Ramaprasad ; Tuller, Markus ; Fink, Wolfgang ; ... - Vadose Zone Journal

Advancements in noninvasive imaging methods such as X-ray computed tomography (CT) have led to a recent surge of applications in porous media research with objectives ranging from theoretical aspects of pore-scale fluid and interfacial dynamics to practical applications such as enhanced oil recovery and advanced contaminant remediation. While substantial efforts and resources have been devoted to advance CT technology, microscale analysis, and fluid dynamics simulations, the development of efficient and stable three-dimensional multiphase image segmentation methods applicable to large data sets is lacking. To eliminate the need for wet-dry or dual-energy scans, image alignment, and subtraction analysis, commonly applied inmore »« less
https://doi.org/10.2136/vzj2011.0082
PoreStudio - First Cloud-Based Multiphase Reactive Flow Simulator

Technical Report Shafei, Babak

Reactive transport models (RTMs) are quantitative tools to analyze coupled physical, chemical, and microbiological processes in various material and energy systems. Oil and gas, mining, nuclear waste management, and environmental consulting companies use RTMs to acquire critical information which is essential to estimate the oil and gas production rates under different hydraulic fracturing and enhanced oil recovery strategies, minimize the risk of groundwater contamination by acid mine drainage, assess the safety of cement-based engineered barrier systems in nuclear waste repositories, and design the efficient treatment and remediation strategies for contaminated sites. Cloud-based applications have emerged as primary tools as engineersmore »« less

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Title: Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

Abstract

Citation Formats

Multiscale Modeling of Multiphase flow with Complex Interactions journal, January 2009

Lattice Boltzmann Method for Fluid Flows journal, January 1998

Use of the Boltzmann Equation to Simulate Lattice-Gas Automata journal, November 1988

Boltzmann Approach to Lattice Gas Simulations journal, August 1989

Lattice Gas Dynamics with Enhanced Collisions journal, June 1989

A Simple Lattice Boltzmann Scheme for Navier-Stokes Fluid Flow journal, July 1991

Lattice Boltzmann model for simulation of magnetohydrodynamics journal, December 1991

Lattice BGK Models for Navier-Stokes Equation journal, February 1992

The lattice Boltzmann equation: theory and applications journal, December 1992

Lattice-Boltzmann Method for Complex Flows journal, January 2010

Lattice Boltzmann 2038 journal, March 2015

A higher order lattice BGK model for simulating some nonlinear partial differential equations journal, June 2009

Lattice Boltzmann model for nonlinear convection-diffusion equations journal, January 2009

The lattice Boltzmann model for the second-order Benjamin–Ono equations journal, April 2010

Lattice Boltzmann model for generalized nonlinear wave equations journal, October 2011

Numerical Study of the Nonlinear Combined Sine-Cosine-Gordon Equation with the Lattice Boltzmann Method journal, March 2012

Lattice Boltzmann model for the complex Ginzburg-Landau equation journal, June 2010

Lattice Boltzmann across scales: from turbulence to DNA translocation journal, February 2008

Lattice Boltzmann model of immiscible fluids journal, April 1991

A lattice Boltzmann model for multiphase fluid flows journal, October 1993

Two-color nonlinear Boltzmann cellular automata: Surface tension and wetting journal, April 1995

Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents journal, March 2003

Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids journal, May 2005

Lattice Boltzmann model for simulating immiscible two-phase flows journal, March 2007

Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations journal, April 2012

Lattice Boltzmann model for simulating flows with multiple phases and components journal, March 1993

Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation journal, April 1994

Equations of state in a lattice Boltzmann model journal, April 2006

Mesoscopic interparticle potentials in the lattice Boltzmann equation for multiphase fluids journal, June 2006

Bubble formation in lattice Boltzmann immiscible shear flow journal, March 2007

Generalized lattice Boltzmann method with multirange pseudopotential journal, February 2007

Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow journal, October 2010

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model journal, May 2013

Lattice Boltzmann simulations of liquid-gas and binary fluid systems journal, November 1996

