Biomod/2013/NanoUANL/Reactor: Difference between revisions
(New page: == 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 ty...) |
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== What is a reactor? == | == What is a reactor? == | ||
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Mass balance was presented as such: | Mass balance was presented as such: | ||
'''INTAKE= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION | |||
''' | |||
where | where | ||
Intake= F<sub>0</sub> | |||
Outflow= F<sub>0</sub>(1-X<sub>S</sub>) | |||
Disappearance = V(-r<sub>S</sub> | Disappearance = V(-r<sub>S</sub> | ||
Accumulation = <math>\tfrac{d[P]}{dt}</math> | Accumulation = <math>\tfrac{d[P]}{dt}</math> | ||
F<sub>0</sub> = F<sub>0</sub>(1-X<sub>S</sub>) - V(-r<sub>S</sub>) + <math>\tfrac{d[P]}{dt}</math> | |||
The intake and outflow flux were determined by diffusion , considering a spherical container. | |||
[[Image:CCMV2.jpg]] | |||
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>\frac{d}{dr}(r^2N_{Ar})=0</math> | |||
where N<sub>Ar</sub> represents molar flux. For N<sub>Br</sub> we obtain: | |||
<math>\frac{d}{dr}(r^2\frac{cD_{AB}}{1-x_A}\frac{dx_A}{dr})=0</math> | |||
At a constant temperature the product (cD<sub>AB</sub>) is equally constant and x<sub>A</sub>=1-x<sub>B</sub>, the equation can be integrated into the following expression: | |||
<math>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> | |||
Revision as of 22:45, 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:
INTAKE= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION
where
Intake= 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]
