Phase-field Lattice Boltzmann Research Articles

Dynamics of droplet adsorption by liquid film on a grooved surface

Abstract Understanding the dynamics of droplet adsorption by liquid film on a grooved surface is of great significance for the possible manipulation of dropwise condensation on the grooved surface. In this study, an improved phase-field lattice Boltzmann model is proposed to describe the process of droplet adsorption from the ridge to the liquid film within the channel. The results indicate that the leading edge of the droplet undergoes two accelerations during the adsorption process, obeying the power law of l/R = t^2.2 and l/R = t^0.9, respectively. The adsorption process between droplets with different sizes and the liquid film exhibits self-similarity characteristics including the same first peak velocity, the similar droplet displacement-time curve and the equal dimensionless spreading length of l/R=5.5. Decreasing the contact angle of the droplet from θe = 120° to θe = 60° accelerates the displacement of the leading edge and extends the spreading length. These findings may help reveal the mechanics of droplet adsorption by the liquid film on the grooved surface and thus manipulate the condensation behavior for the heat transfer enhancement.

Alternative wetting boundary condition for binary fluids based on phase-field lattice Boltzmann method

Alternative wetting boundary condition for binary fluids based on phase-field lattice Boltzmann method

Examining a Conservative Phase-Field Lattice Boltzmann Model for Two-Phase Flows

In this study, a conservative phase-field lattice Boltzmann model is examined for simulating immiscible two-phase flows with large density and viscosity ratios. This model is built upon the Allen–Cahn equation, incorporating a filtered collision operator and high-order corrections in the equilibrium distribution functions. The numerical model is also integrated with the volumetric boundary scheme and the immersed boundary method to achieve various stationary and moving boundary conditions on arbitrary geometries for different application scenarios. A comprehensive evaluation of this phase-field solver is conducted through a range of academic and industrial cases. First, droplet splashing cases at different Reynolds numbers are studied. The phase-field LB model effectively captures the surface wave motion and splashing of the droplet, although some smearing of small structures is observed due to the diffused interface property of the numerical model. Second, a tuned liquid damper is simulated, accurately capturing sloshing forces on solid walls. In the simulation of a dam-breaking case, predicted gauge pressure and free-surface elevation time histories compare well with experimental data. Lastly, a gearbox case under dip lubrication is simulated, with both the gearbox churning loss and oil distribution being well predicted across a range of rotating speeds. The validation studies demonstrate the effectiveness of the present phase-field lattice Boltzmann model in simulating immiscible two-phase flows with large and realistic density and viscosity ratios. The strengths, limitations, and weaknesses of the conservative phase-field LB model are discussed, and suggestions for the development and application of this numerical model are provided.

A numerical model for solitary wave breaking based on the phase-field lattice Boltzmann method

This study presents a numerical investigation of a solitary wave breaking over a slope by using the phase-field lattice Boltzmann method. The incompressible two-phase flow equations are solved by using a velocity-based formulation of the two-phase lattice Boltzmann method with a central-moment collision model to accurately simulate wave breaking problems. For interface capture, a phase-field lattice Boltzmann method that ensures mass conservation is employed. The validity of the proposed method is confirmed through solitary wave propagation and transformation problems, and the obtained results are in good agreement with the experimental and calculated results. The proposed method is then employed to analyze wave breaking on a slope, demonstrating strong concordance with experimental data and existing computational findings. By analyzing the instantaneous flow characteristics and the temporal evolution of the variation in kinetic, potential, and total energy from deep to shallow water, the model can reveal the macroscopic characteristics of solitary wave breaking. Because the phase-field model effectively simulates wave breaking and air entrainment, it can depict wave energy dissipation more accurately than the single-phase lattice Boltzmann method with free surface tracking.