A Galilean invariant model of the lattice Boltzmann method for multiphase fluid flows using free-energy approach journal, July 2000

Galilean-invariant lattice-Boltzmann simulation of liquid-vapor interface dynamics journal, April 2002

Eliminating spurious velocities in the free-energy lattice Boltzmann method journal, April 2008

A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh–Taylor Instability journal, July 1999

A lattice Boltzmann method for incompressible two-phase flows with large density differences journal, August 2004

A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio journal, June 2005

A lattice Boltzmann model for multiphase flows with large density ratio journal, October 2006

Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces journal, October 2010

Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows journal, February 2012

Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows journal, January 2013

Simulation of Newtonian and non-Newtonian rheology behavior of viscous fingering in channels by the lattice Boltzmann method journal, November 2014

Study of wetting and spontaneous motion of droplets on microstructured surfaces with the lattice Boltzmann method journal, June 2015

Entropic Lattice Boltzmann Method for Multiphase Flows journal, May 2015

Discrete Boltzmann modeling of multiphase flows: hydrodynamic and thermodynamic non-equilibrium effects journal, January 2015

Multi-Relaxation time Lattice Boltzmann Model for Multiphase Flows journal, June 2008

On Simulations of High-Density Ratio Flows Using Color-Gradient Multiphase Lattice Boltzmann Models journal, April 2013

Enhanced equilibrium distribution functions for simulating immiscible multiphase flows with variable density ratios in a class of lattice Boltzmann models journal, December 2013

Unsteady immiscible multiphase flow validation of a multiple-relaxation-time lattice Boltzmann method journal, February 2014

Lattice Boltzmann method for modeling liquid-vapor interface configurations in porous media: LATTICE BOLTZMANN FOR INTERFACE CONFIGURATIONS journal, January 2004

Lattice Boltzmann method for microfluidics: models and applications journal, April 2010

A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications journal, September 2014

Lattice Boltzmann Methods for Multiphase Flow Simulations across Scales journal, February 2011

Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling journal, October 1999

Droplet Collision Simulation by a Multi-Speed Lattice Boltzmann Method journal, May 2011

Multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio journal, January 2015

A hybrid phase field multiple relaxation time lattice Boltzmann method for the incompressible multiphase flow with large density contrast: HYBRID LBM FOR MULTIPHASE FLOWS journal, January 2015

A pressure-evolution-based multi-relaxation-time high-density-ratio two-phase lattice-Boltzmann model journal, July 2007

Investigations on the Droplet Impact onto a Spherical Surface with a High Density Ratio Multi-Relaxation Time Lattice-Boltzmann Model journal, October 2014

Three-dimensional multi-relaxation time lattice-Boltzmann model for the drop impact on a dry surface at large density ratio journal, September 2014

Numerical investigation on the head-on collision between unequal-sized droplets with multiple-relaxation-time lattice Boltzmann model journal, March 2014

An investigation of water-gas transport processes in the gas-diffusion-layer of a PEM fuel cell by a multiphase multiple-relaxation-time lattice Boltzmann model journal, October 2007

Impact of GDL structure and wettability on water management in polymer electrolyte fuel cells journal, January 2007

An approach to modeling two-phase transport in the gas diffusion layer of a proton exchange membrane fuel cell journal, January 2008

Multi-phase micro-scale flow simulation in the electrodes of a PEM fuel cell by lattice Boltzmann method journal, March 2008

Numerical simulation of liquid water and gas flow in a channel and a simplified gas diffusion layer model of polymer electrolyte membrane fuel cells using the lattice Boltzmann method journal, August 2009

Mesoscopic modeling of two-phase behavior and flooding phenomena in polymer electrolyte fuel cells journal, November 2009

Lattice Boltzmann simulations of liquid droplet dynamic behavior on a hydrophobic surface of a gas flow channel journal, May 2009

Pore-scale simulations on relative permeabilities of porous media by lattice Boltzmann method journal, April 2010

Liquid water transport mechanism in the gas diffusion layer journal, March 2010

Pore-scale flow and mass transport in gas diffusion layer of proton exchange membrane fuel cell with interdigitated flow fields journal, January 2012

