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3.4. DISCUSSION 3. PROPERTIES OF MICRO-DISCHARGES can be rewritten as α = 2fNavgτ ∫ V ∫ Tf ∂nCO dtdV (3.9) ΦCO2τ(1−α) 0 0 ∂t If we assume that, the rate of production of CO is independent of volume (or uniform over the volume of the filament), then α = CO2 avg (1 − α) V CO dt (3.10) ∂t Φ filament 2fN ∫Tf ∂n The constant production across the volume is a major assumption and it is not necessarily true. In the next chapter, it will be shown that along the filament the electron density in- creases, thus the production term changes over the volume. However, to keep the analysis simpler, we can assume an average production rate along the volume. The implications of this assumption will be discussed further in the chapter. The rate of production can be known from the rate coefficient of electron impact dissociation (or an effective rate coefficient primarily depending only on electrons), k1 2fN α = avg ΦCO2 (1 − α) ∫ Tf 0 2 Vfilament k1n′enCO dt (3.11) 0 If we further assume that the change in CO2 density is negligible which is very much valid in the light of low conversions, then it can be brought out of the integral, and can be written in terms of pressure (P ) in the reactor 2fN PV ∫Tf α = avg filament ΦCO2 (1 − α)kT 0 k1n′edt (3.12) this equation can be further transformed into energy consumed in CO production, if the integrand, which is the rate of power transferred into electron impact dissociation is multiplied with the corresponding threshold energy, then α = 2fNavgPVfilament ECO (3.14) ΦCO2 (1 − α)kT εCO If we assume that Vfilament does not change so much and using the definition of resid- ence time, α(1 − α) = 2f Navg τ Vf ilament ECO (3.15) kεCOV 2fN PV ∫Tf α = avg filament k1n′eεCOdt (3.13) here, εCO, is the threshold energy of electron impact dissociation. The integral becomes ΦCO2 (1 − α)kT εCO 0 energy transferred into CO production in one filament, ECO 61PDF Image | Understanding CO2 containing non-equilibrium plasmas
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