Concentration polarization current density calculation

For a solution of differential equations (18.12) and (18.15) and for a quantitative calculation of the current distribution, we must know how the current density depends on polarization at constant reactant concentrations or on reactant concentrations at constant polarization. We must also formulate the boundary conditions. Examples of such calculations are reported below. 

A. A dilute Na2S04 solution is to be electrolyzed with a pair of smooth Pt electrodes at a current density of 100 A An2 and a current of 0.100 A. The products are H2(g) and Oz(g) at 1.00 bar. Calculate the required voltage if the cell resistance is 2.00 il and there is no concentration polarization. What would your answer be if the Pt electrodes were replaced by Au electrodes ... 

The concentration polarization occurring in electrodialysis, that is, the concentration profiles at the membrane surface can be calculated by a mass balance taking into account all fluxes in the boundary layer and the hydrodynamic conditions in the flow channel between the membranes. To a first approximation the salt concentration at the membrane surface can be calculated and related to the current density by applying the so-called Nernst film model, which assumes that the bulk solution between the laminar boundary layers has a uniform concentration, whereas the concentration in the boundary layers changes over the thickness of the boundary layer. However, the concentration at the membrane surface and the boundary layer thickness are constant along the flow channel from the cell entrance to the exit. In a practical electrodialysis stack there will be entrance and exit effects and concentration... 

Investment costs in electrodialysis with bipolar membranes Investment costs include nondepreciable items such as land and depreciable items such as the electrodialysis stacks, pumps, electrical equipment, and monitoring and control devices. The investment costs are determined mainly by the required membrane area for a certain plant capacity. The required membrane area for a given capacity plant can be calculated from the current density in a stack that is in electrodialysis with a bipolar membrane not limited by concentration-polarization effects. The required membrane area for a given plant capacity is given by ... 

At the transition between the two current density ranges, the polarization curve for Cu deposition starts diverging from the calculated Tafel curve. This divergence was attributed to the transition from charge transfer to concentration overvoltage control of the copper reduction. It was concluded from these results that the reduction at the cathode surface of metal ions adsorbed on the particles plays a fundamental role in the codeposition mechanism. 

Figure 4. Calculated TE polarized modal gain Figure 5. Calculated TE polarized modal gain Gmod versus carrier concentration Nso (cm ) for Gmod versus total current density J,ot for the the dilute-N " W" and "M" laser structures at RT. dilute-N "W" and "M" laser structures at RT.

The polarization para mater i im/N can be calculated next. During the experiments to determine ilinl, data may be taken on voltage, corrent, membrane area, and number of cell pairs in the experimental slack. The cell-pair voltage can be determined for various values of concentration JV, and current density i. and curves of (p versus i for various values of N can be prepared. The entreat efficiency to he expected in large-scale use can be calculated from the experiments to determine i,im ... 

An intrinsic time-dependent one-dimensional (ID) model and a macro two-dimensional (2D) model for the anode of the DMFC are presented in [178]. The two models are based on the dual-site mechanism, which includes the coverage of intermediate species of methanol, OH, and CO on the surface of Pt and Ru. The intrinsic ID model focused on the analysis of the effects of operating temperature, methanol concentration, and overpotential on the transient response. The macro 2D model emphasizes the dimensionless distributions of methanol concentration, overpotential and current density in the CL which were affected by physical parameters such as thickness, specific area, and operating conditions such as temperature, bulk methanol concentration, and overpotential. The models were developed and solved in the PDEs module of COMSOL Multiphysics, giving good agreement with experimental data. The dimensionless distributions of methanol concentration, overpotential, and current density and the efficiency factor were calculated quantitatively. The models can be used to give accurate simulations for the polarizations of methanol fuel cell. 

Ri, the internal resistance, is a critical parameter and it can be calculated from electrical characterization of an MFC. A polarization curve measurement is a popular method to extract / ,. An example of polarization curve is shown in Fig. 3. At low current density, activation resistance dominates, and the voltage across external load drops very fast with the increase of current. When the current density increases to be an intermediate range, the voltage versus current profile becomes approximately linear, indicating ohmic resistance dominates. As the current density further increases, the increase rate slows down and the voltage drops quickly this is because the concentration resistance dominates. 

Polarization curves for the average values for the copper deposition have been successfully calculated from the stationary polarization curve using Eq. (4.35) for [18]. This is good evidence that in PO deposition, the average current density also determines the surface concentration of the depositing ion. 

The chemical passivation of a rotating stainless steel cylinder immersed in an acidic solution is studied as Fe ions are gradually added to the solution. The Fe " ions are reduced to Fe " " at the limiting current as the metal corrodes. The radius of the cylinder is 2 cm, and the rotation rate is 1000 rpm. The diffusion coefficient of the Fe " ions is equal to 0.7 x 10 cm s the cinematic viscosity of the solution is v = 0.011 cm s In the absence of Fe , the anodic polarization curve indicates a passivation current density of L = 30 mA cm , independent of the rotation rate. Calculate the concentration of Fe " " required to passivate the alloy. 

In the electrolytic cell, the cupric ions and sulfate ions both contribute to the conduction mechanisms. But only cupric ions enter into the electrode reaction and pass through the electrode-solution interface. The electrode therefore acts like a semipermeable membrane which is permeable to the Cu ions but impermeable to the 80 ions. Anions accumulate near the anode and become depleted near the cathode, resulting in concentration gradients in the solution near the electrodes of both ions. This is termed as concentration polarization. Let us determine the current-voltage characteristic of the cell, that is, the concentration polarization. To do this, we must calculate the flux of metal ions (cations) arriving at the cathode and depositing on it. We assume that the overall rate of the electrode reaction is determined by this flux. Once the cation distribution is known, the potential drop can be calculated. Note that anions are effectively motionless and do not produce a current. Let us assume that electrodes of the electrolytic cell are infinite planes at the anode (y = 0) and cathode (y = h) (Figure 6.3). The electrolyte velocity is zero. The definition of the current densities is... 

The pK of the equilibrium sulfite/bisulfite, i.e., the pK2 of sulfurous acid, is 7.2 from data reported in Wagman et al. [48]. The equilibrium concentration of the two ionic species can be readily calculated showing that the bisulfite ion is increasingly present in sulfite solution as the pH drops below about 9.0. This observation could explain the observed increase of the limiting current density with lowering pH and eventually allowed to ascribe the wave in the polarization curve to the cathodic reduction of bisulfite. 

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