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Understanding the behavior of multiple cavitation bubbles and their interactions is important for developing deeper insight into cavitation phenomena. Using a revised single-component multiphase Lattice Boltzmann method, the weak and strong interactions between two neighboring cavitation bubbles and the mutual interaction among a cluster of cavitation bubbles are simulated. The simulated bubble evolutions have satisfying agreement with previous experimental results. Details of the multiple bubble interactions (the pressure and velocity fields) are presented. In the case of two-bubble interactions, typical phenomena such as bubble toroidal deformation, micro-jets, the thinning of the liquid film, and bubble coalescence are successfully reproduced. The bubble radius changes under two-bubble weak interaction are adequately described by a revised 2-D Rayleigh-Plesset equation. The transition from the strong to weak interactions with increasing initial distance between the two bubbles is analyzed. The behaviors of a cluster of bubbles are also simulated, where the shield effect of outer layer bubbles and the micro-jets are accurately captured. The present multiphase Lattice Boltzmann method is a promising tool to investigate complex cavitation problems.

We develop a semi-analytical model to calculate the entry pressure in rough capillaries based on an energy balance principle and wetting theory on rough surfaces. During the drainage process, we assume fluids form arc menisci at corners of capillary cross-sections depending on the apparent angle, and that there is a wetting phase film adsorbed on the rough surface depending on the wetting condition. A Logistic model is proposed to explain the contact angle dependence on the structure of rough surfaces. Then the capillary entry pressure is calculated by extended MS-P (Mayer, Stowe and Princen) method. We verify the model using the pseudopotential Lattice Boltzmann model and obtain good agreement between the analytical and simulated pressures. Taking capillaries with triangular sections with pillar pillar-type rough surfaces as example, we discuss how rough structures and contact angles influence capillary behaviors. The results reveal that both the wetting phase saturation and entry pressure of rough capillaries are larger than those in smooth capillaries under the same conditions. Moreover, the entry pressure is not sensitive to the roughness factor under strong wetting conditions and is much more sensitive to the pillar asperity height than the other structure parameters.

In contrast to typical applications of the pseudopotential Lattice Boltzmann model to two components, quantitative validations and applications for three-component Shan-Chen model are performed here. First, the qualitative and quantitative validations for the following three cases were performed, i.e., three-phase separation, meniscus-induced bubble movement, and the three-phase layered flow. A scheme to control the simulated contact angle of droplets on the interface is provided for the three fluid phase Lattice Boltzmann model. The effects of droplet shape, the strength of gravity, droplet size, and meniscus curvature for the spontaneous motion of droplets and bubbles are investigated in detail. It is found that without gravity, droplets tend to move to the wall on a concave upwards meniscus when they have a big “head” and a small “belly”. Gravity may enhance rather than inhibit the motion towards the wall when the density of the droplet or bubble is relatively small. Finally, smaller droplet size and larger meniscus curvatures enhance the spontaneous movement towards a wall. The conclusions are relevant to practical applications such as water treatment, oil spill remediation, and droplet-based microfluidics.

This article describes the simulation of three-dimensional buoyancy-driven bubble rise using a phase-field-based incompressible Lattice Boltzmann model. The effect of the Cahn–Hilliard mobility parameter, which is the rate of diffusion relaxation from non-equilibrium toward equilibrium state of chemical potential, is evaluated in detail. In contrast with previous work that pursues a high density ratio of binary fluids in the hydrodynamic equation, we apply a large dynamic viscosity ratio, together with a matched density pair and a separate compensating gas phase buoyant force, and the numerical results fit previous experimental results well. Through analysis, it is noted that for cases with moderate Reynolds number, a large value of mobility keeps a relatively sharp interface, while smaller values of mobility would result in diffusive interfacial regions. Moreover, for cases with large Reynolds number, small bubbles at the tail tend to separate more easily when the value of mobility is larger. This article offers some potentially useful details for performing phase-field-based simulations.

Using a hybrid thermal Lattice Boltzmann method, the dynamics of laser-produced single cavitation bubbles in bulk liquid and the bubble collapse process near a solid boundary are numerically investigated. The simulated bubble evolutions satisfyingly agree with the theoretical calculations and the previous experimental results. The simulated bubble radius changes in bulk liquid are in good accordance with the calculations of a revised 2-D Rayleigh–Plesset equation that incorporates an extra thermal effect term. The maximum bubble radius is linearly proportional to the bubble collapse time and the input laser energy, which is consistent with the experimental data and bubble dynamics theory. Processes of a single cavitation bubble collapse at various distances from a solid boundary are analyzed in detail. The velocity vectors, density, pressure, and temperature fields are presented. The retarding effect of a solid boundary is successfully reproduced in the LBM simulations and leads to bubble elongation, the formation of micro-jet, bubble toroidal deformation, and the attraction of the bubble to the boundary during the collapse phase. The attraction effect, maximum jet velocity, and maximum pressure at the solid boundary all increase with reduced non-dimensional distance. A critical non-dimensional distance of 2.2 is validated by both the simulation and experiment. The hybrid thermal Lattice Boltzmann method is a reliable tool to investigate non-isothermal cavitation bubble dynamics.

