Contact angles in the pseudopotential lattice Boltzmann modeling of wetting

Mesoscopic modeling the interaction of two attached-wall cavitation bubbles

A hybrid thermal lattice Boltzmann cavitation model based on a nonorthogonal framework is developed to investigate the interaction of two attached-wall cavitation bubbles. The interaction modes are systematically analyzed, with an emphasis on how varying contact angles influence the flow and temperature distributions, as well as the evolution of wall heat flux under strong and weak interaction conditions. Bubbles formed on the hydrophobic surface display increased contact radius and greater curvature radii compared to those on the hydrophilic wall, leading to greater volumes but weaker collapse intensity. The growth rate of the bubble equivalent radius for the weak interaction modes consistently follows the relation U∝2p∞/3ρl. Additionally, bubble coalescence occurs at the interface regions along the hydrophobic surface, altering the final collapse dynamics and resulting in distinct temperature and velocity distributions. Finally, the instantaneous heat flux characteristics are explored. Due to differences in the contact points motion rate and microjet angle with the solid wall, the peak value and number of heat flux peaks vary on walls with different wettability.

Applicability of the thermodynamic and mechanical route to Young's equation for rigid and flexible solids: A molecular dynamics simulations study of a Lennard-Jones system model

The wetting properties of a liquid in contact with a solid are commonly described by Young's equation, which defines the relationship between the angle made by a fluid droplet onto the solid surface and the interfacial properties of the different interfaces involved. When modeling such interfacial systems, several assumptions are usually made to determine this angle of contact, such as a completely rigid solid or the use of the tension at the interface instead of the surface free energy. In this work, we perform molecular dynamics simulations of a Lennard-Jones liquid in contact with a Lennard-Jones crystal and compare the contact angles measured from a droplet simulation with those calculated using Young's equation based on surface free energy or surface stress. We analyze cases where the solid atoms are kept frozen in their positions and where they are allowed to relax and simulate surfaces with different wettability and degrees of softness. Our results show that using either surface free energy or surface stress in Young's equation leads to similar contact angles but different interfacial properties. We find that the approximation of keeping the solid atoms frozen must be done carefully, especially if the liquid can efficiently pack at the interface. Finally, we show that to correctly reproduce the measured contact angles when the solid becomes soft, the quantity to be used in Young's equation is the surface free energy only and that the error committed in using the surface stress becomes larger as the softness of the solid increases.

Characterizing Dynamic Contact Angle during Gas-Liquid Imbibition in Microchannels by Lattice Boltzmann Method Modeling

Spontaneous imbibition in microchannels is a critical phenomenon in various industrial applications, such as enhanced oil recovery and microfluidic systems. One of the key factors influencing the imbibition process is the dynamic wetting effect, which governs the interaction between the liquid and solid surfaces. This paper improves the original pseudopotential model for interfluid forces by coupling it with the Peng-Robinson equation of state. The model's accuracy is verified through thermodynamic consistency checks, simulations of gas-liquid interfacial tensions, and testing of static equilibrium contact angles. Following model validation, we use it to simulate spontaneous gas-liquid imbibition in microchannels and investigate dynamic contact angle evolution during the process. The results demonstrate that (1) as the microchannel width increases, inertia forces become more significant during the initial imbibition stages, leading to a greater difference between the dynamic and static contact angles. (2) A decrease in fluid-solid interaction strength results in a larger gap between dynamic and static contact angles. (3) Higher interfacial tension strengthens the capillary forces, accelerating the imbibition rate and enlarging the difference between the dynamic and static contact angles. Furthermore, the dynamic contact angle data obtained from our simulations can be used to correct the traditional Lucas-Washburn equation. The corrected equation predicts imbibition distances that closely match the simulation results.

