A Computational Model for Adjusting Surface Tension Coefficient in Pseudo-potential Lattice Boltzmann Method

The curvature and temperature dependency of the liquid-vapor surface tension has a significant influence on the accurate prediction of the nanobubble/nanodrop nucleation process. In this work, a mesoscopic approach combining the pseudo-potential multiphase lattice Boltzmann method (LBM), the principle of dynamic similarity, and the van der Waals theory of corresponding states is adopted to quantitatively investigate the curvature and temperature dependency of the surface tension and Tolman length for real fluids (water and R134a). By Tolman length, we mean the distance from the surface of tension to the equimolar surface, which measures the extent by which the surface tension of a nanodrop/nanobubble deviates from the corresponding flat interface limit. We show that the Tolman lengths for flat liquid-vapor interfaces (δF) increase with the increase of temperature and are proportional to (1−Tr)−1.044. Equations for predicting surface tensions of water and R134a with effects of temperature and curvature radius taken into consideration are proposed. We demonstrate that the surface tensions increase while the Tolman lengths (δB) decrease with the increase of curvature for nanobubbles. For nanodroplets, however, the surface tensions decrease while the Tolman lengths (δD) increase with the increase of curvature. Effects of the equation of state for real fluids, which determines the interparticle interaction force in the pseudo-potential LBM, are also discussed. This mesoscopic approach can quantify the curvature dependency of liquid-vapor surface tensions for various real fluids in a wide temperature range with low computation costs, providing a new avenue for the accurate prediction of nucleation processes in micro-/nanoscale phase change heat transfer with applications to boiling, evaporation, and condensation.

Abstract: Recently, unmanned aerial vehicles (UAVs) have been widely used to spray pesticides to control diseases and pests of many crops. During the process of pesticide application by UAV spraying, aerial spraying tank-mix adjuvants are usually mixed with pesticide solution to improve the efficiency of pesticides. Preventing pesticides depositing in off-target area is important in enhancing pesticide utilization. Improving the wetting and spreading of pesticides is one of the most important ways to reduce pesticide droplets running off from the target. This study is focusing on the effects of aerial spraying tank-mix organosilicone adjuvant (OA) on surface tension and spreading coefficient of pesticide solutions. Six pesticide solutions used alone and mixed together of different concentrations are prepared under field application conditions. Surface tension and spreading coefficient of the solution with and without OA were measured, respectively. The results show that OA could significantly lower surface tension and increase spreading coefficient of pesticide solutions regardless of solution concentrations. OA with concentration higher than critical micelle concentration (CMC) could not further decrease surface tension, but still could significantly increase spreading coefficient of the solution. For solutions with single pesticide belongs to different formulations, the minimum needed concentration of OA is different due to formulation type. The minimum concentration of OA for solution of suspension concentrate and aqueous solution (0.5‰-0.7‰) is lower than that of solutions of emulsifiable concentrate (EC) (2.0‰-5.0‰). For solutions of several pesticides mixed together, the minimum concentration of OA is related to the number of EC formulation in the solution. For pesticide solutions containing one EC formulation, the minimum concentration of OA is 2.0‰; for pesticide solutions containing two or three EC formulation, the minimum concentration of OA is recommended to be 5.0‰-10.0‰. These results suggest that the concentration of OA needed for pesticide solution should be evaluated before field application considering pesticide belonging to different formulations mixing together for application. Keywords: aerial spraying adjuvant, organosilicone, surface tension, spreading coefficient DOI: 10.33440/j.ijpaa.20210401.159 Citation: Meng Y H, Wang M M, Wang Z G, Hu H Y, Ma Y. Surface tension and spreading coefficient of single-and mix-pesticide solutions with aerial spraying organosilicone adjuvant. Int J Precis Agric Aviat, 2021; 4(1): 6–13.

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

Boiling heat transfer plays a crucial role in various engineering applications, requiring accurate numerical modeling to capture phase-change dynamics. This study employs the pseudopotential lattice Boltzmann method (LBM) to simulate boiling heat transfer at different reduced temperatures, aiming to provide deeper insights into bubble dynamics and heat transfer mechanisms. The LBM framework incorporates a multi-relaxation-time approach and the Peng–Robinson equation of state to enhance numerical stability and thermodynamic consistency. Simulations were performed to analyze bubble nucleation, growth, and detachment across varying reduced temperatures, considering the influence of surface wettability, surface tension and gravitational acceleration. The results indicate a strong dependence of bubble behavior on the reduced temperature, affecting both heat flux and boiling regimes. The numerical findings show reasonable agreement with theoretical predictions and experimental trends, validating the effectiveness of the LBM approach for phase-change simulations. Additionally, this study highlights the role of contact angle variation in modifying boiling characteristics, emphasizing the necessity of accurate surface interaction modeling. The outcomes of this work contribute to advancing computational methodologies for boiling heat transfer, supporting improved thermal management in industrial applications.

