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In this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.

Even though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.

The numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.

The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.

For the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).

This study aims at developing a comprehensive model for the analysis of electro-osmotic flow (EOF) through a fluid-saturated porous medium. To fully understand and exploit a number of applications, such a model for EOF through porous media is essential.

The proposed model is based on a generalised set of governing equations used for modelling flow through fluid saturated porous media. These equations are modified to incorporate appropriate modifications to represent electro-osmosis (EO). The model is solved through the finite element method (FEM). The validity of the proposed numerical model is demonstrated by comparing the numerical results of internal potential and velocity distribution with corresponding analytical expressions. The model introduced is also used to carry out a sensitivity analysis of the main parameters that control EOF.

The analysis carried out confirms that EO in free channels without porous obstruction is effective only at small scales, as largely discussed in the available literature. Using porous media makes EO independent of the channel scale. Indeed, as the channel size increases, the presence of the charged porous medium is essential to induce fluid flow. Moreover, results demonstrate that flow is significantly affected by the characteristics of the porous medium, such as particle size, and by the zeta potential acting on the charged surfaces.

To the best of the authors’ knowledge, a comprehensive FEM model, based on the generalised equations to simulate EOF in porous media, is proposed here for the first time.

This paper aims to provide a comprehensive literature review on modelling electro-osmotic flow in porous media.

Modelling electro-osmosis in fluid systems without solid particles has been first introduced. Then, after a brief description of the existing approaches for porous media modelling, electro-osmotic flow in porous media has been considered by analysing the main contributions to the development of this topic.

The analysis of literature has highlighted the absence of a universal model to analyse electro-osmosis in porous media, whereas many different methods and assumptions are used.

For the first time, the existing approaches for modelling electro-osmotic flow in porous have been collected and analysed to provide detailed indications for future works concerning this topic.