Mesoscopic Model for Disjoining Pressure Effects in Nanoscale Thin Liquid Films and Evaporating Extended Meniscuses

Disjoining pressure effect is the key to describe contact line dynamics, micro/nanoscale liquid-vapor phase change heat transfer, and liquid transport in nanopores. In this paper, by combining a mesoscopic approach for nanoscale liquid-vapor interfacial transport and a mean-field approximation of the long-range solid-fluid molecular interaction, a mesoscopic model for the disjoining pressure effect in nanoscale thin liquid films is proposed. The capability of this model to delineate the disjoining pressure effect is validated. We demonstrate that the Hamaker constant determined from our model agrees very well with molecular dynamics (MD) simulation and that the transient evaporation/condensation mass flux predicted by this mesoscopic model is also consistent with the kinetic theory. Using this model, we investigate the characteristics of the evaporating extended meniscus in a nanochannel. The nonevaporating film region, the evaporating thin-film region, and the intrinsic meniscus region are successfully captured by our model. Our results suggest that the apparent contact angle and thickness of the nonevaporating liquid film are self-tuned according to the evaporation rate, and a higher evaporation rate results a in larger apparent contact angle and thinner nonevaporating liquid film. We also show that disjoining pressure plays a dominant role in the nonevaporating film region and suppresses the evaporation in this region, while capillary pressure dominates the intrinsic meniscus region. Strong evaporation takes place in the thin-film region, and both the disjoining pressure and capillary pressure contribute to the total pressure difference that delivers the liquid from the intrinsic meniscus region to the evaporating thin-film region, compensating for the liquid mass loss due to strong evaporation. Our work provides a new avenue for investigating thin liquid film spreading, liquid transport in nanopores, and microscopic liquid-vapor phase change heat/mass transfer mechanisms near the three-phase contact line region.

Simplified wetting boundary scheme in phase-field lattice Boltzmann model for wetting phenomena on curved boundaries

In this work, a simplified wetting boundary scheme in the phase-field lattice Boltzmann model is developed for wetting phenomena on curved boundaries. The proposed scheme combines the advantages of the fluid-solid interaction scheme and geometric scheme-easy to implement (no need to interpolate the values of parameters exactly on solid boundaries and find proper characteristic vectors), the value of contact angle can be directly prescribed, and no unphysical spurious mass layer-and avoids mass leakage. Different from previous works, the values of the order parameter gradient on fluid boundary nodes are directly determined according to the geometric formulation rather than indirectly regulated through the order parameters on ghost solid nodes (i.e., ghost contact-line region). For this purpose, two numerical approaches to evaluate the order parameter gradient on fluid boundary nodes are utilized, one with the prevalent isotropic central scheme and the other with a local gradient scheme that utilizes the distribution functions. The simplified wetting boundary schemes with both numerical approaches are validated and compared through several numerical simulations. The results demonstrate that the proposed model has good ability and satisfactory accuracy to simulate wetting phenomena on curved boundaries under large density ratios.

Improved partially saturated method for the lattice Boltzmann pseudopotential multicomponent flows

This paper extends the partially saturated method (PSM), used for curved or complex walls, to the lattice Boltzmann (LB) pseudopotential multicomponent model and adapts the wetting boundary condition to model the contact angle. The pseudopotential model is widely used for various complex flow simulations due to its simplicity. To simulate the wetting phenomenon within this model, the mesoscopic interaction force between the boundary fluid and solid nodes is used to mimic the microscopic adhesive force between the fluid and the solid wall, and the bounce-back (BB) method is normally adopted to achieve the no-slip boundary condition. In this paper, the pseudopotential interaction forces are computed with eighth-order isotropy since fourth-order isotropy leads to the condensation of the dissolved component on curved walls. Due to the staircase approximation of curved walls in the BB method, the contact angle is sensitive to the shape of corners on curved walls. Furthermore, the staircase approximation makes the movement of the wetting droplet on curved walls not smooth. To solve this problem, the curved boundary method may be used, but due to the interpolation or extrapolation process, most curved boundary conditions suffer from massive mass leakage when applied to the LB pseudopotential model. Through three test cases, it is found that the improved PSM scheme is mass conservative, that nearly identical static contact angles are observed on flat and curved walls under the same wetting condition, and that the movement of a wetting droplet on curved and inclined walls is smoother compared to the usual BB method. The present method is expected to be a promising tool for modeling flows in porous media and in microfluidic channels.