Simulation of a single droplet impact onto a thin liquid film using the lattice Boltzmann method

Surface tension plays a crucial role in governing interfacial dynamics during phase change phenomena spanning natural systems and industrial applications. The phase-field lattice Boltzmann (LB) method has emerged as a powerful approach for modeling phase change, particularly due to its inherent ability to capture interfacial tension effects in multiphase systems. However, there has been no three-dimensional phase-field LB method capable of simulating phase change initialed from a single-phase medium. In this study, we propose a phase-field-based LB method for modeling thermal phase change. A source term is derived to accurately describe phase change. A key distinguishing feature of our model is its capability to initiate phase change driven by the sensible heat of superheated or supercooled phases, thereby enabling the presence of superheated liquid and supercooled vapor. To validate the proposed model, we perform a series of benchmark tests using D3Q19 LB models with density ratios up to 1:1000. These include (i) a comparison between numerical results and analytical solutions of the one-dimensional Stefan problem and (ii) a quantitative evaluation of bubble departure diameter against the Fritz relation for bubble generation in a pure liquid phase under wall heating. The results demonstrate agreement with theoretical predictions, underscoring the accuracy and robustness of the proposed approach. This study extends the applicability of the LB method to scenarios requiring consideration of both surface tension and thermal phase change, offering a valuable tool for simulating complex multiphase systems.

The pseudopotential method has grown as a powerful tool for multiphase fluid flow simulations within the lattice Boltzmann method framework. We consider that due to its simplicity and computational efficiency, the pseudopotential method could be explored also inside the framework of more traditional Computational Fluid Dynamic methods such as Finite Difference, Finite Volume or Finite Element methods. Following this idea, in this work we start from the macroscopic equations resulting from the pseudopotential lattice Boltzmann method and discretize it by a simple Finite Difference scheme. This pseudopotential based finite difference method is then tested in different benchmark problems such as a planar interface, a smooth droplet oscillation, and a single droplet evaporation. Excellent results were obtained in all tests. One of the advantages of the proposed method is that mesh refinement is straightforward, and converged solutions can be used as a tool of validation for the lattice Boltzmann method. Results indicate that the pseudopotential method is suitable to be used with standard discretization methods such as Finite Difference and that in future works more robust discretizations can be used to further enhance the pseudopotential method application.

Thermophysical property prediction of biodiesel mixtures at extreme conditions using molecular dynamics simulation

The wetting and spreading of droplets on solid walls are commonly seen in nature. The study of such a phenomenon can deepen our understanding of solid-liquid interaction and promote the development of relevant cutting-edge technological applications. In this work, the lattice Boltzmann method based on phase field theory is used to investigate the wetting and spreading of a compound droplet on a wedge. This method combines the finite-difference solution of the Cahn-Hilliard equations for ternary fluids to capture the interface dynamics and the lattice Boltzmann method for the hydrodynamics of the flow. Symmetric compound droplets with equal interfacial tensions on a wedge are considered first. Through theoretical analysis and numerical simulation, it is found that the wetted area on the wedge increases with the decrease of the contact angle of the wedge surface and the wedge apex angle. Depending on these two factors, the droplet may or may not split on the wedge. We also find that the droplet near the critical state predicted not to split by static equilibrium analysis could split during the spreading along the wall of the wedge under certain density and viscosity ratios. Based on the simulation results, a phase diagram of the droplet splitting state is generated with the density ratio and viscosity ratio as the coordinates. As the density ratio and kinematic viscosity ratio increase, the inertia effect becomes more prominent in the wetting and spreading process and the droplet is more likely to split. By comparing the phase diagrams in different initial conditions, it is found that under the same conditions, the compound droplet with an equilibrium initial state is less likely to split than that with an unequilibrium initial state, which is possibly because the initial total energy of the former is relatively small. Our study also shows that the kinematic viscosity ratio between the left half and the right half droplet may affect the results of droplet splitting. The increase of such a viscosity difference is conducive to the splitting of the compound droplet. Besides, asymmetric compound droplets with unequal interfacial tensions are also simulated, and it is found that the greater the wrapping degree between the left half and right half, the more difficult it is to separate the compound droplet.

