Lattice Boltzmann Model For Two-phase Flows Research Articles

Entropic Multi-Relaxation-Time Lattice Boltzmann Model for Large Density Ratio Two-Phase Flows

We propose a multiple relaxation time entropic realization of a two-phase flow lattice Boltzmann model we introduced in earlier works arXiv:2112.01975 S.A. Hosseini, B. Dorschner, and I. V. Karlin, arXiv preprint, arXiv:2112.01975 (2021). While the original model with a single relaxation time allows us to reach large density ratios, it is limited in terms of stability with respect to non-dimensional viscosity and Courant--Friedrichs--Lewy number. Here we show that the entropic multiple relaxation time model extends the stability limits of the model significantly, which allows us to reach larger Reynolds numbers for a given grid resolution. The thermodynamic properties of the solver, using the Peng--Robinson equation of state, are studied first using simple configurations. Co-existence densities and temperature scaling of both the interface thickness and the surface tension are shown to agree well with theory. The model is then used to simulate the impact of a drop onto a thin liquid film with density and viscosity ratios matching those of water and air both in 2-D and 3-D. The results are in very good agreement with theoretically predicted scaling laws and experimental data.

Lattice Boltzmann modeling of primary liquid film breakup at the prefilmer edge: Effects of surface wettability

In this paper, numerical predictions are performed for a planar prefilming atomizer using the lattice Boltzmann (LB) method. The main target is to inspect the effects of surface wettability on the primary liquid film breakup at the prefilmer edge. To this end, a phase-field-based multiple-relaxation-time LB model for two-phase flow is derived and verified for the present study, as well as the wetting boundary scheme. After that, the effects of surface wettability are assessed by specifying different contact angles during the simulations. Numerical results indicate that the whole primary breakup process of the liquid film can be roughly divided into three interactive stages: (i) liquid accumulation at the trailing edge; (ii) ligament formation and its flapping movements; (iii) ligament breakup and droplet formation. It is visible that the liquid accumulation and the following ligament breakup show similar periodic patterns with quite consistent frequencies. Besides, when the contact angle is increased, the volume of liquid accumulated at the prefilmer edge declines, the maximum flapping region of ligaments shrinks, the ligament breakup length reduces, but the ligament breakup frequency increases. Based on the above-mentioned results, it can be concluded that the prefilmer with hydrophobic surfaces benefits the primary liquid film breakup in the close vicinity of the prefilmer edge.

A numerical study on splash of oblique drop impact on wet walls

Oblique impact of a liquid drop onto a wet solid wall with a moderate Weber number is simulated numerically by using a two-phase flow lattice Boltzmann model. The simulation is conducted for a wide range of impact angle θ from 0° to 60°. The characteristics of drop splashing on the wall are determined together with the flow patterns accompanying drop impact. The effects of the impact angle on the crown formation and its evolution are quantified. Results show that in the case of θ>0°, splashing is asymmetric. The increase of the angle leads to the transition from splash to partial splash, which indicates the existence of a critical θc for the studied conditions. Above this critical θc, the drop splashing is completely suppressed on the downstream side. In addition, a comparison of flow patterns of oblique drop impact on a stationary wall and normal drop impact on a moving wall is made to show their similarities and differences.

Lattice Boltzmann simulation of a drop impact on a moving wall with a liquid film

A liquid drop impact on a moving wall with a pre-existing thin film of the same liquid is simulated by using a two-phase flow lattice Boltzmann model. A perturbation to flow near the wall is introduced shortly after the moment of impact to reflect the instability of drop impact dynamics. The present simulations not only confirm the splash behavior of a drop impact on a stationary wall with the liquid film, but also reveal some interesting dynamics features of the drop impact on a moving wall with the liquid film. It is found that the moving wall can act to enhance or suppress the splash. The influence of a moving wall on the drop splashing is studied by examining the interface shapes, velocity and vorticity fields. The numerical results indicate that a critical threshold of wall velocity exists, which is determined by the Reynolds number, Weber number and the film thickness. If the wall velocity were larger than this critical value, only a part of the drop could splash on the wall.

