Equations of state in a lattice Boltzmann model

Yuan, Pingzhi; Schaefer, Laura

doi:10.1063/1.2187070

Cited by 783 publications

(536 citation statements)

References 20 publications

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“…38 The pseudo-potential model introduces the nearest-neighboring interaction between fluid particles to describe the intermolecular potential, and the phase separation occurs with a properly chosen potential function. Although significant advances have recently been made, [43][44][45] further improvements are necessary for the pseudo-potential model to minimize spurious velocities at interface and control numerical instability for the flows with low capillary number and viscosity ratio. The free-energy model suffers from the lack of Galilean invariance, 32 although the local conservation of mass and momentum is satisfied.…”

Section: Methodsmentioning

confidence: 99%

Droplet formation in microfluidic cross-junctions

2011

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Using a lattice Boltzmann multiphase model, three-dimensional numerical simulations have been performed to understand droplet formation in microfluidic cross-junctions at low capillary numbers. Flow regimes, consequence of interaction between two immiscible fluids, are found to be dependent on the capillary number and flow rates of the continuous and dispersed phases. A regime map is created to describe the transition from droplets formation at a cross-junction (DCJ), downstream of cross-junction to stable parallel flows. The influence of flow rate ratio, capillary number, and channel geometry is then systematically studied in the squeezing-pressure-dominated DCJ regime. The plug length is found to exhibit a linear dependence on the flow rate ratio and obey power-law behavior on the capillary number. The channel geometry plays an important role in droplet breakup process. A scaling model is proposed to predict the plug length in the DCJ regime with the fitting constants depending on the geometrical parameters.

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Section: Methodsmentioning

confidence: 99%

Droplet formation in microfluidic cross-junctions

2011

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“…However, use of this equation of state limits the density ratio between the heavy and light phases to about 100 and results in large spurious currents at the liquid-gas interface that hamper the tracking of passive tracer particles in this region. Here, following previous work [39,40], the Carnahan-Starling equation of state,…”

Section: Simulation Methodsmentioning

confidence: 99%

Mixing and internal dynamics of droplets impacting and coalescing on a solid surface

et al. 2013

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The coalescence and mixing of a sessile and an impacting liquid droplet on a solid surface are studied experimentally and numerically in terms of lateral separation and droplet speed. Two droplet generators are used to produce differently colored droplets. Two high-speed imaging systems are used to investigate the impact and coalescence of the droplets in color from a side view with a simultaneous gray-scale view from below. Millimeter-sized droplets were used with dynamical conditions, based on the Reynolds and Weber numbers, relevant to microfluidics and commercial inkjet printing. Experimental measurements of advancing and receding static contact angles are used to calibrate a contact angle hysteresis model within a lattice Boltzmann framework, which is shown to capture the observed dynamics qualitatively and the final droplet configuration quantitatively. Our results show that no detectable mixing occurs during impact and coalescence of similar-sized droplets, but when the sessile droplet is sufficiently larger than the impacting droplet vortex ring generation can be observed. Finally we show how a gradient of wettability on the substrate can potentially enhance mixing.

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“…In addition, Sbragaglia et al [20] have devised a free-energy formulation of the pseudopotential LB model. Furthermore, several attempts have been made by Yuan and Schaefer [21], Falcucci et al [22], and Kupershtokh et al [23] to break through the low-density-ratio restriction.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

2013

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Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/ √ a. Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature.

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Equations of state in a lattice Boltzmann model

Cited by 783 publications

References 20 publications

Droplet formation in microfluidic cross-junctions

Droplet formation in microfluidic cross-junctions

Mixing and internal dynamics of droplets impacting and coalescing on a solid surface

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

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