Wall wettability effect on process of collapse of single cavitation bubbles in near-wall region using pseudo-potential lattice Boltzmann method

This study investigates the effect of wall wettability on cavitation collapse based on a large-density-ratio lattice Boltzmann method (LBM) pseudo-potential model. The validity and superiority of the proposed model in simulation of cavitation under complex conditions are confirmed by comparing with theories, experiments, and numerical results by other models. Our simulations indicate that wall wettability has a significant influence on near-wall cavitation of an order no less than the effect of the initial bubble distance. A criterial initial distance exists in near-wall cavitation within which the micro-jet will direct toward the wall. This criterial distance is shown to be positively correlated with the contact angle by a cosine function. Within this distance, the lifetime of the bubble decreases by up to 50%, and the increase of the maximum micro-jet velocity and collapse pressure are up to 131% and 65%, respectively, when the contact angle increases from the hydrophilic 53° to the hydrophobic 113°. Without considering the shock-wave mechanism, the impact pressure transmitted to the hydrophilic wall is of the same order as the maximum collapse pressure while the impact velocity is an order smaller than the maximum micro-jet velocity. Wall wettability affects collapse through the Bjerknes force and the pressure around the bubble. Preliminary analysis also suggests that the relation between the pressure difference and the intensity of collapse exhibits more patterns than we have assumed, which fits a logistic curve well, and appears not changing with the contact angle or the initial bubble distance.

Lattice Boltzmann Modeling of a Sessile and a Body Force-Driven Sliding Droplet over a Grooved Surface

This work presents the numerical modeling of a droplet’s sessile and dynamic behavior on a grooved surface. A droplet is placed on horizontal and vertical sliding conditions to observe its behavior under wettable and non-wettable conditions. The numerical analysis uses the multicomponent multiphase Shan-Chen Lattice Boltzmann Model (SC-LBM). The Cassie–Baxter and Wenzel states are reproduced for the sessile condition, and the enhancement of the contact angle is appreciated under the action of the grooved-ridged horizontal surface. The sliding droplet is analyzed through the Bond number by varying the ratio between the body force and the surface tension number. For Cassie–Baxter and Wenzel wettability conditions, a critical Bond number was discovered above which the sliding droplet will continue to deform indefinitely. The numerical model proved its suitability to predict the gradual deformation of a droplet over a grooved vertical surface subject to a tangential body force until the droplet eventually reaches a sessile condition or a breakup.

Asymmetric Condensation Characteristics during Dropwise Condensation in the Presence of Non-condensable Gas: A Lattice Boltzmann Study

In this work, the condensation characteristics of droplets considering the non-condensable gas with different interaction effects are numerically studied utilizing a multicomponent multiphase thermal lattice Boltzmann (LB) model, with a special focus on the asymmetric nature induced by the interaction effect. The results demonstrate that for isolated-like growth with negligible interactions, the condensation characteristics, that is, the concentration profile, the temperature distribution, and the flow pattern, are typically symmetric in nature. For the growth regime in a pattern, the droplet has to compete with its neighbors for catching vapor, which leads to an overlapping concentration profile (namely the interaction effect). The distribution of the condensation flux on the droplet surface is consequently modified, which contributes to the asymmetric flow pattern and temperature profile. The condensation characteristics for droplet growth in a pattern present an asymmetric nature. Significantly, the asymmetric condensation flux resulting from the interaction effect can induce droplet motion. The results further demonstrate that the interaction strongly depends on the droplet's spatial and size distribution, including two crucial parameters, namely the inter-distance and relative size of droplets. The asymmetric condensation characteristics are consequently dependent on the difference in the interaction intensities on both sides of the droplet. Finally, we demonstrate numerically and theoretically that the evolution of the droplet radius versus time can be suitably described by a power law; the corresponding exponent is kept at a constant of 0.50 for isolated-like growth and is strongly sensitive to the interaction effect for the growth in a pattern.

ImmunoDisk—A Fully Automated Bead-Based Immunoassay Cartridge with All Reagents Pre-Stored

In this paper, we present the ImmunoDisk, a fully automated sample-to-answer centrifugal microfluidic cartridge, integrating a heterogeneous, wash-free, magnetic- and fluorescent bead-based immunoassay (bound-free phase detection immunoassay/BFPD-IA). The BFPD-IA allows the implementation of a simple fluidic structure, where the assay incubation, bead separation and detection are performed in the same chamber. The system was characterized using a C-reactive protein (CRP) competitive immunoassay. A parametric investigation on air drying of protein-coupled beads for pre-storage at room temperature is presented. The key parameters were buffer composition, drying temperature and duration. A protocol for drying two different types of protein-coupled beads with the same temperature and duration using different drying buffers is presented. The sample-to-answer workflow was demonstrated measuring CRP in 5 µL of human serum, without prior dilution, utilizing only one incubation step, in 20 min turnaround time, in the clinically relevant concentration range of 15–115 mg/L. A reproducibility assessment over three disk batches revealed an average signal coefficient of variation (CV) of 5.8 ± 1.3%. A CRP certified reference material was used for method verification with a concentration CV of 8.6%. Our results encourage future testing of the CRP-ImmunoDisk in clinical studies and its point-of-care implementation in many diagnostic applications.

