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

Line 22: | Line 22: | ||

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>) | ||

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}>> K_{1}and K_{2} - One enzyme per reactor/VLP
- Tortuosity approaches zero during diffusion

Mass balance was presented as such:

**INFLOW= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION**

where

Inflow= F_{0}

Outflow= F_{0}(1-X_{S})

Disappearance = V(-r_{S}

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}}**

F_{0} = F_{0}(1-X_{S}) - V(-r_{S}) + **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.

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 N_{Ar} represents molar flux. For N_{Br} 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 (cD_{AB}) is equally constant and x_{A}=1-x_{B}, 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
D_{AB}°=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