Equation-of-state-dependent surface free-energy density for wettability in lattice Boltzmann method.

In thermodynamic theory, the liquid-vapor fluids can be described by a single multiphase equation of state and the surface wettability is usually characterized by the surface free-energy density. In this work, we propose an equation-of-state-dependent surface free-energy density for the wettability of the liquid-vapor fluids on a solid surface, which can lead to a simple closed-form analytical expression for the contact angle. Meanwhile, the thermodynamically derived equilibrium condition is equivalent to the geometric formulation of the contact angle. To numerically validate the present surface free-energy density, the mesoscopic multiphase lattice Boltzmann model with self-tuning equation of state, which is strictly consistent with thermodynamic theory, is employed, and the two-dimensional wetting condition treatment is extended to the three-dimensional situation with flat and curved surfaces. Two- and three-dimensional lattice Boltzmann simulations of static droplets on flat and curved surfaces are first performed, and the obtained contact angles agree well with the closed-form analytical expression. Then, the three-dimensional lattice Boltzmann simulation of a moving droplet on an inclined wall, which is vertically and sinusoidally oscillated, is carried out. The dynamic contact angles well satisfy the Cox-Voinov law. The droplet movement regimes are consistent with previous experiments and two-dimensional simulations. The dependence of the droplet overall velocity with respect to the dimensionless oscillation strength is also discussed in detail.

Equations of state in multiphase lattice Boltzmann method revisited.

The single-component multiphase fluids can be described by a single equation of state (EOS), and various EOSs have been employed in the multiphase lattice Boltzmann (LB) method. In this work, we revisit five commonly used EOSs, including the van der Waals EOS, the Redlich-Kwong EOS, the Redlich-Kwong-Soave EOS, the Peng-Robinson EOS, and the Carnahan-Starling EOS. The recent multiphase LB model with self-tuning EOS is employed because of its thermodynamic consistency in a strict sense and clear physical picture at the microscopic level. First, the way to incorporate these multiphase EOSs is proposed. Two scaling factors are introduced to independently adjust the surface tension and interface thickness, and the lattice sound speed is EOS-dependent to ensure the numerical stability. Then, numerical tests are conducted to validate the incorporations of these EOSs and compare their numerical performances. The surface tension and interface thickness are set to the same values for different EOSs in the comparisons. The liquid and gas densities, surface tension, and interface thickness by the LB simulation agree well with the thermodynamic results. The maximum density ratios achieved with different EOSs are at the same level and could be very close to each other when the interface thickness is relatively small. The effects of multiphase EOS, density ratio, and dimensionless relaxation time on the spurious current are discussed in detail. It is interesting to find the van der Waals EOS shows the best numerical performance in reducing the spurious current.

Coalescence-Induced Bubble Departure: Effects of Dynamic Contact Angles.

Coalescence-induced bubble departure is a common phenomenon in boiling and gas evolution reactions, which has significant impacts on the heat/mass transport. In this work, we systematically investigate the effects of dynamic contact angles on the coalescence and departure processes of two equal-sized bubbles. A critical contact angle (θcr) of 76° is determined for an ideal surface on the basis of a surface energy analysis, beyond which the coalesced bubble does not depart from the wall. Using 3D multi-relaxation-time (MRT) lattice Boltzmann simulations, we demonstrate that the advancing contact angle mainly governs the movement of the outer side of the contact lines, and the increase of the advancing contact angle may delay or even prevent the departure of the coalesced bubble. On the other hand, the receding contact angle dominates the motion of the inner side of the contact lines, and the decrease of the receding contact angle facilitates the departure of the coalesced bubble. We identify a regime map for the coalescence-induced bubble departure with respect to the contact angles, which includes four regions: the all-departure region, the advancing contact angle dominated region, the receding contact angle dominated region, and the nondeparture region. Numerically simulated critical contact angles that separate the above-mentioned regions agree well with theoretical analyses. The results of this study will contribute to the manipulation of bubble behaviors and the optimal design of working surfaces in a variety of energy systems involving boiling and gas-evolving reaction processes.

Mesoscopic Lattice Boltzmann Modeling of the Liquid-Vapor Phase Transition.

We develop a mesoscopic lattice Boltzmann model for liquid-vapor phase transition by handling the microscopic molecular interaction. The short-range molecular interaction is incorporated by recovering an equation of state for dense gases, and the long-range molecular interaction is mimicked by introducing a pairwise interaction force. Double distribution functions are employed, with the density distribution function for the mass and momentum conservation laws and an innovative total kinetic energy distribution function for the energy conservation law. The recovered mesomacroscopic governing equations are fully consistent with kinetic theory, and thermodynamic consistency is naturally satisfied.