Motion of a planar interface in incompressible Richtmyer–Meshkov (RM) and Rayleigh–Taylor (RT) instabilities with surface tension is investigated numerically by using the boundary integral method. It is shown that when the Atwood number is small, an interface rolls up without regularization of the interfacial velocity. A phenomenon known as “pinching” in the physics of drops is observed in the final stage of calculations at various Atwood numbers and surface tension coefficients, and it is shown that this phenomenon is caused by a vortex dipole induced on the interface. It is also shown that when the surface tension coefficient is large, finite amplitude standing wave solutions exist for the RM instability. This standing wave solution is investigated in detail by nonlinear stability analysis. When gravity is taken into account (RT instability), linearly stable but nonlinearly unstable motion can occur under a critical condition that the frequency of the linear dispersion relation in the system is equal to zero. Further, it is shown that the growth rate of bubbles and spikes under this critical motion is neither of the exponential type nor of the power law type at both the linear stage and the asymptotic stage.

The coalescence of liquid lenses is relevant in various applications, including inkjet printing and fog harvesting. However, the dynamics of liquid-lens coalescence have been relatively underexplored, particularly in the case of liquid lenses with larger contact angles. The coalescence of low-viscosity liquid lenses is numerically investigated by means of the pseudopotential multi-component lattice Boltzmann method over a wide range of contact angles. In two-dimensional simulations, numerical results on the growth of the bridge height are in quantitative agreement with experimental measurements for small contact angles. In addition, a comparison of the simulation results with a theoretical approach based on the thin-sheet equations for liquid lenses shows that these equations accurately capture the bridge-growth dynamics up to moderate contact angles. For the three-dimensional case, the growth of the bridge radius is independent of the equilibrium contact angle of the liquid lenses at the initial stage of growth. The dependency between the growth of the bridge height and the bridge radius exhibits a non-linear to linear transition. Document Type: Original article Cited as: Xie, Q., Harting, J. Simulations of inertial liquid-lens coalescence with the pseudopotential lattice Boltzmann method. Capillarity, 2026, 18(2): 41-49. https://doi.org/10.46690/capi.2026.02.01

In this paper, a new corresponding state principle (CSP)-based model is proposed to calculate the surface tension of hydrocarbons based on the National Institute of Standards and Technology (NIST) database. This model requires the critical point temperature, the lowest temperature available for surface tension data and the corresponding maximum surface tension value as inputs. It includes two adjustable coefficients which are fitted by using NIST data of three hydrocarbons. To test the applicability of this model, we applied it to predict the surface tension values of other 16 hydrocarbons. For all the 19 hydrocarbons available in NIST database, the average absolute deviations of 16 hydrocarbons are less than 5%. We also compared this new proposed model with other three existing corresponding state models, and found that this model is the best in predicting the surface tension data of hydrocarbons.

Improvements in the surface tension measurement using the capillary rise method and its application to water under external magnetic fields

A lattice Boltzmann model for multi-component two-phase gas-liquid flow with realistic fluid properties

A comparative analysis of the experimental data on the surface tension (ST) of low- melting metals, obtained by the method of maximum pressure in a drop and the method of a large drop, shows that the values of ST obtained by the large drop method for all studied metals are noticeably higher than those obtained by the method of maximum pressure in a drop. The reasons for such discrepancies, although in some cases they exceed the total errors of the ST measurement by the indicated methods, have not yet been clarified. In this regard, the paper gives a comparative analysis of the methodological specificity of measuring the surface tension by the methods of maximum pressure in a gas bubble or a drop and a lying or “large” drop. It is shown that these methods are theoretically substantiated, technically perfect, have a sufficiently high accuracy and are relatively simple. Based on the identification and critical analysis of the influence of the main factors on the measured value of the surface tension, the main reasons for the discrepancy between the experimental data on the surface tension of low-melting metals obtained by different methods are determined. It is shown that the underestimated ST values obtained by the method of maximum pressure in a droplet are due to the fact that all factors influencing the measured value of surface tension are directed towards a decrease in its value. Although the influence of each of these factors separately is insignificant, they together lead to a noticeable decrease in the value of surface tension. It is shown in the work that the method of maximum pressure in a drop, being the most accurate method for measuring ST, gives somewhat underestimated ST values for all low-melting metals.