(270e) Numerical Simulation of Marangoni Convection with Lattice Boltzmann Method Based On the Field Mediators

The Marangoni convection contributes to the renewal of the interfacial surface and is capable of increasing the mass transfer rate, resulting in the intensification of separation processes such as distillation, extraction, absorption, and desorption. Liquid-liquid mass transfer is showed experimentally dominating in gas-liquid and gad-liquid-solid catalytic reactions, especially in microchannels. Marangoni effect has been extensively studied for the case of liquid-liquid interface [1] and it is a promising topic to make full use of the Marangoni effect to enhance the mass transfer of two-phase flow in microchannels.

Computer fluid dynamics (CFD) can avoid the difficulties in experimental measurements and theoretical solutions. Over the last decade, the lattice Boltzmann method (LBM) has become an established numerical approach in CFD, because of its capability to simulate flow in multiphase systems. In particular, phase segregation and interfacial dynamics, which are essential in multiphase flows and difficult to be simulated by traditional approaches, can be modeled in LBM by the incorporation of molecular interactions. The sharp interface between different immiscible phases can be automatically maintained without any artificial treatment.

Therefore, the goal of this investigation is to gain insight into the mass transfer behaviour at liquid-liquid interfaces in microchannel. To investigate the mass transfer behaviour close to the liquid-liquid interface in microchannel, LBM based on the field mediators has been performed. Santos et al. [2] extended the field mediator concept to the Boltzmann models of immiscible fluids and the obtained predictions were compared with simulation results well. For popular LB methods, the chromodynamic, pseudopotential and the free-energy models can lead to unphysical behavior, such as the spurious current around interfaces, thermodynamic inconsistencies and the lack of Galilean invariance[3]. To some degree, LBM based on the field mediators can avoid the unphysical behavior because the LB model has been tested on its ability in describing the dynamical behaviors of the interface and Galilean invariance.

In a microchannel the mass transfer of different phases relies on the molecular diffusion under laminar flow, thus extraordinarily high efficiency and low liquid velocity are the main characteristics of mass transfer in a microchannel [4]. During the mass transfer process, the temperature gradient and concentration gradient can cause interfacial tension gradient and density gradient, by which Marangoni convection is induced. The treatment of interface between two phases is the most important to simulate accurately the Marangoni effect in microchannel, so the two-phase LB model is capable to deal with interface between two fluids in microchannel.

Now some scientists devoted to simulating the mass transfer process with LBM[5,6] but the numerical simulation of Marangoni effect with LBM is little, and it is far less than that of Marangoni effect caused by interfacial tension by other numerical methods.

In this paper, the Marangoni effect induced by interfacial tension gradient in the liquid-liquid two-phase system was investigated with LBM based on the field mediators. We first added the convection-diffusion equation of mass transfer into the two-phase LB model based on the field mediators, which describe accurately the dynamical behavior of the interface and Galilean invariance. The two-phase LB model coupled the convection-diffusion equation can capture the mass transfer and flow behavior on the interface between two phases. The influence of various process parameters (diffusion coefficients, concentrations, velocities and geometry) on the mass transfer was also explored. The quantitative numerical results of Marangoni convection induced by the interfacial tension gradient in the mass process was carried out and discussed in terms of mixing between two fluids to provide the flow information by comparison with the published data. The paper explored the influence of Marangoni effect on the mass transfer in two-phase systems and is helpful to explain the mechanism of that Marangoni effect induced by mass transfer.

References

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[2]. L. O. E. Santos, P. C. Facin, P. C. Philippi, Lattice-Boltzmann model based on field mediators for immiscible fluids, Phys. Rev. E., 2003, 68: 056302

[3]. X. Y. He, S. Y. Chen, R. Y. Zhang, A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh?Taylor instability, J. Comput. Phys., 1999, 152: 642

[4]. Z. Yu, H. Orin, L. S Fan, Experiment and lattice Boltzmann simulation of two-phase gas-liquid flows in microchannels, Chem. Eng. Sci., 2007, 62: 7172

[5]. Q. M. Chang, J. I. D. Alexander, Study of Marangoni-natural convection in a two-layer liquid system with density inversion using a lattice Boltzmann model, Physics of Fluids, 2007, 19: 102107

[6]. J. Chen, X. F. Peng, D. J. Lee, Diffusion coefficient of Brownian particle in rough micro-channel, J. Colloid Interface Sci., 2006, 296: 737