Improved thermal multiple-relaxation-time lattice Boltzmann model for liquid-vapor phase change.

In this paper, an improved thermal multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change. A temperature equation is first derived for liquid-vapor phase change, where the latent heat of vaporization is decoupled with the equation of state. Therefore, the latent heat of vaporization can be arbitrarily specified in practice, which significantly improves the flexibility of the present LB model for liquid-vapor phase change. The Laplacian term of temperature is avoided in the proposed temperature equation and the gradient term of temperature is calculated through a local scheme. To solve the temperature equation accurately and efficiently, an improved MRT LB equation with nondiagonal relaxation matrix is developed. The implicit calculation of the temperature, caused by the source term and encountered in previous works, is avoided by approximating the source term with its value at the previous time step. As demonstrated by numerical tests, the results by the present LB model agree well with analytical results, experimental results, or the results by the finite difference method where the fourth-order Runge-Kutta method is employed to implement the discretization of time.

Lattice Boltzmann simulations of thermal flows beyond the Boussinesq and ideal-gas approximations.

In this work, the recent lattice Boltzmann model with self-tuning equation of state (EOS) [R. Huang et al., J. Comput. Phys. 392, 227 (2019)]JCTPAH0021-999110.1016/j.jcp.2019.04.044 is improved in three aspects to simulate the thermal flows beyond the Boussinesq and ideal-gas approximations. First, an improved scheme is proposed to eliminate the additional cubic terms of velocity, which can significantly improve the numerical accuracy. Second, a local scheme is proposed to calculate the density gradient instead of the conventional finite-difference scheme. Third, a scaling factor is introduced into the lattice sound speed, which can be adjusted to effectively enhance numerical stability. The thermal Couette flow of a nonattracting rigid-sphere fluid, which is described by the Carnahan-Starling EOS, is first simulated, and the better performance of the present improvements on the numerical accuracy and stability is demonstrated. As a further application, the turbulent Rayleigh-Bénard convection in a supercritical fluid slightly above its critical point, which is described by the van der Waals EOS, is successfully simulated by the present lattice Boltzmann model. The piston effect of the supercritical fluid is successfully captured, which induces a fast and homogeneous increase of the temperature in the bulk region, and the time evolution from the initiation of heating to the final turbulent state is analyzed in detail and divided into five stages.

Density gradient calculation in a class of multiphase lattice Boltzmann models.

The multiphase lattice Boltzmann (LB) models based on pairwise interactions show great potential for simulating multiphase flows due to the conceptual and computational simplicity. Although the dynamics of multiphase flows are reproduced by the pairwise interaction force, the gradient of density (or effective density, i.e., pseudopotential) is implicitly involved in these models via the specialized forcing scheme or the consistent scheme for ɛ^{3}-order term. This work focuses on the calculation of density gradient in this class of multiphase LB models. Theoretical analyses are first carried out to reveal the involvement and calculation of density gradient. On the basis of a low Mach number approximation, an improved scheme is then proposed to calculate the density gradient for the recent LB model with self-tuning equation of state. Analytical and numerical calculations show that the improved scheme is more accurate and can help to reduce the numerical error when the reduced temperature is relatively low.

Lattice Boltzmann model with self-tuning equation of state for multiphase flows.

A lattice Boltzmann (LB) model for multiphase flows is developed that complies with the thermodynamic foundations of kinetic theory. By directly devising the collision term for the LB equation at the discrete level, a self-tuning equation of state is achieved, which can be interpreted as the incorporation of short-range molecular interaction. A pairwise interaction force is introduced to mimic the long-range molecular interaction, which is responsible for interfacial dynamics. The derived pressure tensor is naturally consistent with thermodynamic theory, and surface tension and interface thickness can be independently prescribed. Numerical tests, including static and dynamic cases, are carried out to validate the present model and good results are obtained. As a further application, head-on collision of equal-sized droplets is simulated and the elusive "bouncing" regime is successfully reproduced.

Eliminating cubic terms in the pseudopotential lattice Boltzmann model for multiphase flow.