Two phase flow simulation in a channel of a polymer electrolyte membrane fuel cell using the lattice Boltzmann method journal, February 2012

Lattice Boltzmann simulations of liquid droplets development and interaction in a gas channel of a proton exchange membrane fuel cell journal, March 2012

Lattice Boltzmann simulation of liquid water transport in turning regions of serpentine gas channels in proton exchange membrane fuel cells journal, November 2012

Multiscale Modeling of Multiphase flow with Complex Interactions
journal, January 2009

Lattice Boltzmann Method for Fluid Flows
journal, January 1998

Use of the Boltzmann Equation to Simulate Lattice-Gas Automata
journal, November 1988

Boltzmann Approach to Lattice Gas Simulations
journal, August 1989

Lattice Gas Dynamics with Enhanced Collisions
journal, June 1989

A Simple Lattice Boltzmann Scheme for Navier-Stokes Fluid Flow
journal, July 1991

Lattice Boltzmann model for simulation of magnetohydrodynamics
journal, December 1991

Lattice BGK Models for Navier-Stokes Equation
journal, February 1992

The lattice Boltzmann equation: theory and applications
journal, December 1992

Lattice-Boltzmann Method for Complex Flows
journal, January 2010

Lattice Boltzmann 2038
journal, March 2015

A higher order lattice BGK model for simulating some nonlinear partial differential equations
journal, June 2009

Lattice Boltzmann model for nonlinear convection-diffusion equations
journal, January 2009

The lattice Boltzmann model for the second-order Benjamin–Ono equations
journal, April 2010

Lattice Boltzmann model for generalized nonlinear wave equations
journal, October 2011

Numerical Study of the Nonlinear Combined Sine-Cosine-Gordon Equation with the Lattice Boltzmann Method
journal, March 2012

Lattice Boltzmann model for the complex Ginzburg-Landau equation
journal, June 2010

Lattice Boltzmann across scales: from turbulence to DNA translocation
journal, February 2008

Lattice Boltzmann model of immiscible fluids
journal, April 1991

A lattice Boltzmann model for multiphase fluid flows
journal, October 1993

Two-color nonlinear Boltzmann cellular automata: Surface tension and wetting
journal, April 1995

Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents
journal, March 2003

Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids
journal, May 2005

Lattice Boltzmann model for simulating immiscible two-phase flows
journal, March 2007

Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations
journal, April 2012

Lattice Boltzmann model for simulating flows with multiple phases and components
journal, March 1993

Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation
journal, April 1994

Equations of state in a lattice Boltzmann model
journal, April 2006

Mesoscopic interparticle potentials in the lattice Boltzmann equation for multiphase fluids
journal, June 2006

Bubble formation in lattice Boltzmann immiscible shear flow
journal, March 2007

Generalized lattice Boltzmann method with multirange pseudopotential
journal, February 2007

Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow
journal, October 2010

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model
journal, May 2013

Lattice Boltzmann simulations of liquid-gas and binary fluid systems
journal, November 1996

A Galilean invariant model of the lattice Boltzmann method for multiphase fluid flows using free-energy approach
journal, July 2000

Galilean-invariant lattice-Boltzmann simulation of liquid-vapor interface dynamics
journal, April 2002

Eliminating spurious velocities in the free-energy lattice Boltzmann method
journal, April 2008

A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh–Taylor Instability
journal, July 1999

A lattice Boltzmann method for incompressible two-phase flows with large density differences
journal, August 2004

A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio
journal, June 2005

A lattice Boltzmann model for multiphase flows with large density ratio
journal, October 2006

Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces
journal, October 2010

Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows
journal, February 2012

Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows
journal, January 2013

Simulation of Newtonian and non-Newtonian rheology behavior of viscous fingering in channels by the lattice Boltzmann method
journal, November 2014

Study of wetting and spontaneous motion of droplets on microstructured surfaces with the lattice Boltzmann method
journal, June 2015