A novel phase-field lattice Boltzmann framework for diffusion-driven multiphase evaporation

Heat transfer and phase change phenomena, particularly diffusion-driven droplet evaporation, play pivotal roles in various industrial applications and natural processes. Despite advancements in computational fluid dynamics, modeling multiphase flows with large density ratios remains challenging. In this study, we developed a robust and stable conservative Allen–Cahn-based phase-field lattice Boltzmann method to solve the flow field equations. This method is coupled with the finite difference discretization of vapor species transport equation and the energy equation. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius–Clapeyron correlation. Our approach is capable of simulations under real physical conditions and is compatible with graphics processing unit architecture, making it ideal for large-scale industrial simulations. Three validation test cases are conducted to demonstrate the consistency of the presented model, including simulations of Stefan flow, the evaporation of suspended droplets containing water, acetone, and ethanol in the air, and the evaporation of a water sessile droplet on a flat surface. The results show that the model is able to predict the behavior and characteristics of each case accurately. Notably, our numerical results exhibit a maximum relative error of approximately 1% in simulations of Stefan flow. In the case of suspended droplet evaporation, the observed maximum difference between the calculated wet bulb temperatures and those derived from psychrometric charts is approximately 0.9 K. Moreover, our analysis of the sessile droplet reveals a good agreement between the results obtained by our model for the evaporative mass flux and those obtained from the existing models in the literature for different contact angles.

Lattice Boltzmann simulation of plunging breakers

ABSTRACT In the present work, the conservative phase-field lattice Boltzmann model is applied to simulate plunging breakers in shallow waters. The solver is computationally efficient as it is explicit in time stepping and does not require a solution for the pressure Poisson equation. Nevertheless, the solver can simultaneously handle a large Reynolds number ( = 10 4 ) and a high-density ratio of 1000. Simulations are performed by varying initial steepness and dispersion parameters, which influence the nonlinearity degree of wave (or the growth speed of instability) and the oscillatory motion (limited by the bottom) on the breaking characteristics. Detailed analyses of kinematics, air entrainment, vorticity, and energy dissipation are presented.

Lattice Boltzmann simulation of breaking waves

Water wave breaking at the ocean’s surface is a turbulent phenomenon and encompasses a wide range of physical processes such as generation of bubbles/drops with different spatio-temporal scales. In the present study, breaking of periodic waves in deep water regime has been simulated using phase-field lattice Boltzmann method (LBM). Compared to direct Navier–Stokes equation based numerical models, the present LB model is Poisson-free and explicit in time integration. Both the flow field and interface are solved using LBM with two sets of distribution functions. The normalized pressure-velocity formulation is used for the flow field, whereas the conservative Allen–Cahn equation is used to capture the interface. An impulsively started wave approach with Stokes third order wave profile has been used to initiate the breaking process. Through systematic variation of Weber number and initial steepness, the effect of surface tension on the kinematic, geometric, and energy dissipation characteristics has been studied for three breaker types, viz., spilling, weak plunging, and plunging breakers. The results are in good agreement with the past experimental observations and direct numerical simulation. In particular, the obtained breaking strength for different Weber numbers agrees well with the semi-empirical relation used in a wind-wave forecasting models.

Long-distance settling simulation of equiaxed dendrite by a moving-frame algorithm: phase-field lattice Boltzmann study with parallel-GPU AMR

In large-ingot castings, the settling of equiaxed dendrites often results in distinct cone-shaped negative segregation in the lower region of the ingot. To accurately predict and control such macrosegregation, it is important to understand the kinetic behavior of equiaxed dendrites in the melt. The phase-field lattice Boltzmann (PF-LB) model is powerful for simulating dendrite growth with melt convection and solid motion. However, it is computationally expensive and represents only the short-distance motion of dendrites in three-dimensional (3D) simulations. For an efficient 3D evaluation of the effect of dendrite motion and rotation on growth behavior, we introduce the moving frame algorithm to PF-LB simulations. Here, the computational domain tracks the settling dendrite to express long-distance settling without restricting the domain size. The PF-LB simulations were accelerated by parallel computing using a combination of multiple GPUs and adaptive mesh refinement (AMR), also referred to as parallel GPU-AMR. The moving-frame algorithm was modified to adapt to AMR. From the simulation results, we demonstrate that the proposed method helps evaluate the effect of dendrite rotation on the settling and growth velocities of equiaxed dendrites in 3D.

