scholarly journals A Mathematical Model of a Direct Propane Fuel Cell

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Hamidreza Khakdaman ◽  
Yves Bourgault ◽  
Marten Ternan
Keyword(s):  
Mathematical Model ◽  
Fuel Cell ◽  
Current Density ◽  
Concentration Gradient ◽  
Chemical Potential ◽  
Electrical Potential ◽  
Potential Gradient ◽  
Chemical Potential Gradient ◽  
Proton Concentration ◽  
Electrical Potential Gradient

A rigorous mathematical model for direct propane fuel cells (DPFCs) was developed. Compared to previous models, it provides better values for the current density and the propane concentration at the exit from the anode. This is the first DPFC model to correctly account for proton transport based on the combination of the chemical potential gradient and the electrical potential gradient. The force per unit charge from the chemical potential gradient (concentration gradient) that pushes protons from the anode to the cathode is greater than that from the electrical potential gradient that pushes them in the opposite direction. By including the chemical potential gradient, we learn that the proton concentration gradient is really much different than that predicted using the previous models that neglected the chemical potential gradient. Also inclusion of the chemical potential gradient made this model the first one having an overpotential gradient (calculated from the electrical potential gradient) with the correct slope. That is important because the overpotential is exponentially related to the reaction rate (current density). The model described here provides a relationship between the conditions inside the fuel cell (proton concentration, overpotential) and its performance as measured externally by current density and propane concentration.

Failure of Flip-Chip Circuit Interconnects under High Current Density

2010 ◽  
Vol 118-120 ◽  
pp. 449-453
Author(s):  
Yu Dong Lu ◽  
Xiao Qi He ◽  
Yun Fei En ◽  
Xin Wang ◽  
Zhi Qiang Zhuang
Keyword(s):  
Current Density ◽  
Flip Chip ◽  
Chemical Potential ◽  
High Current Density ◽  
Potential Gradient ◽  
High Current ◽  
Wind Force ◽  
Chemical Potential Gradient ◽  
Solder Bumps ◽  
Electron Wind

Both Al interconnects and flip-chip solder bumps were sensitive to high current. The failure mechanism of circuits interconnects would be more complicated if the current density in circuits was exceed the critical magnitudes of electromigration in both Al interconnects and solder bumps. The failure of circuit interconnects under different magnitudes of current density was studied and the interaction of electromigration in solder bumps and Al interconnects was discussed. The circuit interconnects of flip chip show three failure phenomena under high current density: voids in Al final metal, inter-diffusion of Al and SnPb, and melting of solder bumps. The voids in Al metal show the directional diffusion of Al atoms was mainly controlled by the electron wind fore. However the inter-diffusion of Al and SnPb demonstrated the electron wind force to Sn and Pb atoms would be ignored in contrast with chemical potential gradient or intrinsic stress. The flow of Sn and Pb atoms under high current density was in opposite direction with electron wind force and uniform with chemical potential gradient.

scholarly journals Pronounced electromigration of Cu in molten Sn-based solders

2008 ◽  
Vol 23 (1) ◽  
pp. 250-257 ◽  
Author(s):  
J.R. Huang ◽  
C.M. Tsai ◽  
Y.W. Lin ◽  
C.R. Kao
Keyword(s):  
Current Density ◽  
Flip Chip ◽  
Chemical Potential ◽  
High Current Density ◽  
Potential Gradient ◽  
Back Stress ◽  
Molten State ◽  
Electron Current ◽  
Chemical Potential Gradient ◽  
Order Of Magnitude

The high local temperature in flip-chip solder joints of microprocessors has raised concerns that the solder, a low melting temperature alloy, might locally liquefy and consequently cause failure of the microprocessors. This article reports a highly interesting electromigration behavior when the solder is in the molten state. A 6.3 × 103 A/cm2 electron current was applied to molten Sn3.5Ag solder at 255 °C through two Cu electrodes. The high current density caused rapid dissolution of the Cu cathode. The dissolved Cu atoms were driven by electrons to the anode side and precipitated out as a thick, and sometimes continuous, layer of Cu6Sn5. The applied current caused the dissolution rate of the Cu cathode to increase by one order of magnitude. A major difference between the electromigration in the solid and molten state was identified to be the presence of different countering fluxes in response to electromigration. For electromigration in the molten state, the back-stress flux, which was operative for electromigration in the solid state, was missing, and instead a countering flux due to the chemical potential gradient was present. An equation for the chemical potential gradient, dμ/dx, required to balance the electromigration flux was derived to be dμ/dx = N°z*eρJ, where N° is Avogadro’s number, z* is the effective charge of Cu, e is the charge of an electron, ρ is the resistivity of the solder, and J is the electron current density.

Analysis of a Permselective Membrane-Free Alkaline Direct Ethanol Fuel Cell

2013 ◽  
Author(s):  
Jing Huang ◽  
Hafez Bahrami ◽  
Amir Faghri
Keyword(s):  
Fuel Cell ◽  
Ion Transport ◽  
Current Density ◽  
Concentration Gradient ◽  
Potential Gradient ◽  
Cell Voltage ◽  
Alkaline Electrolyte ◽  
Ethanol Fuel ◽  
Direct Ethanol Fuel Cell ◽  
Permselective Membrane

A physical model is developed to study the coupled mass and charge transport in a permselective membrane-free alkaline direct ethanol fuel cell. This type of fuel cell is not only free of expensive ion exchange membranes and platinum based catalysts, but also features a facile oxygen reduction reaction due to the presence of alkaline electrolyte. The proposed model is first validated by comparing its predictions to the experimental results from literature and then used to predict the overall performance of the cell and reveal the details of ion transport, distribution of electrolyte potential and current density. It is found that: (i) KOH concentration lower than 1 M notably impairs cell performance due to low electrolyte conductivity; (ii) the concentration gradient and electrical field are equally important in driving ion transport in the electrolyte; (iii) the current density distributions in the anode and cathode catalyst layers keep non-uniform due to different reasons. In the anode, it is caused by the ethanol concentration gradient, while in the cathode it is because of the electrolyte potential gradient; and (iv) at low cell voltage, current density distribution in the catalyst layer shows stronger non-linearity in the anode than in the cathode.

