Numerical Investigation for The Valorization of Waste from HMD Cell Using Electrodialysis

The Hydromagnetic desalination (HMD) system is a continuous process with several advantages, including a high water recovery ratio, and can be favored economically by producing several industrial byproducts instead of discharging the highly concentrated brine to the environment. In the current work, the ions concentration in the Electrodialysis (ED) technique is simulated using COMSOL Multiphysics V.5.2 software. The ED cell simulated in this paper contains two selective membranes (anion and cation) with a width of 0.25 mm each. The salt is to be taken away in the middle domain. The cell operation has been simulated to separate the sodium and chlorine ions from the HMD brine waste solution at 40 or 55ºC temperatures at different voltages and concentrations. In this two-dimensional model, the Nernst-Plank equation has been used to describe ion flux and charge transport in the electrolyte solution. Secondary current distribution theory and the electroneutrality condition have been used in the mathematical model. Finally, Donnan equations have been used to provide the exact fulfillment of boundary conditions for constant voltage mode. The simulation shows that the highest efficiency is obtained at high temperatures and voltage with the lowest feed concentration. Finally, the results have been validated using experimental data from the literature, and a satisfying agreement has been found.

Multiphasic Finite Element Framework for Modeling Hydrated Mixtures With Multiple Neutral and Charged Solutes

Computational tools are often needed to model the complex behavior of biological tissues and cells when they are represented as mixtures of multiple neutral or charged constituents. This study presents the formulation of a finite element modeling framework for describing multiphasic materials in the open-source finite element software febio.1 Multiphasic materials may consist of a charged porous solid matrix, a solvent, and any number of neutral or charged solutes. This formulation proposes novel approaches for addressing several challenges posed by the finite element analysis of such complex materials: The exclusion of solutes from a fraction of the pore space due to steric volume and short-range electrostatic effects is modeled by a solubility factor, whose dependence on solid matrix deformation and solute concentrations may be described by user-defined constitutive relations. These solute exclusion mechanisms combine with long-range electrostatic interactions into a partition coefficient for each solute whose value is dependent upon the evaluation of the electric potential from the electroneutrality condition. It is shown that this electroneutrality condition reduces to a polynomial equation with only one valid root for the electric potential, regardless of the number and valence of charged solutes in the mixture. The equation of charge conservation is enforced as a constraint within the equation of mass balance for each solute, producing a natural boundary condition for solute fluxes that facilitates the prescription of electric current density on a boundary. It is also shown that electrical grounding is necessary to produce numerical stability in analyses where all the boundaries of a multiphasic material are impermeable to ions. Several verification problems are presented that demonstrate the ability of the code to reproduce known or newly derived solutions: (1) the Kedem–Katchalsky model for osmotic loading of a cell; (2) Donnan osmotic swelling of a charged hydrated tissue; and (3) current flow in an electrolyte. Furthermore, the code is used to generate novel theoretical predictions of known experimental findings in biological tissues: (1) current-generated stress in articular cartilage and (2) the influence of salt cation charge number on the cartilage creep response. This generalized finite element framework for multiphasic materials makes it possible to model the mechanoelectrochemical behavior of biological tissues and cells and sets the stage for the future analysis of reactive mixtures to account for growth and remodeling.

Joule Heating Effect in Constant Voltage Mode Isotachophoresis in a Microchannel

Microchip ITP (isotachophoresis) is getting popularity as a preparative technique for preconcentration and separation of chemical species and/or ions in liquid phase. In constant voltage mode ITP, generally a high electric potential difference is applied to a discontinuous buffer for faster and higher resolution separation. However, the higher current from the applied electric field induces Joule heating in the buffer which modifies the mobility and diffusion coefficient of analytes in the system. This change in mobility and diffusion coefficient strongly influences the transient separation process in ITP. In this study the effect of Joule heating on separation behavior of analyte compounds has been presented in a constant voltage mode ITP where two chemical species are separated from an initial mixture. The model is based on mass, energy, and charge conservation and electroneutrality condition in the system. A set of nonlinear governing equations are solved numerically for temperature dependent properties such as diffusion coefficient, effective electrophoretic mobility, and thermal conductivity using a finite volume based model. Numerical results suggest that for temperature dependent properties of control parameters, the separation speed of analytes is significantly different from that of constant temperature case. In constant voltage mode ITP, the temperature peak forms at the location of trailing electrolyte, and its influence propagates toward the direction of band movement as separation proceeds.

Modeling and Simulation of pH Dependent Isotachophoresis

This paper presents a mathematical model for pH gradient ITP in a microfluidic system. The mathematical model is based on mass conservation, charge conservation and electroneutrality condition in the system. A finite volume based numerical model is developed to simulate pH dependent isotachophoresis (ITP) in microfluidic devices. Numerical results of pH dependent ITP are obtained for straight and dog-leg microchannels. For both channels, five ionic components are used to simulate the model ITP system. The ITP results obtained from dog-leg microchannel capture the band broadening and band dispersion observed in T-channel junction. However, no such dispersion is noticed for ITP in the straight microchannel.