Droplet dynamics passing through the flexible constriction in the channel

We conducted a numerical investigation into droplet dynamics within a flexible constriction using the phase-field lattice Boltzmann method. Our study focused on constriction bending stiffness, Weber number, and constriction-to-droplet diameter ratio. Flexibility impedes droplet passage at low Weber numbers but significantly facilitates it at moderate and high Weber numbers. Passage times decrease with increasing Weber numbers and are proportional to the droplet's maximum deformed length. An anomalous phenomenon is observed: “more haste, less speed.” The underlying mechanics arising from the interaction between the flexible constriction and the droplet are elucidated. The findings enhanced our understanding of droplet behavior in constrained environments.

Implementation of contact line motion based on the phase-field lattice Boltzmann method.

This paper proposes a strategy to implement the free-energy-based wetting boundary condition within the phase-field lattice Boltzmann method. The greatest advantage of the proposed method is that the implementation of contact line motion can be significantly simplified while still maintaining good accuracy. For this purpose, the liquid-solid free energy is treated as a part of the chemical potential instead of the boundary condition, thus avoiding complicated interpolations with irregular geometries. Several numerical testing cases, including droplet spreading processes on the idea flat, inclined, and curved boundaries, are conducted, and the results demonstrate that the proposed method has good ability and satisfactory accuracy to simulate contact line motions.

Modeling coupled growth and motion of solid-air dendrite induced by convection in liquid hydrogen using phase-field lattice Boltzmann method

The safety hazard arising from the growth, condensation and accumulation of trace air in liquid hydrogen deserves attention. In order to predict the microstructural growth evolution and oxygen solute segregation distribution characteristics during solid-air dendrite motion induced by solution convection, a partially saturated bounce-back lattice Boltzmann coupled non-isothermal phase field method (PSLBM-PF) is proposed in this study. The partially saturated bounce-back lattice Boltzmann method (PSLBM) is employed to calculate the flow field and the forces and moments between the fluid and solid phases, and the phase field method (PF) is utilized for the computation of the growth of solid-air dendrites and the distribution of solute segregation. The motion of solid-air dendrites is determined by the momentum equation. The accuracy of the calculated interaction forces between fluid and solid phases was validated through the sedimentation process of circular particles in the liquid, and the capability of the present model to preserve the shape during solid-air dendrite motion (translational and rotational) was confirmed. Subsequently, this model was employed to investigate the growth and sedimentation motion of solid-air dendrites with different growth orientations in the solution. During dendrite settlement, the growth of the lower dendrite arms is promoted, while the settlement velocity and the solid phase fraction are almost unaffected by the growth orientation. Then, the differences in morphology evolution and solute distribution under conditions of forced convection for both stationary and motion are comparatively investigated, utilizing the free growth of solid-air dendrites under convection-free conditions as a reference. Finally, the model was utilized to study the growth of individual solid-air dendrites as well as translational and rotational motion under the action of shear flow. The presence of convection significantly alters the solute and temperature distributions at the solid-liquid interface, thereby influencing the dendrite growth process. The simulation results indicate that this model can predict the solid-air dendrites microstructural growth evolution and oxygen solute segregation distribution accompanying the convection and motion.