The primary and key task of binary fluid flow modeling is to track the interface with good accuracy, which is usually challenging due to the sharp-interface limit and numerical dispersion. This article concentrates on further development of the conservative Allen-Cahn equation (ACE) [Geier et al., Phys. Rev. E 91, 063309 (2015)10.1103/PhysRevE.91.063309] under the framework of the lattice Boltzmann method (LBM), with incorporation of the incompressible hydrodynamic equations [Liang et al., Phys. Rev. E 89, 053320 (2014)10.1103/PhysRevE.89.053320]. Utilizing a modified equilibrium distribution function and an additional source term, this model is capable of correctly recovering the conservative ACE through the Chapman-Enskog analysis. We also simulate four phase-tracking benchmark cases, including one three-dimensional case; all show good accuracy as well as low numerical dispersion. By coupling the incompressible hydrodynamic equations, we also simulate layered Poiseuille flow and the Rayleigh-Taylor instability, illustrating satisfying performance in dealing with complex flow problems, e.g., high viscosity ratio, high density ratio, and high Reynolds number situations. The present work provides a reliable and efficient solution for binary flow modeling.

SEAWAT is a finite-difference computer code designed to simulate coupled variable-density ground water flow and solute transport. This paper describes a new version of SEAWAT that adds the ability to simultaneously model energy and solute transport. This is necessary for simulating the transport of heat and salinity in coastal aquifers for example. This work extends the equation of state for fluid density to vary as a function of temperature and/or solute concentration. The program has also been modified to represent the effects of variable fluid viscosity as a function of temperature and/or concentration. The viscosity mechanism is verified against an analytical solution, and a test of temperature-dependent viscosity is provided. Finally, the classic Henry-Hilleke problem is solved with the new code.

Application of the lattice Boltzmann method (LBM) to invasion percolation of single component multiphase fluids in porous media offers an opportunity for more realistic modeling of the configurations and dynamics of liquid/vapor and liquid/solid interfaces. The complex geometry of connected paths in standard invasion percolation models arises solely from the spatial arrangement of simple elements on a lattice. In reality, fluid interfaces and connectivity in porous media are naturally controlled by the details of the pore geometry, its dynamic interaction with the fluid, and the ambient fluid potential. The multiphase LBM approach admits realistic pore geometry derived from imaging techniques and incorporation of realistic hydrodynamics into invasion percolation models.

Lattice Boltzmann method (LBM) and direct simulation Monte Carlo (DSMC) method are used for analysis of moderate Knudsen number phenomena. Simulation results are presented for pressure-driven isothermal rarefied channel flow at various pressure ratios. Analytical equations for non-linear pressure distribution and velocity profiles along the channel axis are used to verify the present LBM and DSMC results. We conclude that the LBM method can be used as an alternative model to DSMC simulations.Copyright © 2009 by ASME

Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law-based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions.

We propose a method for approximating the adhesion parameters in the Shan and Chen multicomponent, multiphase lattice Boltzmann model that leads to the desired fluid-solid contact angle. The method is a straightforward application of Young's equation with substitution of the Shan and Chen cohesion parameter and a density factor for the fluid-fluid interfacial tension, and the adhesion parameters for the corresponding fluid-solid interfacial tensions.

This study describes the behavior of bubbles rising under gravity using the Shan and Chen-type multicomponent multiphase lattice Boltzmann method (LBM) [X. Shan and H. Chen, Phys. Rev. E47, 1815 (1993)]. Two-dimensional (2D) single bubble motions were simulated, considering the buoyancy effect for which the topology of the bubble was characterized by the nondimensional Eötvös (Eo), and Morton (M) numbers. In this study, a new approach based on the "effective buoyancy" was adopted and proven to be consistent with the expected bubble shape deformation. This approach expands the range of effective density differences between the bubble and the liquid that can be simulated. Based on the balance of forces acting on the bubble, it can deform from spherical to ellipsoidal shape with skirts appearing at high Eo number. A benchmark computational case for qualitative and quantitative validation was performed using COMSOL Multiphysics based on the level set method. Simulations were conducted for 1 ≤ Eo ≤ 100 and 3 × 10-6≤ M ≤ 2.73 × 10-3. Interfacial tension was checked through simulations without gravity, where Laplace's law was satisfied. Finally, quantitative analyses based on the terminal rise velocity and the degree of circularity was performed for various Eo and M values. Our results were compared with both the theoretical shape regimes given in literature and available simulation results.