Lattice Boltzmann modeling of two-phase electrohydrodynamic flows under unipolar charge injection

In this work, a two-dimensional droplet confined between two parallel electrodes under the combined effects of a nonuniform electric field and unipolar charge injection is numerically investigated using the lattice Boltzmann method (LBM). Under the non-Ohmic regime, the interfacial tension and electric forces at the droplet surface cooperate with the volumetric Coulomb force, leading to complex deformation and motion of the droplet while at the same time inducing a bulk electroconvective flow. After we validate the model by comparing with analytical solutions at the hydrostatic state, we perform a quantitative analysis on the droplet deformation factor D and bulk flow stability criteria T_{c} under different parameters, including the electric capillary number Ca, the electric Rayleigh number T, the permittivity ratio ɛ_{r}, and the mobility ratio K_{r}. It is found that the bulk flow significantly modifies the magnitude of D, which in turn decreases T_{c} of the electroconvective flow. For a droplet repelled by the anode, ɛ_{r}>1, an interesting linear relationship can be observed in the D-Ca curves. However, for a droplet attracted to the anode, ɛ_{r}<1, the system is potentially unstable. After first evolving into a quasisteady state, the droplet successively experiences steady flow, periodic flow, second steady flow, and oscillatory flow with increasing T. Moreover, discontinuities can be observed in the D-T curves due to the transitions of bulk flow.

Unified lattice Boltzmann method with improved schemes for multiphase flow simulation: Application to droplet dynamics under realistic conditions

As a powerful mesoscale approach, the lattice Boltzmann method (LBM) has been widely used for the numerical study of complex multiphase flows. Recently, Luo et al. [Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 379, 20200397 (2021)10.1098/rsta.2020.0397] proposed a unified lattice Boltzmann method (ULBM) to integrate the widely used lattice Boltzmann collision operators into a unified framework. In this study, we incorporate additional features into this ULBM in order to simulate multiphase flow under realistic conditions. A nonorthogonal moment set [Fei et al., Phys. Rev. E 97, 053309 (2018)10.1103/PhysRevE.97.053309] and the entropic-multi-relaxation-time (KBC) lattice Boltzmann model are used to construct the collision operator. An extended combined pseudopotential model is proposed to realize multiphase flow simulation at high-density ratio with tunable surface tension over a wide range. The numerical results indicate that the improved ULBM can significantly decrease the spurious velocities and adjust the surface tension without appreciably changing the density ratio. The ULBM is validated through reproducing various droplet dynamics experiments, such as binary droplet collision and droplet impingement on superhydrophobic surfaces. Finally, the extended ULBM is applied to complex droplet dynamics, including droplet pancake bouncing and droplet splashing. The maximum Weber number and Reynolds number in the simulation reach 800 and 7200, respectively, at a density ratio of 1000. The study demonstrates the generality and versatility of ULBM for incorporating schemes to tackle challenging multiphase 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.

A unified lattice Boltzmann model and application to multiphase flows

In this work, we develop a unified lattice Boltzmann model (ULBM) framework that can seamlessly integrate the widely used lattice Boltzmann collision operators, including the Bhatnagar-Gross-Krook or single-relation-time, multiple-relaxation-time, central-moment or cascaded lattice Boltzmann method and multiple entropic operators (KBC). Such a framework clarifies the relations among the existing collision operators and greatly facilitates model comparison and development as well as coding. Importantly, any LB model or treatment constructed for a specific collision operator could be easily adopted by other operators. We demonstrate the flexibility and power of the ULBM framework through three multiphase flow problems: the rheology of an emulsion, splashing of a droplet on a liquid film and dynamics of pool boiling. Further exploration of ULBM for a wide variety of phenomena would be both realistic and beneficial, making the LBM more accessible to non-specialists. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Fluid-wall interactions in pseudopotential lattice Boltzmann models

Designing proper fluid-wall interaction forces to achieve proper wetting conditions is an important area of interest in pseudopotential lattice Boltzmann models. In this paper, we propose a modified fluid-wall interaction force that applies for pseudopotential models of both single-component fluids and partially miscible multicomponent fluids, such as hydrocarbon mixtures. A reliable correlation that predicts the resulting liquid contact angle on a flat solid surface is also proposed. This correlation works well over a wide variety of pseudopotential lattice Boltzmann models and thermodynamic conditions.

