Lattice Boltzmann modeling and simulation of liquid jet breakup

Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments

We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen et al. [Phys. Rev. E 100, 023301 (2019)2470-004510.1103/PhysRevE.100.023301] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of 1000. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.

Color-gradient lattice Boltzmann model for immiscible fluids with density contrast

We present a color-gradient-based lattice Boltzmann model for immiscible fluids with a large density contrast. The model employs the velocity-based equilibrium distribution function, initially proposed for the phase-field-based model by Zu and He [Phys. Rev. E 87, 043301 (2013)1539-375510.1103/PhysRevE.87.043301], with a modification necessary to satisfy the kinematic condition at the interface. Different from the existing color-gradient models, the present model allows to specify interface mobility that is independent of the fluid density ratio. Further, we provide a unified framework, which uses the recursive representation of the lattice Boltzmann equation, to derive the governing equations of the system. The emergent color dynamics thus obtained, through an analysis of the segregation operator, is shown to obey the locally conservative Allen-Cahn equation. We use a series of benchmarks, which include a stationary drop, a layered Poiseuille flow, translation of a drop under a forced velocity field, the Rayleigh-Taylor instability, and the capillary intrusion test to demonstrate the model's ability in dealing with complex flow problems.

Simulations of surface acoustic wave interactions on a sessile droplet using a three-dimensional multiphase lattice Boltzmann model

This study reports the development of a three-dimensional numerical model for acoustic interactions with a microscale sessile droplet under surface acoustic wave (SAW) excitation using the lattice Boltzmann method (LBM). We first validate the model before SAW interactions are added. The results demonstrate good agreement with the analytical results for thermodynamic consistency, Laplace law, static contact angle on a flat surface, and droplet oscillation. We then investigate SAW interactions on the droplet, with resonant frequencies ranging 61.7-250.1 MHz. According to our findings, an increase in wave amplitude elicits an increase in streaming velocity inside the droplet, causing internal mixing, and further increase in wave amplitude leads to pumping and jetting. The boundaries of wave amplitude at various resonant frequencies are predicted for mixing, pumping, and jetting modes. The modeling predictions on the roles of forces (SAW, interfacial tension, inertia, and viscosity) on the dynamics of mixing, pumping, and jetting of a droplet are in good agreement with observations and experimental data. The model is further applied to investigate the effects of SAW substrate surface wettability, viscosity ratio, and interfacial tension on SAW actuation onto the droplet. This work demonstrates the capability of the LBM in the investigation of acoustic wave interactions between SAW and a liquid medium.

Coupled lattice Boltzmann-large eddy simulation model for three-dimensional multiphase flows at large density ratio and high Reynolds number

A coupled lattice Boltzmann-large eddy simulation model is developed for modeling three-dimensional multiphase flows at large density ratios and high Reynolds numbers. In the framework of the lattice Boltzmann method, the model is proposed based on the standard Smagorinsky subgrid-scale approach, and a reconstructed multiple-relaxation-time collision operator is adopted. The conservative Allen-Cahn equation and Navier-Stokes equations are solved through the lattice Boltzmann discretization scheme for the interface tracking and velocity field evolution, respectively. Relevant benchmark cases are carried out to validate the performance of this model in simulating multiphase flows at a large density ratio and a high Reynolds number, including a stationary droplet, the process of spinodal decomposition, the Rayleigh-Taylor instability, the phenomenon of a droplet splashing on a thin liquid film, and the liquid jet breakup process. The maximum values of density ratio and Re number are 1000 and 10 240, respectively. The capability and reliability of the proposed model have been demonstrated by the good agreement between simulation results and the analytical solutions or the previously available results.