Transport of Wetting and Nonwetting Liquid Plugs in a T-shaped Microchannel

The transport of liquid plugs in microchannels is very important for many applications such as in medical treatments in airways and in extraction of oil from porous rocks. A plug of wetting and non-wetting liquids driven by a constant pressure difference through a T-shaped microchannel is studied numerically with lattice Boltzmann (LB) method. A two-phase flow LB model based on field mediators is built. Three typical flow patterns (blocking, rupture and splitting flow) of plug flow are obtained with different driving pressures. It is found that it becomes difficult for a plug with short initial plug length to leave the microchannel; the flow pattern of plug transport varies with the contact angle, especially from wetting to nonwetting; with the increase of interfacial tension, the front interface of plug moves faster; the front and rear interfaces of the plug with small viscosity ratio move faster in the microchannel than those of the plug with large viscosity ratio. The study is helpful to provide theoretical data for the design and scale-up of liquid-liquid reactors and separators.

Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model

The lattice Boltzmann method is applied to the study of immiscible two-phase flows using a Rothman–Keller-type (RK) model. The focus is on the algorithm proposed by Latva-Kokko and Rothman, which has been modified and integrated into the Reis and Phillips model, which belongs to the RK family. A key element of the RK model is the recoloring step applied at the interface of two fluids, at which the fluids are separated and sent to their own region. When convection is weak, the interface in the Reis and Phillips model suffers from “lattice pinning”, which is a problem that may prevent the interface from moving. While the recoloring algorithm proposed by Latva-Kokko and Rothman diminishes this problem, it was not used in the work of Reis and Phillips. This is the framework in which the present study has been conducted. Its scope is twofold: first, to integrate and adapt the Latva-Kokko and Rothman recoloring algorithms for reducing the lattice pinning problem found in the Reis and Phillips model; and second, to conduct a set of numerical tests to show that the combination of the two algorithms leads to an improvement in the quality of the results, along with a better convergence. The context of the work is two-dimensional, with the D2Q9 lattice used as the basic computational element.

Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model

This study presents the integration of isotropic color gradient discretization into a lattice Boltzmann Rothman–Keller (RK) model designed for two-phase flow simulation. The proposed model removes one limitation of the RK model, which concerns the handling of O(1000) large density ratios between the fluids for a wide range of parameters. Taylor’s series expansions are used to characterize the difference between an isotropic gradient discretization and the commonly used anisotropic gradient. The proposed color gradient discretization can reduce, by one order of magnitude, the spurious current problem that affects the interface between the phases. A set of numerical tests is conducted to show that a rotationally invariant discretization enables widening of the parameter range for the surface tension. Surface tensions from O(10 −2) to O(10 −8), depending on the density ratio, are accurately simulated. An extreme density ratio of O(10,000) is successfully tested for a steady bubble with an error of 0.5% for Laplace’s law across a sharp interface, with a thickness of about 5–6 lattice units.

Numerical simulation of immiscible liquid-liquid flow in microchannels using lattice Boltzmann method

Immiscible kerosene-water two-phase flows in microchannels connected by a T-junction were numerically studied by a Lattice Boltzmann (LB) method based on field mediators. The two-phase flow lattice Boltzmann model was first validated and improved by several test cases of a still droplet. The five distinct flow regimes of the kerosene-water system, previously identified in the experiments from Zhao et al., were reproduced. The quantitative and qualitative agreement between the simulations and the experimental data show the effectiveness of the numerical method. The roles of the interfacial tension and contact angle on the flow patterns and shapes of droplets were discussed and highlighted according to the numerical results based on the improved two-phase LB model. This work demonstrated that the developed LBM simulator is a viable tool to study immiscible two-phase flows in microchannels, and such a tool could provide tangible guidance for the design of various microfluidic devices that involve immiscible multi-phase flows.

Fractional step two-phase flow lattice Boltzmann model implementation

A hybrid method that combines an advanced lattice Boltzmann model with traditionalfinite difference techniques is developed. An operator splitting technique is applied toseparate the numerical scheme into two subproblems. Each subproblem is solved withdifferent techniques, namely lattice Boltzmann and finite differences. This method isapplied for the first time to a two-phase flow simulation case. Major simplifications areobtained in the lattice Boltzmann implementation. Simulations are presented to show theseimprovements and to validate the technique with kinematic viscosity down to10−4 in lattice Boltzmann units. This technique does not add instabilities, and in contrastimproves the stability behavior compared to reducing the relaxation time.