An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models

Holdych, David J.; Rovas, Dimitrios; Georgiadis, John G.; Buckius, Richard O.

doi:10.1142/s0129183198001266

Cited by 101 publications

(87 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…al. [2,3,4,5] developed an algorithm based on implementing a pressure tensor and Shan et al [6,7,8] developed an algorithm based on mimicking microscopic interactions. These algorithms have been succesfully applied to simulations of phase-separation [9], drop-collisions [1,10], wetting dynamics and spreading [11], and the study of dynamic contact angles [12,13,14].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Interface width and bulk stability: Requirements for the simulation of deeply quenched liquid-gas systems

Wagner

Pooley

2007

Phys. Rev. E

View full text Add to dashboard Cite

Simulations of liquid-gas systems with extended interfaces are observed to fail to give accurate results for two reasons: the interface can get "stuck" on the lattice or a density overshoot develops around the interface. In the first case the bulk densities can take a range of values, dependent on the initial conditions. In the second case inaccurate bulk densities are found. In this communication we derive the minimum interface width required for the accurate simulation of liquid gas systems with a diffuse interface. We demonstrate this criterion for lattice Boltzmann simulations of a van der Waals gas. When combining this criterion with predictions for the bulk stability we can predict the parameter range that leads to stable and accurate simulation results. This allows us to identify parameter ranges leading to high density ratios of over 1000. This is despite the fact that lattice Boltzmann simulations of liquid-gas systems were believed to be restricted to modest density ratios of less than 20 [1].Application of lattice Boltzmann methods to the simulation of liquid-gas systems has been one of the early successful applications of lattice Boltzmann. Two very different algorithms were developed to do this: Swift et. al. [2,3,4,5] developed an algorithm based on implementing a pressure tensor and Shan et al. [6,7,8] developed an algorithm based on mimicking microscopic interactions. These algorithms have been succesfully applied to simulations of phase-separation [9], drop-collisions [1, 10], wetting dynamics and spreading [11], and the study of dynamic contact angles [12,13,14]. Only recently has it been shown that both algorithms perform very similarly when higher order corrections are taken into account [15].Previously there have been only heuristic analysis of what range of paramteres lead to accurate simulation results. In some parameter ranges not too far from the critical point too thin interefaces can lead to interfaces that stick to the lattice. This can lead to non-unique bulk densities for the liquid and gas phases that depend on the inital contitions. Further from the critical point density overshooting is observed at the interfaces. This also leads to incorrect bulk densities. In this communication we present a criterion that allows us to predict the range of acceptable values for the interface width. We will show that the accuracy of the algorithm rapidly deteriorates when this limit is exceeded. The second important contribution of this communication is a more general definition of the equation of state. Usual lattice Boltzmann methods recover the ideal gas equation of state with a pressure of p = ρ/3 when the gas is dilute. While relaxing this requirement has no effect on the interfacial properties it allows us to adjust the bulk-stability of the lattice Boltzmann method. Taken together this allows us to determine sets of paramters for which very deep quenches can be simulated. This is an important result since lattice Boltzmann methods were previously believed to be limited to density ranges of...

show abstract

mentioning

confidence: 99%

“…and Π = ρu 2 + P + νu∂ x ρ [3,15] where ν = (τ − 0.5)/3. To second order the resulting equations of motion are, as usual, the continuity equation…”

mentioning

confidence: 99%

Interface width and bulk stability: Requirements for the simulation of deeply quenched liquid-gas systems

Wagner

Pooley

2007

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…(6) and is not Galilean invariant. Holdych et al showed that the addition of this term led any nonGalilean invariant terms to be of the same order as nite lattice corrections to the Navier-Stokes equations [47]. In order to fully constrain the coe cients, a fourth condition is needed, which is [44] The pressure tensor can be de ned as [48]:…”

Section: Simulation Methodsmentioning

confidence: 99%

A note on the critical gap of bubble coalescence during foaming process: A diffuse-interface modeling

Rad

2017

Scientia Iranica

View full text Add to dashboard Cite

Abstract. Bubble coalescence is an important stage of foaming process. A goal of foaming is to produce numerous, uniform-size bubbles. Therefore, suppression of bubble coalescence is desirable during foaming process. For stationary bubbles, if their distance is less than a critical gap, they will coalesce. Actually, in this case, attractive forces attract the outer surfaces to touch each other and form a growing gas bridge, which nally merges the bubbles. For bigger distance, the attractive forces cannot make a bridge and coalescence will not happen. In this study, the dynamics of bubble coalescence are modeled using a di use-interface LBM. Then, critical gap of bubble coalescence is de ned as the maximum distance between the stationary bubbles where the coalescence will happen. Sensibility of critical gap is obtained with respect to critical properties of material, bubble size, viscosity of gas and liquid, density ratio, surface tension, temperature, and interface thickness. The results show that interface thickness is the only factor that controls the critical gap. In other words, in the case of stationary bubbles, by a precise estimation of interface thickness, the coalescence can be predicted. Critical gap is a useful parameter in foaming where the maximum number of bubbles is desirable.

show abstract

“…43 However, with thermal fluctuations present, density fluctuates locally (δρ = 0, but still small) and, therefore, the bulk viscosity coefficient is relevant. Previous LB studies 20,25,26,[29][30][31] incorporating noise have assumed the speed of sound squared v 2 s = v 2 c /3, a choice which zeroes the viscosity coefficient of the ∂ γ u γ term in Eq.…”

Section: B Thermal Noise In the Lattice-boltzmann Modelmentioning

confidence: 99%

“…We note that calculation of P αβ (x, n) must take into account corrections to reduce errors in non-Galilean invariant terms as presented in Ref. 43.…”

Section: Appendix A: Details For the D3q15 Latticementioning

confidence: 99%

Fluctuating lattice-Boltzmann model for complex fluids

Ollila

Denniston

Karttunen

et al. 2011

The Journal of Chemical Physics

View full text Add to dashboard Cite

We develop and test numerically a lattice-Boltzmann (LB) model for nonideal fluids that incorporates thermal fluctuations. The fluid model is a momentum-conserving thermostat, for which we demonstrate how the temperature can be made equal at all length scales present in the system by having noise both locally in the stress tensor and by shaking the whole system in accord with the local temperature. The validity of the model is extended to a broad range of sound velocities. Our model features a consistent coupling scheme between the fluid and solid molecular dynamics objects, allowing us to use the LB fluid as a heat bath for solutes evolving in time without external Langevin noise added to the solute. This property expands the applicability of LB models to dense, strongly correlated systems with thermal fluctuations and potentially nonideal equations of state. Tests on the fluid itself and on static and dynamic properties of a coarse-grained polymer chain under strong hydrodynamic interactions are used to benchmark the model. The model produces results for singlechain diffusion that are in quantitative agreement with theory.

show abstract

An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models

Cited by 101 publications

References 9 publications

Interface width and bulk stability: Requirements for the simulation of deeply quenched liquid-gas systems

Interface width and bulk stability: Requirements for the simulation of deeply quenched liquid-gas systems

A note on the critical gap of bubble coalescence during foaming process: A diffuse-interface modeling

Fluctuating lattice-Boltzmann model for complex fluids

Contact Info

Product

Resources

About