Hybridized method of pseudopotential lattice Boltzmann and cubic-plus-association equation of state assesses thermodynamic characteristics of associating fluids

It is crucial to properly describe the associating fluids in terms of phase equilibrium behaviors, which are needed for design, operation, and optimization of various chemical and energy processes. Pseudopotential lattice Boltzmann method (LBM) appears to be a reliable and efficient approach to study thermodynamic behaviors and phase transition of complex fluid systems. However, when cubic equations of state (EOSs) are incorporated into single-component multiphase LBM, simulation results are not well matched with experimental data. This study presents the utilization of cubic-plus-association (CPA) EOS in the LBM structure to obtain more accurate modeling results for associating fluids. An approach based on the global search optimization algorithm is introduced to find the optimal association parameters of CPA EOS for water and primary alcohols in the lattice units. The thermodynamic consistency is verified by the Maxwell construction and is also improved by the forcing scheme of [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)]. The spurious velocity is reduced with increasing isotropy in the gradient operator. Furthermore, an extended version of CPA EOS is introduced, which increases the system stability at low reduced temperatures. There is a very good match between the LBM results and experimental data, confirming the reliability of the model developed in the present study. The introduced approach has potential to be employed for simulating transport phenomena and interfacial characteristics of associating fluids in porous systems.

Figure 1

Experimental and modeling approaches to investigate transport phenomena in porous media, modified after Refs. [1, 2]. (QMS is the quantum molecular simulation; MD is the molecular-dynamic simulation; DSMC refers to the direct simulation Monte Carlo; DPD is the dissipative particle dynamics; LBM refers to the lattice Boltzmann method; DNS is the direct numerical simulation; LES represents the large eddy simulation; RANS refers to the Reynolds-averaged Navier-Stokes; TEM is the transmission electron microscopy; and SEM denotes the scanning electron microscope.) (The scale of methods is shown approximately and there are overlaps between different methods.)

Figure 2

Different orders of isotropy in 2D domain. The value of weights is determined by the size and color of grids.

Figure 3

Simple sketch of (a) a 4C model of water molecules and (b) a 2B model of alcohols.

Figure 4

Work flow for association parameters optimization.

Figure 5

Fluctuations of the maximum spurious velocity at different time steps.

Figure 6

Comparison of coexistence curves based on LBM simulations and Maxwell construction.

Figure 7

Comparison between the reduced densities of the gas phase of the coexistence phases determined from the LBM simulation and Maxwell construction when PR and CPA EOSs are employed.

Figure 8

Reduced density of both liquid and gas phases versus reduced temperature based on LBM simulations and Maxwell construction when the Li et al. forcing scheme is employed.

Figure 9

Variation of the maximum magnitude of spurious velocity with (a) reduced temperature and (b) density ratio for the CPA and PR EOSs.

Figure 10

Velocity field and contour for a static droplet on the basis of (a) Li et al. and (b) SC forcing schemes.

Figure 11

Comparison of the values of saturated water density obtained from experiments and LBM strategy based on CPA and PR EOSs.

Figure 12

Coexistence curves results of the LBM simulation and Maxwell equal area construction with eighth order of isotropy in the discrete gradient operator.

Figure 13

The pressure difference ($\mathrm{\Delta }p$) against 1/$r$ for water at $T_r=0.7929$.

Figure 14

Interfacial tension versus the reduced temperature in the lattice units for water.

Figure 15

Workflow of Maxwell construction while utilizing CPA EOS (RE stands for the relative error).