User:Nseidm1

Hello
My full name is Noah Seidman. I went to Hofstra University, on Long Island, in New York State for Electrical Engineering. I'm on a Wikibreak putting my computer in a time locked safe.

Brown's Gas
I do not retail. I am a consultant.

Voltage Analysis


||   ||rowspan=4| where
 * $$V_\mathrm{cell} = \frac{1}{2} \cdot V_\mathrm{in}$$
 * Vin is the voltage across the entire electrolyzer. This is specifically for a 2 cell electrolyzer.


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A more general form of the above expression can utilize a variable to represent the total number of cells.



||   ||rowspan=4| where
 * $$V_\mathrm{cell} = \frac{R}{X \cdot R} \cdot V_\mathrm{in}$$
 * R is the resistance of the electrolyte solution measured in ohms,
 * and X is the total number of cells in the electrolyzer.


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The above equation can be simplified by dividing both the numerator and denominator by R.



||   ||rowspan=4| where
 * $$V_\mathrm{cell} = \frac{1}{X} \cdot V_\mathrm{in}$$
 * X is the total number of cells in the electrolyzer.


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Then by multiplying the numerator by Vin the equation becomes:



||   ||rowspan=4| where
 * $$V_\mathrm{cell} = \frac{V_\mathrm{in}}{X}$$
 * X is still the total number of cells in the electrolyzer.


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Vtotal is Vcell times the number of cells, which will be equal to Vin:



||   ||rowspan=4| where
 * $$V_\mathrm{total} = V_\mathrm{cell} \cdot X = V_\mathrm{in}$$
 * X is still the total number of cells in the electrolyzer.


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Current Analysis
Utilizing a capacitor in series effectively established a maximum magnitude of current flow.



where
 * $$I_\mathrm{max} = C\frac{dV_\mathrm{in}}{dt}$$ ||   ||rowspan=4|
 * I is the current flowing in the conventional direction, measured in amperes,
 * dVin/dt is the time derivative of voltage, measured in volts per second, and
 * C is the capacitance in farads.


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For example: if you want to set the maximum current flow then the following equation is useful:



where
 * $$C = \frac{I_\mathrm{max}}{{dV_\mathrm{in}}/{dt}}$$ ||   ||rowspan=4|
 * dVin/dt is still the time derivative of voltage, measured in volts per second, and
 * C is the capacitance in farads.


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The period of a signal is inversely proportional to the frequency, therefore the value of the capacitor can be expressed as follows:



where
 * $$C = \frac{I_\mathrm{max}}{V_\mathrm{in} \cdot f}$$ ||    ||rowspan=4|
 * C is the capacitance in farads,
 * Vin is the voltage input, and
 * f is the frequency of the input voltage signal.


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Power Analysis
Overall the total power delivered to each individual cell can be express as:



||   ||rowspan=4| where
 * $$P_\mathrm{cell} = \frac{V_\mathrm{in}}{X} \cdot C\frac{dV_\mathrm{in}}{dt}$$
 * Pcell is the total power delivered to each individual cell,
 * Vin is the voltage input,
 * dVin/dt is still the time derivative of voltage, measured in volts per second,
 * R is the resistance of the electrolyte solution, and
 * X is the total number of cells in the electrolyzer.


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Simplifying the above equation results in:



||   ||rowspan=4| where
 * $$P_\mathrm{cell} = \frac{V_\mathrm{in} \cdot C}{X} \cdot \frac{dV_\mathrm{in}}{dt}$$
 * Pcell is the total power delivered to each individual cell,
 * Vin is the voltage input,
 * dVin/dt is still the time derivative of voltage, measured in volts per second, and
 * X is the total number of cells in the electrolyzer.


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Using the frequency of Vin results in:



||   ||rowspan=4| where
 * $$P_\mathrm{cell} = \frac{V_\mathrm{in}^2 \cdot C \cdot f}{X}$$
 * Pcell is the total power delivered to each individual cell,
 * Vin is the voltage input,
 * C is the capacitance in farads,
 * X is the total number of cells in the electrolyzer, and
 * f is the frequency of Vin.


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The total power consumed by the electrolyzer is:



||   ||rowspan=4| where
 * $$P_\mathrm{total} = P_\mathrm{cell} \cdot X$$
 * Ptotal is the total power consumed by the electrolyzer,
 * Pcell is the power delivered to each cell, and
 * X is the total number of cells in the electrolyzer.


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Therefore Ptotal equals:



||   ||rowspan=4| where
 * $$P_\mathrm{total} = V_\mathrm{in}^2 \cdot C \cdot f$$
 * Vin is magnitude of the input voltage,
 * C is chosen value of the amperage limiting capacitor, and
 * f is the frequency of Vin.


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The units for C, as shown above are Imax divided by Vin times f; therefore after substitution the equation is shown to be mathematically consistent:



||   ||rowspan=4| where
 * $$P_\mathrm{total} = V_\mathrm{in} \cdot I_\mathrm{max}$$
 * Vin is magnitude of the input voltage, and
 * Imax I the maximum amount of current passing through the capacitor in series.


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Math Talk
There is an exponential proportionality between Vin and Pcell, therefore minimizing Vin is important to mitigate power consumption. If the electrolyzer is connected to a high voltage source, compensation can be achieved by making X significantly large; because Pcell is inversely proportional to X, as the number of cells increase the total power delivered, to each cell, will decrease linearly. Although since there is a proportional relationship between X and Ptotal minimizing the number of cells is also encouraged to mitigate power consumption.

There is a proportional relationship between the frequency of Vin and Pcell, therefore lower frequencies are encouraged to mitigate power consumption. Although there is a proportional relationship between Imax and the frequency of Vin, therefore increasing the frequency is also encouraged to increase gas production.

What is clearly observed is a balancing act; it is both encouraged and discouraged, to increase and decrease various parameters.

Efficiency Analysis
When an electrolyzer operates for a substantial period of time the electrolyte solution will increase in temperature. As temperature increases the resistance of the electrolyte solution decreases. Considering Ohm's Law As the resistance of the electrolyte solution decreases there will be a proportional decrease in Vin or an increase in Imax. Since Imax is a limited value, and cannot increase due to the nature of a capacitor, Vin must decrease. Because electrolysis is a current driven reaction, and no change in Imax can be experienced, the same quantity of gas has to be produced. The same quantity of gas production, coupled with a decrease in Vin results in efficiency improvement.

Discussion


There is much about water that is yet to be understood. Research has been conducted Dr. Anders Nilsson, of Stanford University, who:

used X-ray absorption spectroscopy and X-ray Raman scattering to probe water in the range 25º C to 90º C. The findings showed that at room temperature 80% of molecules form only two strong hydrogen bonds, and that this rises to 85% at 90º C. This arrangement of water molecules is very different from that in ice structures where they form four hydrogen bonds. Paper #6 indicates that liquid water consist mainly of chains and rings, held together by these two strong hydrogen bonds and embedded in a disordered cluster network of water molecules connected by weak hydrogen bonds.

The purpose of Dr. Anders Nilsson is "to measure how the water X-ray spectra change with variations in the thermodynamic or chemical conditions, and eventually to obtain a more detailed understanding" of water's properties. "Instead of settling into a crinkly layer, as researchers had thought, x-ray experiments show that water molecules form a plane of "flat ice" on a platinum surface".