Biomod/2013/NanoUANL/Reactor: Difference between revisions
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Mass balance was presented as such: | Mass balance was presented as such: | ||
''' | '''INFLOW= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION | ||
''' | ''' | ||
where | where | ||
Inflow= F<sub>0</sub> | |||
Outflow= F<sub>0</sub>(1-X<sub>S</sub>) | Outflow= F<sub>0</sub>(1-X<sub>S</sub>) | ||
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\frac{4\pi cD_{AB}}{1/r_1=1/r_2} | \frac{4\pi cD_{AB}}{1/r_1=1/r_2} | ||
\ln\frac{x_{B2}}{x_{B1}} | \ln\frac{x_{B2}}{x_{B1}} | ||
</math> | |||
where ''x'' are the fractions, ''c'' is the concentration and ''r'' are the respective radii. | |||
This equation defines the nanoreactor inflow; a similar analysis yields the reactor outflow. | |||
The ionic silver diffusion coefficient in function to the solution is described by Nerst's equation (1888)<sup>1</sup>: | |||
<math>D_{AB}°= | |||
\frac{RT}{F^2} | |||
\frac{\lambda^o_+\lambda^o_-}{\lambda^o_++\lambda^o_-} | |||
\frac{|Z_-|+|Z_+|}{|Z_+Z_-|} | |||
</math> | </math> | ||
where | |||
F = Faraday's constant | |||
D<sub>AB</sub>°=Diffusion coefficient at infinite dilution | |||
λ<sub>+</sub>°=Cationic conductivity at infinite dilution | |||
λ<sub>-</sub>°=Anionic conductivity at infinite dilution | |||
Z<sup>+</sup>=Cation valence | |||
Z<sup>-</sup>=Anionic valence | |||
T=Absolute temperature | |||
Revision as of 23:19, 11 October 2013
What is a reactor?
Introduction
The CCMV capsid was considered as a continuous stirred-tank reactor with accumulation of the product.
For an enzymatic reaction of the type:
[math]\displaystyle{ E + S \leftrightarrow ES \rightarrow E^0 + P }[/math]
with a reaction rate of:
[math]\displaystyle{ \frac{d[ES]}{dt}=k_1[E][S]-k_{-1}[ES]-k_2[ES] }[/math]
We established the following in our system:
- Uniform distribution throughout the reactor
- K-1 >> K1 and K2
- One enzyme per reactor/VLP
- Tortuosity approaches zero during diffusion
Mass balance was presented as such:
INFLOW= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION
where
Inflow= F0
Outflow= F0(1-XS)
Disappearance = V(-rS
Accumulation = [math]\displaystyle{ \tfrac{d[P]}{dt} }[/math]
F0 = F0(1-XS) - V(-rS) + [math]\displaystyle{ \tfrac{d[P]}{dt} }[/math]
The intake and outflow flux were determined by diffusion , considering a spherical container.
For the simplification of the diffusion phenomenon we considered:
- Constant temperature
- Constant pressure
- Species B stays in a stationary state (it does not diffuse in A)
- The container (VLP) has a spherical shape
A mass balance, taking into account a spherical envelope leads to:
[math]\displaystyle{ \frac{d}{dr}(r^2N_{Ar})=0 }[/math]
where NAr represents molar flux. For NBr we obtain:
[math]\displaystyle{ \frac{d}{dr}(r^2\frac{cD_{AB}}{1-x_A}\frac{dx_A}{dr})=0 }[/math]
At a constant temperature the product (cDAB) is equally constant and xA=1-xB, the equation can be integrated into the following expression:
[math]\displaystyle{ F_A=4\pi r_1^2N_{Ar}|_{r=r1}= \frac{4\pi cD_{AB}}{1/r_1=1/r_2} \ln\frac{x_{B2}}{x_{B1}} }[/math]
where x are the fractions, c is the concentration and r are the respective radii.
This equation defines the nanoreactor inflow; a similar analysis yields the reactor outflow.
The ionic silver diffusion coefficient in function to the solution is described by Nerst's equation (1888)1:
[math]\displaystyle{ D_{AB}°= \frac{RT}{F^2} \frac{\lambda^o_+\lambda^o_-}{\lambda^o_++\lambda^o_-} \frac{|Z_-|+|Z_+|}{|Z_+Z_-|} }[/math]
where
F = Faraday's constant DAB°=Diffusion coefficient at infinite dilution λ+°=Cationic conductivity at infinite dilution λ-°=Anionic conductivity at infinite dilution Z+=Cation valence Z-=Anionic valence T=Absolute temperature
