Thermohaline convection (THC) in porous media is frequently investigated using the problem of porous enclosure. Most of the existing modeling-based studies are limited to 2-D simulations, because 2-D assumption is widely used to deal with computational requirement of 3-D numerical solutions. Analytical solutions serve as an alternative to deal with computational requirement of numerical solutions. Existing analytical solutions of THC are mostly limited to 2-D and also under steady-state regime. In this work, we develop a meshless 3-D semianalytical solution for the problem of THC in a porous box under crossed thermal and solute gradients, for both steady state and transient regimes. The semianalytical solution is developed using the Fourier series (FS) method applied to the vector potential form of the governing equations. The extension to transient solutions represents an important technical feature of this work, as the applications of the FS method to density-driven problems have been limited to steady-state conditions. The FS solution is validated against a finite element solution obtained using COMSOL Multiphysics. Numerical experiments show the worthiness of the developed FS solution as a benchmark because it clearly allows making distinction between different numerical techniques. The effects of governing parameters on three-dimensional THC have not been investigated previously. We perform a detailed parameter sensitivity analysis to address this gap. A vortex convective flow is observed and the orientation and intensity of the flow is sensitive to the gravity number. The increase in the temperature gradient reduces the salinity flux.
In multispecies electrolyte solutions, each individual species can migrate according to its specific ionic properties. This process is called electrochemical migration or electro-diffusion and is well-described by the Nernst–Planck equation. The common approach for solving the corresponding mathematical system is based on the null current (NC) assumption, which expresses the electric potential in terms of charges and concentrations of chemical components. This assumption has a great advantage as it eliminates the electric potential from the Nernst–Planck equation. However, the NC assumption has limited capacities in describing electro-diffusion processes when the domain is subjected to an external electric field. The validity of the NC assumption could be questionable, even in the absence of an external electric field. This topic has never been investigated in the past. The main goal of this work is to evaluate the validity of the NC assumption and to understand its effect on the model outputs. Thus, we present a new reactive transport model that allows for a reliable representation of the electrochemical migration process. This model is based on the Nernst–Planck and Poisson (NPP) equations which are solved together. We also implement a model based on the NC assumption. Both models have been validated by comparison with CrunchFlow, based on several benchmarks. The results show that in the case of high sorptivity, the NC assumption is no longer valid. Therefore, in the case of sorption processes, the NPP should be used to simulate coulombic interactions.
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