Rebound Behaviors of Multiple Droplets Simultaneously Impacting a Superhydrophobic Surface

The rebound behaviors of multiple droplets simultaneously impacting a superhydrophobic surface were investigated via lattice Boltzmann method (LBM) simulations. Three rebound regions were identified, i.e., an edge-dominating region, a center-dominating region, and an independent rebound region. The occurrence of the rebound regions strongly depends on the droplet spacing and the associated Weber and Reynolds numbers. Three new rebound morphologies, i.e., a pin-shaped morphology, a downward comb-shaped morphology, and an upward comb-shaped morphology, were presented. Intriguingly, in the edge-dominating region, the central droplets experience a secondary wetting process to significantly prolong the contact time. However, in the center-dominating region, the contact time is dramatically shortened because of the strong interactions generated by the central droplets and the central ridges. These findings provide useful information for practical applications such as self-cleaning, anticorrosion, anti-icing, and so forth.

Shape Optimization of a Microhole Surface for Control of Droplet Wettability via the Lattice Boltzmann Method and Response Surface Methodology

The chief aim is to explore the wetting state on a microhole surface and to optimize the shape parameters of a microhole surface. A two-dimensional pseudopotential model was established, and the effects of shapes on the wetting behavior were explored. The shape parameters were optimized via the response surface methodology. The results reveal that the microhole surface can achieve a superhydrophobic state. When the diameter varies from 25 to 200 μm, the droplet is gradually lifted. However, when the diameter of the microhole is too large, the contact angle decreases rapidly. When the microhole diameter increases, relative radii of the x- and y-directions exhibit increasing trends. With the increase of the spacing, the gaps between the microholes are gradually filled with the droplet. When spacing increases, relative radii of x- and y-directions exhibit decreasing trends. The largest contact angle of 171.246° at the diameter of 76 μm and the spacing of 48 μm is observed.

Achieving thermodynamic consistency in a class of free-energy multiphase lattice Boltzmann models

The free-energy lattice Boltzmann (LB) model is one of the major multiphase models in the LB community. The present study is focused on a class of free-energy LB models in which the divergence of thermodynamic pressure tensor or its equivalent form expressed by the chemical potential is incorporated into the LB equation via a forcing term. Although this class of free-energy LB models may be thermodynamically consistent at the continuum level, it suffers from thermodynamic inconsistency at the discrete lattice level owing to numerical errors [Guo et al., Phys. Rev. E 83, 036707 (2010)10.1103/PhysRevE.83.036707]. The numerical error term mainly includes two parts: one comes from the discrete gradient operator and the other can be identified in a high-order Chapman-Enskog analysis. In this paper, we propose an improved scheme to eliminate the thermodynamic inconsistency of the aforementioned class of free-energy LB models. The improved scheme is constructed by modifying the equation of state of the standard LB equation, through which the discretization of ∇(ρc_{s}^{2}) is no longer involved in the force calculation and then the numerical errors can be significantly reduced. Numerical simulations are subsequently performed to validate the proposed scheme. The numerical results show that the improved scheme is capable of eliminating the thermodynamic inconsistency and can significantly reduce the spurious currents in comparison with the standard forcing-based free-energy LB model.