The Shan and Chen single component multiphase lattice Boltzmann model is used to simulate homogeneous and heterogeneous cavitation. The simulations show excellent agreement with the equation of state for homogeneous cavitation and with energy considerations based on interface formation and bubble expansion for heterogeneous cavitation.

[1] The lattice Boltzmann method (LBM) has emerged as a powerful tool for simulating the behavior of multiphase fluid systems in complex pore networks. Specifically, the single component multiphase LBM can simulate the interfacial phenomena of surface tension and adsorption and thus be used for modeling fluids such as water and its vapor in porous media. This paper provides an introduction to LBM applications to interface configurations in partially saturated porous media. Key elements of this LBM application are fluid-fluid and fluid-solid interactions that successfully mimic the Young-Laplace equation and liquid film adsorption. LBM simulations of liquid behavior in simple pore geometry considering capillarity and adsorption are in good agreement with analytical solutions and serve as critical first steps toward validating this approach. We demonstrate the usefulness of LBM in constructing virtual liquid retention measurements based on porous media imagery. Results of this study provide a basis for application of LBM to understanding liquid configurations in more complex geometries and clear a path for applications involving interface migration, flow, and transport in partially saturated porous media.

Originally, the color-gradient model proposed by Rothman and Keller (R–K) was unable to simulate immiscible two-phase flows with different densities. Later, a revised version of the R–K model was proposed by Grunau et al. [D. Grunau, S. Chen and K. Eggert, Phys. Fluids A: Fluid Dyn. 5, 2557 (1993).] and claimed it was able to simulate two-phase flows with high-density contrast. Some studies investigate high-density contrast two-phase flows using this revised R–K model but they are mainly focused on the stationary spherical droplet and bubble cases. Through theoretical analysis of the model, we found that in the recovered Navier–Stokes (N–S) equations which are derived from the R–K model, there are unwanted extra terms. These terms disappear for simulations of two-phase flows with identical densities, so the correct N–S equations are fully recovered. Hence, the R–K model is able to give accurate results for flows with identical densities. However, the unwanted terms may affect the accuracy of simulations significantly when the densities of the two fluids are different. For the simulations of spherical bubbles and droplets immersed in another fluid (where the densities of the two fluids are different), the extra terms may not be important and hence, in terms of surface tension, accurate results can be obtained. However, generally speaking, the unwanted term may be significant in many flows and the R–K model is unable to obtain the correct results due to the effect of the extra terms. Through numerical simulations of parallel two-phase flows in a channel, we confirm that the R–K model is not appropriate for general two-phase flows with different densities. A scheme to eliminate the unwanted terms is also proposed and the scheme works well for cases of density ratios less than 10.

Numerous lattice Boltzmann (LB) methods have been proposed for solution of the convection?diffusion equations (CDE). For the 2D problem, D2Q9, D2Q5 or D2Q4 velocity models are usually used. When LB convection?diffusion models are used to solve a CDE coupled with Navier?Stokes equations, boundary conditions are found to be critically important for accurately solving the coupled simulations. Following the idea of a regularized scheme (Latt et al 2008 Phys.?Rev.?E 77 056703), a regularized boundary condition for solving a CDE is proposed. A simple extrapolation scheme is also proposed for the Neumann boundary condition. Spatial accuracies of three existing and the proposed boundary conditions are discussed in details. The numerical evaluations are based on simulations of steady and unsteady natural convection flows in a cavity and an unsteady Taylor?Couette flow. Our studies show that the simplest D2Q4 model with terms of O(u) in the equilibrium distribution function is capable of obtaining results of equal accuracy as D2Q5 or D2Q9 models for the CDE. A slightly revised LB equation for solving a CDE that is used to cancel some unwanted terms does not seem to be necessary for incompressible flows. The regularized boundary condition for solving the CDE has second-order spatial accuracy and it is the best one in terms of the spatial accuracy. The regularized scheme and non-equilibrium extrapolation scheme are applicable to handle both the Dirichlet and Neumann boundary conditions. For the Neumann boundary condition with zero flux, all the five boundary conditions are applicable to give accurate results and the bounce-back scheme is the simplest one.