Entropic Lattice Boltzmann Method for Multiphase Flows
journal, May 2015

Discrete Boltzmann modeling of multiphase flows: hydrodynamic and thermodynamic non-equilibrium effects
journal, January 2015

Multi-Relaxation time Lattice Boltzmann Model for Multiphase Flows
journal, June 2008

On Simulations of High-Density Ratio Flows Using Color-Gradient Multiphase Lattice Boltzmann Models
journal, April 2013

Enhanced equilibrium distribution functions for simulating immiscible multiphase flows with variable density ratios in a class of lattice Boltzmann models
journal, December 2013

Unsteady immiscible multiphase flow validation of a multiple-relaxation-time lattice Boltzmann method
journal, February 2014

Lattice Boltzmann method for modeling liquid-vapor interface configurations in porous media: LATTICE BOLTZMANN FOR INTERFACE CONFIGURATIONS
journal, January 2004

Lattice Boltzmann method for microfluidics: models and applications
journal, April 2010

A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications
journal, September 2014

Lattice Boltzmann Methods for Multiphase Flow Simulations across Scales
journal, February 2011

Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling
journal, October 1999

Droplet Collision Simulation by a Multi-Speed Lattice Boltzmann Method
journal, May 2011

Multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio
journal, January 2015

A hybrid phase field multiple relaxation time lattice Boltzmann method for the incompressible multiphase flow with large density contrast: HYBRID LBM FOR MULTIPHASE FLOWS
journal, January 2015

A pressure-evolution-based multi-relaxation-time high-density-ratio two-phase lattice-Boltzmann model
journal, July 2007

Investigations on the Droplet Impact onto a Spherical Surface with a High Density Ratio Multi-Relaxation Time Lattice-Boltzmann Model
journal, October 2014

Three-dimensional multi-relaxation time lattice-Boltzmann model for the drop impact on a dry surface at large density ratio
journal, September 2014

Numerical investigation on the head-on collision between unequal-sized droplets with multiple-relaxation-time lattice Boltzmann model
journal, March 2014

An investigation of water-gas transport processes in the gas-diffusion-layer of a PEM fuel cell by a multiphase multiple-relaxation-time lattice Boltzmann model
journal, October 2007

Impact of GDL structure and wettability on water management in polymer electrolyte fuel cells
journal, January 2007

An approach to modeling two-phase transport in the gas diffusion layer of a proton exchange membrane fuel cell
journal, January 2008

Multi-phase micro-scale flow simulation in the electrodes of a PEM fuel cell by lattice Boltzmann method
journal, March 2008

Numerical simulation of liquid water and gas flow in a channel and a simplified gas diffusion layer model of polymer electrolyte membrane fuel cells using the lattice Boltzmann method
journal, August 2009

Mesoscopic modeling of two-phase behavior and flooding phenomena in polymer electrolyte fuel cells
journal, November 2009

Lattice Boltzmann simulations of liquid droplet dynamic behavior on a hydrophobic surface of a gas flow channel
journal, May 2009

Pore-scale simulations on relative permeabilities of porous media by lattice Boltzmann method
journal, April 2010

Liquid water transport mechanism in the gas diffusion layer
journal, March 2010

Pore-scale flow and mass transport in gas diffusion layer of proton exchange membrane fuel cell with interdigitated flow fields
journal, January 2012

Two phase flow simulation in a channel of a polymer electrolyte membrane fuel cell using the lattice Boltzmann method
journal, February 2012

Lattice Boltzmann simulations of liquid droplets development and interaction in a gas channel of a proton exchange membrane fuel cell
journal, March 2012

Lattice Boltzmann simulation of liquid water transport in turning regions of serpentine gas channels in proton exchange membrane fuel cells
journal, November 2012

Numerical studies of interfacial phenomena in liquid water transport in polymer electrolyte membrane fuel cells using the lattice Boltzmann method
journal, April 2013

Lattice Boltzmann simulation of water and gas flow in porous gas diffusion layers in fuel cells reconstructed from micro-tomography
journal, March 2013

Impact of PTFE distribution on the removal of liquid water from a PEMFC electrode by lattice Boltzmann method
journal, May 2014