Computational study of a thin film flow over a topographical feature using phase-field lattice Boltzmann method

The study employs the phase-field lattice Boltzmann method (PFLBM) to explore the dynamics of a thin film flowing over a topographical feature such as a mound or a trench. The mesoscopic nature of PFLBM makes it a suitable technique for problems involving tracking the evolution of a liquid–air interface. PFLBM simulation results are validated with experimental and analytical results confirming the viability of the numerical approach for such problems. The effect of changing the topographical height, aspect ratio, viscosity ratio, and presence of multiple mounds on the film profiles are systematically analyzed. It is observed that a steady-state solution could not be obtained for large height topographical features. The transition from a steady-state interfacial pattern to an unsteady-steady state is found to depend on the width of the topography. Geometry-based condition is employed to deal with the contact points present in the film dynamics beyond rupture. For large contact angles, the unsteady cases result in film rupture and form a continuous array of droplets of equivalent dimensions at a periodic interval. Increasing the aspect ratio reduces the width of the capillary ridge formed above the topographical feature, while the viscosity ratio reduces the maximum height of the ridge. The shapes of the capillary ridges formed over multiple mounds in the flow direction are independent if the separation between the successive mounds is beyond a critical value. This critical value strongly depends on the capillary number and is independent of the dimensions of the mound.

Wetting and Spreading Behavior of Axisymmetric Compound Droplets on Curved Solid Walls Using Conservative Phase Field Lattice Boltzmann Method.

Compound droplets have received increasing attention due to their applications in many several areas, including medicine and materials. Previous works mostly focused on compound droplets on planar surfaces and, as such, the effects of curved walls have not been studied thoroughly. In this paper, the influence of the properties of curved solid wall (including the shape, curvature, and contact angle) on the wetting behavior of compound droplets is explored. The axisymmetric lattice Boltzmann method, based on the conservative phase field formulation for ternary fluids, was used to numerically study the wetting and spreading of a compound droplet of the Janus type on various curved solid walls at large density ratios, focusing on whether the separation of compound droplets occurs. Several types of wall geometries were considered, including a planar wall, a concave wall with constant curvature, and a convex wall with fixed or variable curvature (specifically, a prolate or oblate spheroid). The effects of surface wettability, interfacial angles, and the density ratio (of droplet to ambient fluid) on the wetting process were also explored. In general, it was found that, under otherwise identical conditions, droplet separation tends to happen more likely on more hydrophilic walls, under larger interfacial angles (measured inside the droplet), and at larger density ratios. On convex walls, a larger radius of curvature of the surface near the droplet was found to be helpful to split the Janus droplet. On concave walls, as the radius of curvature increases from a small value, the possibility to observe droplet separation first increases and then decreases. Several phase diagrams on whether droplet separation occurs during the spreading process were produced for different kinds of walls to illustrate the influences of various factors.

Phase-field lattice Boltzmann model with singular mobility for quasi-incompressible two-phase flows.

In this paper, a lattice Boltzmann for quasi-incompressible two-phase flows is proposed based on the Cahn-Hilliard phase-field theory, which can be viewed as an improved model of a previous one [Yang and Guo, Phys. Rev. E 93, 043303 (2016)2470-004510.1103/PhysRevE.93.043303]. The model is composed of two LBE's, one for the Cahn-Hilliard equation(CHE) with a singular mobility, and the other for the quasi-incompressible Navier-Stokes equations(qINSE). Particularly, the LBE for the CHE uses an equilibrium distribution function containing a free parameter associated with the gradient of chemical potential, such that the variable (and even zero) mobility can be handled. In addition, the LBE for the qINSE uses an equilibrium distribution function containing another free parameter associated with the local shear rate, such that the large viscosity ratio problems can be handled. Several tests are first carried out to test the capability of the proposed LBE for the CHE in capturing phase interface, and the results demonstrate that the proposed model outperforms the original LBE model in terms of accuracy and stability. Furthermore, by coupling the hydrodynamic equations, the tests of double-stationary droplets and droplets falling problems indicate that the proposed model can reduce numerical dissipation and produce physically acceptable results at large time scales. The results of droplets falling and phase separation of binary fluid problems show that the present model can handle two-phase flows with large viscosity ratio up to the magnitude of 10^{4}.