Three-dimensional pseudopotential lattice Boltzmann model for multiphase flows at high density ratio

In this study, we extend the pseudopotential lattice Boltzmann model proposed by Huang and Wu [J. Comput. Phys. 327, 121 (2016)10.1016/j.jcp.2016.09.030] to a three-dimensional model for practical simulations of multiphase flows with high density ratio. In this model, an additional source term is introduced into the evolution function, and the performed high-order Chapman-Enskog analysis demonstrates that the Navier-Stokes equations with accurate pressure tensor are recovered. Also, an alternative geometric formulation is developed to obtain various contact angles and an iteration scheme is involved in the initialization to improve the stability of the model. Theoretical and numerical investigations both validate that the thermodynamic consistency and tuning surface tension independently of density ratio is achieved through varying the two free parameters in the source term. Numerical simulations of droplet wetting indicate that a large degree range of contact angles can be precisely realized with the implementation of the wetting boundary scheme. Further dynamic examinations of droplet impingement on a thin film and a dry surface also verify the stability and capability of the proposed pseudopotential lattice Boltzmann model.

Lattice Boltzmann Modeling of Condensation Heat Transfer on Downward-Facing Surfaces with Different Wettabilities

The model of vapor condensation heat transfer on downward-facing surfaces with different wettabilities is built by a two-dimensional (2D) lattice Boltzmann method. Dynamic evolution of condensate microdroplets on different wettability surfaces is simulated and the influence on heat transfer performance is analyzed. Moreover, the mechanism of a heterogeneous wettability surface enhancing condensation heat transfer is explored by investigating the condensate behaviors in the process of condensation. The numerical results indicate that as the contact angle of the homogeneous wettability surface increases, the initial nucleation time of the condensate is prolonged, while the departure time of the condensate is reduced significantly. The temperature adjacent to the gas-liquid interface, especially in the three-phase contact line region, is much higher than elsewhere due to the release of latent heat during condensation. Coalescence and detachment behaviors of condensate droplets cause the average heat flux to fluctuate locally with time. For the hybrid wettability surface, if the proportion of hydrophobic regions is small, the condensation heat transfer performance will be deteriorated. However, increasing the hydrophobic-hydrophilic ratio has a positive effect on enhancing heat transfer. It is found that a critical hydrophobic-hydrophilic ratio exists to optimize the heat transfer performance. For the gradient wettability surface, directional migration induced by capillary force facilitates the removal of condensate droplets, thereby enhancing the condensation heat transfer. Furthermore, a larger wetting gradient benefits to further improve the heat transfer performance. The results are valuable for optimally designing the heat transfer enhancement of vapor condensation on functionalized surfaces with heterogeneous wettability.

Effects of hysteresis window on contact angle hysteresis behaviour at large Bond number

Contact angle hysteresis, defined as the difference between advancing and receding contact angles, is an important phenomenon in multiphase flow on a wetting surface. In this study, a modified pseudo-potential lattice Boltzmann (LB) multiphase model with tunable surface tension is proposed, which is further coupled with the geometrical formulation contact angle scheme to investigate the motion of droplets invoking the contact angle hysteresis. We focus on the dynamic behaviour of droplets driven by a body force at the Bond number ranging from 1 to 6, which is defined as the ratio of the body force to the capillary force. The droplet morphology change is examined by varying (i) the Bond number and (ii) the hysteresis window. Results show the droplet morphology evolution can be classified into different stages, including stretch, relaxation, and equilibrium. The droplet oscillation phenomenon at large Bond numbers at the equilibrium stage is observed for the first time. In addition, it is found that such oscillation can lead to the breakup and/or coalescence of droplets when the surface waves spread on the top of the droplet. Furthermore, there is slight oscillation of the normalized length, width and height at the equilibrium stage for the neutral hysteresis window while more dramatic oscillation will appear for the hydrophobic hysteresis window.

Implementation of contact angles in pseudopotential lattice Boltzmann simulations with curved boundaries

The pseudopotential multiphase lattice Boltzmann (LB) model is a very popular model in the LB community for simulating multiphase flows. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. In this work, we aim at investigating the implementation of contact angles in the pseudopotential LB simulations with curved boundaries. In the pseudopotential LB model, the contact angle is usually realized by employing a solid-fluid interaction or specifying a constant virtual wall density. However, it is shown that the solid-fluid interaction scheme yields very large spurious currents in the simulations involving curved boundaries, while the virtual-density scheme produces an unphysical thick mass-transfer layer near the solid boundary although it gives much smaller spurious currents. We also extend the geometric-formulation scheme in the phase-field method to the pseudopotential LB model. Nevertheless, in comparison with the solid-fluid interaction scheme and the virtual-density scheme, the geometric-formulation scheme is relatively difficult to implement for curved boundaries and cannot be directly applied to three-dimensional space. By analyzing the features of these three schemes, we propose an improved virtual-density scheme to implement contact angles in the pseudopotential LB simulations with curved boundaries, which does not suffer from a thick mass-transfer layer near the solid boundary and retains the advantages of the original virtual-density scheme, i.e., simplicity, easiness for implementation, and low spurious currents.

