Difference between revisions of "Biomod/2013/NanoUANL/Reactor"

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Line 22: Line 22:
 
Mass balance was presented as such:
 
Mass balance was presented as such:
  
'''INTAKE= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION
+
'''INFLOW= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION
 
'''
 
'''
  
 
where
 
where
  
Intake= F<sub>0</sub>
+
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>)
Line 61: Line 61:
 
\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 22:19, 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle E + S \leftrightarrow ES \rightarrow E^0 + P}

with a reaction rate of:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{d[ES]}{dt}=k_1[E][S]-k_{-1}[ES]-k_2[ES]}

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 = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \tfrac{d[P]}{dt}}

F0 = F0(1-XS) - V(-rS) + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \tfrac{d[P]}{dt}}

The intake and outflow flux were determined by diffusion , considering a spherical container.

File: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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{d}{dr}(r^2N_{Ar})=0}

where NAr represents molar flux. For NBr we obtain:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{d}{dr}(r^2\frac{cD_{AB}}{1-x_A}\frac{dx_A}{dr})=0}

At a constant temperature the product (cDAB) is equally constant and xA=1-xB, the equation can be integrated into the following expression:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\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}} }

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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle D_{AB}°= \frac{RT}{F^2} \frac{\lambda^o_+\lambda^o_-}{\lambda^o_++\lambda^o_-} \frac{|Z_-|+|Z_+|}{|Z_+Z_-|} }

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