Lattice Boltzmann Simulation of Ferrofluids Film Boiling

In the present investigation, two phase film boiling of ferrofluids under an external field delivered around a two-dimensional square cross-section heater was investigated using the lattice Boltzmann technique. The purpose of this work is to find the effect of magnetic field magnitude and direction on the Nusselt number in single and double heater geometry. The improving thermal efficiency in the horizontal and vertical placement of heaters is also presented. The governing equations of mass conservation, momentum conservation, and energy conservation are solved by using a central-moments-based Lattice Boltzmann scheme. The air pocket generated around heater raised incorporating magnetic effects. The heat transfer through this advancement has been explored quantitatively and abstractly. The results shows that with the development in the volumetric applied force at the bubble-fluid interface, the bubble boundary layer thickness around the square heater lessened which cause the Nusselt number augmented. Through the parameter study it found that the Nusselt number can be essentially extended by altering the course of magnet shafts, and that film rising outwardly of the bubble. The improvement and advancement of vapour phase in various heater arrangement made two column of bubble rises at the same time, which rose above each heater and in the end changed into one column of bubble. A correlation considering magnitude and angle of the magnetic field on time-averaged Nusselt number is presented. Finally, the Nusselt number can be controlled with the help of the incorporation of other heaters.

Advances in Computational Fluid Mechanics in Cellular Flow Manipulation: A Review

Recently, remarkable developments have taken place, leading to significant improvements in microfluidic methods to capture subtle biological effects down to single cells. As microfluidic devices are getting sophisticated, design optimization through experimentations is becoming more challenging. As a result, numerical simulations have contributed to this trend by offering a better understanding of cellular microenvironments hydrodynamics and optimizing the functionality of the current/emerging designs. The need for new marketable designs with advantageous hydrodynamics invokes easier access to efficient as well as time-conservative numerical simulations to provide screening over cellular microenvironments, and to emulate physiological conditions with high accuracy. Therefore, an excerpt overview on how each numerical methodology and associated handling software works, and how they differ in handling underlying hydrodynamic of lab-on-chip microfluidic is crucial. These numerical means rely on molecular and continuum levels of numerical simulations. The current review aims to serve as a guideline for researchers in this area by presenting a comprehensive characterization of various relevant simulation techniques.

Improved three-dimensional color-gradient lattice Boltzmann model for immiscible two-phase flows

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible two-phase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulations are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic two-phase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.

Pore-scale characteristics of multiphase flow in heterogeneous porous media using the lattice Boltzmann method

This study provides a pore-scale investigation of two-phase flow dynamics during primary drainage in a realistic heterogeneous rock sample. Using the lattice Boltzmann (LB) method, a series of three-dimensional (3D) immiscible displacement simulations are conducted and three typical flow patterns are identified and mapped on the capillary number (Ca)-viscosity ratio(M) phase diagram. We then investigate the effect of the viscosity ratio and capillary number on fluid saturation patterns and displacement stability in Tuscaloosa sandstone, which is taken from the Cranfield site. The dependence of the evolution of saturation, location of the displacement front, 3D displacement patterns and length of the center of mass of the invading fluid on the viscosity ratio and capillary number have been delineated. To gain a quantitative insight into the characteristics of the invasion morphology in 3D porous media, the fractal dimension D_f of the non-wetting phase displacement patterns during drainage has been computed for various viscosity ratios and capillary numbers. The logarithmic dependence of D_f on invading phase saturation appears to be the same for various capillary numbers and viscosity ratios and follows a universal relation.

Color-gradient lattice Boltzmann model with nonorthogonal central moments: Hydrodynamic melt-jet breakup simulations

We develop a lattice Boltzmann (LB) model for immiscible two-phase flow simulations with central moments (CMs). This successfully combines a three-dimensional nonorthogonal CM-based LB scheme [De Rosis, Phys. Rev. E 95, 013310 (2017)2470-004510.1103/PhysRevE.95.013310] with our previous color-gradient LB model [Saito, Abe, and Koyama, Phys. Rev. E 96, 013317 (2017)2470-004510.1103/PhysRevE.96.013317]. Hydrodynamic melt-jet breakup simulations show that the proposed model is significantly more stable, even for flow with extremely high Reynolds numbers, up to O(10^{6}). This enables us to investigate the phenomena expected under actual reactor conditions.