It is well recognized that there exist additional cubic terms of velocity in the lattice Boltzmann (LB) model based on the standard lattice. In this work, elimination of these cubic terms in the pseudopotential LB model for multiphase flow is investigated, where the force term and density gradient are considered. By retaining high-order (≥3) Hermite terms in the equilibrium distribution function and the discrete force term, as well as introducing correction terms in the LB equation, the additional cubic terms of velocity are entirely eliminated. With this technique, the computational simplicity of the pseudopotential LB model is well maintained. Numerical tests, including stationary and moving flat and circular interface problems, are carried out to show the effects of such cubic terms on the simulation of multiphase flow. It is found that the elimination of additional cubic terms is beneficial to reduce the numerical error, especially when the velocity is relatively large. Numerical results also suggest that these cubic terms mainly take effect in the interfacial region and that the density-gradient-related cubic terms are more important than the other cubic terms for multiphase flow.

Lattice Boltzmann model for the correct convection-diffusion equation with divergence-free velocity field.

A lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) with divergence-free velocity field is proposed, and the Chapman-Enskog analysis shows that the CDE can be recovered correctly. In the present model, the convection term is treated as a source term in the lattice Boltzmann equation (LBE) rather than being directly recovered by LBE; thus the CDE is intrinsically solved as a pure diffusion equation with a corresponding source term. To avoid the adoption of a nonlocal finite-difference scheme for computing the convection term, a local scheme is developed based on the Chapman-Enskog analysis. Most importantly, by properly specifying the discrete source term in the moment space, the local scheme can reach the same order (ɛ^{2}) at which the CDE is recovered by a LB model. Numerical tests, including a one-dimensional periodic problem, diffusion of a Gaussian hill, diffusion of a rectangular pulse, and natural convection in a square cavity, are carried out to verify the present model. Numerical results are satisfactorily consistent with analytical solutions or previous numerical results, and show higher accuracy due to the correct recovery of CDE.

Multiblock approach for the passive scalar thermal lattice Boltzmann method.

A multiblock approach for the passive scalar thermal lattice Boltzmann method (TLBM) with multiple-relaxation-time collision scheme is proposed based on the Chapman-Enskog analysis. The interaction between blocks is executed in the moment space directly and an external force term is considered. Theoretical analysis shows that all the nonequilibrium parts of the nonconserved moments should be rescaled, while the nonequilibrium parts of the conserved moments can be calculated directly. Moreover, a local scheme based on the pseudoparticles for computing heat flux is proposed with no need to calculate temperature gradient based on the finite-difference scheme. In order to validate the multiblock approach and local scheme for computing heat flux, thermal Couette flow with wall injection is simulated and good results are obtained, which show that the adoption of the multiblock approach does not deteriorate the convergence rate of TLBM and the local scheme for computing heat flux has second-order convergence rate. Further application of the present approach is the simulation of natural convection in a square cavity with the Rayleigh number up to 109.

[Raman spectroscopic analysis of Paeoniae Radix Alba decoction based on Raman technology].

OBJECTIVE: To test and analyze chemical composition of Paeoniae Radix Alba decoction at molecular level. METHOD: Raman spectra of decoctions prepared from seven batches of Paeoniae Radix Alba pieces, five batches of Paeoniae Radix Alba medicinal material and five batches of Paeoniae Radix Rubra pieces were measured respectively, and the characteristic Raman bands were tentatively assigned. Raman spectra of decoctions were compared and analysed between Paeoniae Radix Alba pieces and Paeoniae Radix Alba medicinal material, Paeoniae Radix Alba pieces and Paeoniae Radix Rubra pieces. RESULT: Nine Raman bands (637, 783, 847, 981, 1 091, 1 128, 1 336, 1 458 and 1 636 cm(-1)) were observed in the Paeoniae Radix Alba pieces decoction. Compared with the decoction of Paeoniae Radix Alba pieces, the Raman bands of 783, 981, 1 128, 1 336 and 1 458 cm(-1) were also exists in Paeoniae Radix Alba medicinal material decoction, meanwhile, the Raman bands of 633 cm(-1) and 1 633 cm(-1) occurs slight frequency shift, however, the bands of 716, 737, 835, 916, 1 072, 1 271 and 1 600 cm(-1) were disappear. In addition, the Raman spectra are quite different between the decoctions of Paeoniae Radix Alba pieces and Paeoniae Radix Rubra pieces. CONCLUSION: The results showed that Raman spectroscopy might provide a novel method for the fast component detection of the Radix Paeoniae Alba decoction or other traditional Chinese medicine.