Analysis of a Permselective Membrane-Free Alkaline Direct Ethanol Fuel Cell

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Jing Huang ◽  
Hafez Bahrami ◽  
Amir Faghri
Keyword(s):  
Fuel Cell ◽  
Ion Transport ◽  
Current Density ◽  
Concentration Gradient ◽  
Potential Gradient ◽  
Cell Voltage ◽  
Alkaline Electrolyte ◽  
Ethanol Fuel ◽  
Direct Ethanol Fuel Cell ◽  
Permselective Membrane

A physical model is developed to study the coupled mass and charge transport in a permselective membrane-free alkaline direct ethanol fuel cell. This type of fuel cell is not only free of expensive ion exchange membranes and platinum based catalysts, but also features a facile oxygen reduction reaction due to the presence of alkaline electrolyte. The proposed model is first validated by comparing its predictions to the experimental results from literature and then used to predict the overall performance of the cell and reveal the details of ion transport, distribution of electrolyte potential and current density. It is found that: (1) KOH concentration lower than 1 M notably impairs cell performance due to low electrolyte conductivity; (2) the concentration gradient and electrical field are equally important in driving ion transport in the electrolyte; (3) the current density distributions in the anode and cathode catalyst layers keep nonuniform due to different reasons. In the anode, it is caused by the ethanol concentration gradient, while in the cathode it is because of the electrolyte potential gradient; and (4) at low cell voltage, current density distribution in the catalyst layer shows stronger nonlinearity in the anode than in the cathode.

A method of determining electrical potential gradient across mitochondrial membrane in perfused rat hearts

1993 ◽  
Vol 265 (2) ◽  
pp. H445-H452 ◽  
Author(s):  
B. Wan ◽  
C. Doumen ◽  
J. Duszynski ◽  
G. Salama ◽  
K. F. LaNoue
Keyword(s):  
Mitochondrial Membrane ◽  
Electrical Potential ◽  
Potential Gradient ◽  
Order Rate Constant ◽  
Isolated Rat Heart ◽  
First Order ◽  
Order Rate ◽  
Rat Hearts ◽  
Perfused Rat Hearts ◽  
Electrical Potential Gradient

The electrical potential gradient across the mitochondrial membrane (delta psi m) in perfused rat hearts was estimated by calculating the equilibrium distribution of the lipophilic cation tetraphenylphosphonium (TPP+), using measured kinetic constants of uptake and release of TPP+. First-order rate constants of TPP+ uptake were measured during 30-min perfusions of intact rat hearts with tracer amounts (5.0 nM) of tritium-labeled TPP+ ([3H]TPP+) in the perfusate. This was followed by a 30-min washout, during which the first-order rate constant of efflux was estimated. Values of [3H]TPP+ outside the heart and total [3H]TPP+ inside the heart at equilibrium were calculated. From this information and separately estimated time-averaged plasma membrane potentials (delta psi c) it was possible to calculate free cytosolic [3H]TPP+ at equilibrium. It was also possible to calculate free intramitochondrial [3H]TPP+ at equilibrium as the difference between total tissue [3H]TPP+ minus free cytosolic TPP+ and the sum of all the bound [3H]TPP+. Bound [3H]TPP+ was determined from [3H]TPP+ binding constants measured in separate experiments, using both isolated mitochondria and isolated cardiac myocytes under conditions where both delta psi m and delta psi c were zero. Delta psi m was calculated from the intramitochondrial and cytosolic free TPP+ concentrations using the Nernst equation. Values of delta psi m were 144.9 +/- 2.0 mV in hearts perfused with 5 mM pyruvate and 118.2 +/- 1.4 mV in hearts perfused with 11 mM glucose, in good agreement with delta psi m obtained from isolated rat heart mitochondria.(ABSTRACT TRUNCATED AT 250 WORDS)

Active sodium transport in toad bladder despite removal of serosal potassium

1965 ◽  
Vol 208 (2) ◽  
pp. 401-406 ◽  
Author(s):  
Alvin Essig
Keyword(s):  
Sodium Transport ◽  
Chemical Potential ◽  
Potential Gradient ◽  
Ringer Solution ◽  
Active Sodium ◽  
Chemical Potential Gradient ◽  
Control Value ◽  
Active Sodium Transport ◽  
Solution Bathing ◽  
Determining Factor

Previous studies have demonstrated that removal of potassium from sodium-Ringer solution bathing the serosal surface of the toad badder depressed net sodium transport to some 5% of control value, whereas with choline-Ringer solution as serosal medium removal of serosal potassium depressed net sodium transport only to some 55% of control value. Although transport is down a chemical potential gradient in the latter situation, it appears to be an active process, for it is depressed by anaerobiosis, and persists against an electrochemical potential gradient. The data suggest that the concentration of potassium at the serosal aspect of the sodium pump is not in itself the rate-determining factor for active sodium transport following removal of serosal potassium.

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