A second-order phase field-lattice Boltzmann model with equation of state inputting for two-phase flow containing soluble surfactants

In this paper, we propose a phase field-lattice Boltzmann (LB) model with an equation of state (EOS) inputting for two-phase flow containing soluble surfactants. In this model, both the order parameter for the phase field and the surfactant concentration are described by second-order partial differential equations, along with Navier–Stokes equations for the flow field. Changes in surfactant concentration do not affect the order parameter distribution; hence, an unwanted sharpening effect cannot arise. Most importantly, in the existing models, the EOS of surface tension is determined by posterior simulation tests instead of being directly set as an input parameter before the simulations. Hence, it is difficult to determine the model parameters in practical applications. To address this issue, we systematically develop a fully analytical EOS for surface tension based on the Gibbs–Duhem equation. Subsequently, an approximate explicit form for EOS is provided by utilizing the Jacobi–Gauss quadrature rule. Furthermore, a multiple-relaxation-time LB scheme is utilized to numerically solve the governing equations of three physical fields. Two benchmark examples are simulated to validate the accuracy of the present model. The consistency between the numerical results and the analytical EOS is verified. Moreover, the dynamics of droplets with surfactant in simple shear flow is investigated, unveiling the profound impact of various factors, such as surfactant bulk concentration, capillary number, and viscosity ratio, on single droplet deformation and two equal-sized droplets interaction. A detailed exploration of the fluid mechanism involved in two-phase flow with soluble surfactants is presented.

Two-phase flow dynamics study in the trapezoidal gas channel of PEM fuel cell based on lattice Boltzmann model

ABSTRACT Water management is a critical challenge in ensuring the performance and durability of low-temperature proton exchange membrane fuel cells (PEMFCs). This study utilizes the phase-field lattice Boltzmann method to conduct three-dimensional numerical simulations, investigating the dynamics of two-phase flow in the cathode gas channel (GC) of PEMFC with a trapezoidal cross-section. The effects of the water inlet location, the surface wettability of GC, the open angle of GC, and the air velocity on liquid water distribution and discharge are analyzed. The results indicate that positioning the water inlet in the middle of the GC significantly enhances PEMFC performance while having minimal impact on average pressure drop. A wall contact angle of 70° or 110°Can optimize fuel cell performance from different directions. Setting a wall contact angle at 70° optimizes gas flow stability and maintains a low-pressure drop value for the GC. A wall contact angle of 110° focuses on optimizing gas reactant diffusion ability into porous electrodes and GC drainage rate. An opening angle of 55° for the trapezoidal gas channel improves overall fuel cell performance. Increasing air velocity facilitates the film flow formation of liquid water on top wall surfaces within the GC.

Dynamic behaviors and heat transfer characteristics of impacting droplets on heated superhydrophobic surfaces with randomly distributed rough structures: Numerical simulation and theoretical analysis

Due to the extensive usage of superhydrophobic surfaces, numerous studies have investigated the dynamics and heat transfer of a droplet impacting on superhydrophobic surfaces. However, previous studies did not consider the actual superhydrophobic surfaces with randomly distributed rough structures, especially so in heat transfer of droplet impacting on superhydrophobic surfaces with random rough structures. To address this issue, a multiple distribution function phase-field lattice Boltzmann model was developed to model the droplet impacting on randomly rough surfaces. After experimental validation, this model was used in the analysis of the impacting dynamics and heat transfer characteristics. The differences between actual randomly rough surface and ideal smooth surface were revealed. Herein, random rough structures significantly influence the wetting state and heat transfer of impacting droplet on solid surface. Moreover, the effects of roughness on droplet bouncing ability and the total transferred heat were evaluated. The results show that the random rough surface with smaller skewness, a kurtosis of 3.0, and a standard deviation of 0.3 μm could simultaneously promote impacting droplet to rebound from the surface and to reduce the total transferred heat. Subsequently, the predictive correlation for total transferred heat was proposed based on the roughness parameters. This work provides novel insights into the design of rough structures on functional superhydrophobic surfaces.