Hybrid Wettability-Induced Heat Transfer Enhancement for Condensation with NonCondensable Gas

Heat transfer enhancement in dropwise condensation is widely investigated on a superhydrophobic surface with the advances in surface engineering, but the influence of a large amount of noncondensable gas (NCG) has not been clarified. In this work, the condensation heat transfer with a large amount of NCG is investigated by developing a multiphase lattice Boltzmann model for a multicomponent system. First, the condensation of a single droplet on a hydrophobic surface with NCG is simulated, demonstrating the capacity of the present model to capture the behaviors of different components during phase change and predict the significant influence of even a small fraction of the NCG on heat transfer. Then, solid surfaces with mixed wettability are built by introducing a fraction of hydrophilic parts to enhance heat transfer. It is found that there exists an optimized proportion which could maximize the condensation heat transfer efficiency corresponding to a specific mass fraction of NCG. Furthermore, the mechanism of this optimized proportion is revealed by examining the dynamic behaviors of condensation in a typical case, as a balance between a promotion of the nucleation rate and a put off of transition to filmwise condensation.

Entropy production in thermal phase separation: a kinetic-theory approach

Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decrease during the domain growth stage, attaining its maximum at the crossover between the two. Such behaviour provides a natural criterion to identify and discriminate between the two regimes. Furthermore, the effects of heat conductivity, viscosity and surface tension on the entropy production rate are investigated by systematically probing the interplay between non-equilibrium energy and momentum fluxes. It is found that the entropy production rate due to energy fluxes is an increasing function of the Prandtl number, while the momentum fluxes exhibit an opposite trend. On the other hand, both contributions show an increasing trend with surface tension. The present analysis inscribes within the general framework of non-equilibrium thermodynamics and consequently it is expected to be relevant to a broad class of soft-flowing systems far from mechanical and thermal equilibrium.

Chemical-potential-based lattice Boltzmann method for nonideal fluids

Chemical potential, as an important thermodynamic quantity, has been popularly used in thermodynamic modeling for complex systems, especially for those involving the phase transitions and chemical reactions. Here we present a chemical-potential-based multiphase lattice Boltzmann model, in which the nonideal force is directly evaluated by a chemical potential. The numerical computation is more efficient than the pressure-tensor-based model [Wen et al. Europhys. Lett. 112, 44002 (2015)10.1209/0295-5075/112/44002] because the calculations of the pressure tensor and its divergence are avoided. We have derived several chemical potentials of the popular equations of state from the free-energy density function. The theoretical analyses and numerical results support that the present model satisfies thermodynamics and Galilean invariance. An effective chemical-potential boundary condition is also implemented to investigate the wettability of a solid surface, and the contact angle can be linearly tuned by the surface chemical potential.

Revised Chapman-Enskog analysis for a class of forcing schemes in the lattice Boltzmann method

In the lattice Boltzmann (LB) method, the forcing scheme, which is used to incorporate an external or internal force into the LB equation, plays an important role. It determines whether the force of the system is correctly implemented in an LB model and affects the numerical accuracy. In this paper we aim to clarify a critical issue about the Chapman-Enskog analysis for a class of forcing schemes in the LB method in which the velocity in the equilibrium density distribution function is given by u=∑_{α}e_{α}f_{α}/ρ, while the actual fluid velocity is defined as u[over ̂]=u+δ_{t}F/(2ρ). It is shown that the usual Chapman-Enskog analysis for this class of forcing schemes should be revised so as to derive the actual macroscopic equations recovered from these forcing schemes. Three forcing schemes belonging to the above class are analyzed, among which Wagner's forcing scheme [A. J. Wagner, Phys. Rev. E 74, 056703 (2006)10.1103/PhysRevE.74.056703] is shown to be capable of reproducing the correct macroscopic equations. The theoretical analyses are examined and demonstrated with two numerical tests, including the simulation of Womersley flow and the modeling of flat and circular interfaces by the pseudopotential multiphase LB model.