Numerical simulation of factors in charge of dendrite growth in zinc-nickel single flow batteries

There is a potential danger of battery internal short-circuiting and shortened life span in zinc-nickel single flow batteries which is usually caused by the formation of dendritic crystals as a result of non-uniform electrodeposition. For the purpose of restraining dendrite growth and prolonging the battery service life, it is necessary to investigate the mechanism of dendrite growth that occurs on the surface of zinc anode. Here, a model for two-dimensional zinc dendrite growth is established by the phase field-lattice Boltzmann method (PF-LBM) to simulate how the morphology of zinc dendrites evolves as well as the corresponding distribution of the concentration field, potential field and flow field, and to analyze the influences of the applied voltage, electrolyte flow rate, anisotropy strength and exchange current density on dendrite growth. As the results show, higher exchange current density and applied voltage can promote dendrite growth. By choosing a suitable anisotropic strength, it is possible to change the morphology of the dendrites and decrease the formation of dendrites. Enlarging the electrolyte flow rate may make the distribution of ion concentration more uniform, which can inhibit the dendrite growth as well as affect the morphology of dendrites.

Bouncing modes and heat transfer of impacting droplets on textured superhydrophobic surfaces

Superhydrophobic modifications could effectively minimize heat exchange at the interfaces of impacting droplets and solid surfaces. Previous studies have lacked numerical explorations regarding the effect of bouncing modes on the heat transfer characteristics during droplets impacting on textured superhydrophobic surfaces with micro-pillars. To address this issue, a multiple distribution function phase-field lattice Boltzmann model is developed to numerically study dynamic behaviors and heat transfer during droplet impact. Comparisons between the simulations and previous experimental results validate the computation model. Subsequently, the dynamic behaviors of impacting droplets and the effects on the heat transfer were studied using the proposed model. The effects of the textured surface structural parameters on the dynamics and heat transfer are discussed in detail. The numerical results indicate four possible bouncing modes of the impacting droplets: Cassie bouncing, partially penetrated bouncing, pancake bouncing and Wenzel bouncing. These modes depend on the surface energy stored in the penetrating droplet in the microstructures cavities of the surface. Moreover, the synergistic effects of contact time and contact area affect the heat transfer performance. Further, the developed theoretical model to predict the total transferred heat is based on the identified droplet dynamics. Finally, the effects of roughness parameters on total transferred heat are studied, and the design principles of textured superhydrophobic surfaces for heat transfer suppression are given for two application scenarios. The results demonstrate that the control of microstructures would be crucial for the dynamics and heat transfer of impacting droplets on textured superhydrophobic surfaces.

A regularized lattice Boltzmann model with filter for multiphase flow with diffusion-dominated mass transfer considering two-film theory

Complex flow, considering the interfacial mass transfer with the two-film theory, is always encountered in critical industrial processes. The phase-field lattice Boltzmann method (PFLBM) coupling with the revised Fick's law mass transfer convection–diffusion equation (CDE) is a practical approach to predict the bulk concentration distribution in two-phase flows. However, solutions of concentration have oscillations and even diverge near the sharp gradient when the relaxation time of governing equations is close to 0.5 (i.e., diffusion-dominated). In this paper, an integrated PFLBM model considering two-phase flow and interfacial mass transfer with a new filtering algorithm and collision operator was built to extend the wider range of the existing model for the two-film CDE with an extremely low diffusion coefficient. First, the two-film mass transfer model from our team was furthermore developed with the second-order formation to meet the high precision of concentration on two-phase interfaces. Then, directional filtering algorithms and regularized-finite-difference (rLBM-FD) collision operator were introduced to improve the numerical stability and limit the numerical diffusion. Four common collision operators were implemented and thoroughly tested in two cases to verify the robustness and accuracy of our new model. In conclusion, the combination of the rLBM-FD with standard non-linear filter reaches the highest robustness, mass-conservativeness, and limitation on numerical diffusion. The directional non-linear filter has the lowest computational cost of any microscopic variable filter and can increase the robustness by two times. Macro-variable filtering is not appropriate for treating the two-film equilibrium because the mass loss and robustness are unacceptable.