# Biomod/2013/NanoUANL/Reactor

### From OpenWetWare

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where | where | ||

- | F = Faraday's constant | + | *F = Faraday's constant |

- | D<sub>AB</sub>°=Diffusion coefficient at infinite dilution | + | *D<sub>AB</sub>°=Diffusion coefficient at infinite dilution |

- | λ<sub>+</sub>°=Cationic conductivity at infinite dilution | + | *λ<sub>+</sub>°=Cationic conductivity at infinite dilution |

- | λ<sub>-</sub>°=Anionic conductivity at infinite dilution | + | *λ<sub>-</sub>°=Anionic conductivity at infinite dilution |

- | Z<sup>+</sup>=Cation valence | + | *Z<sup>+</sup>=Cation valence |

- | Z<sup>-</sup>=Anionic valence | + | *Z<sup>-</sup>=Anionic valence |

- | T=Absolute temperature | + | *T=Absolute temperature |

+ | |||

+ | Via Joback's method, we obtain the normal boiling temperature: | ||

+ | |||

+ | <math>T_b=\mathbf{198} + \sum_{k} N_k(tbk)</math> | ||

+ | |||

+ | in which ''N<sub>k</sub>'' is the number of times that the contribution occurs in the compound. | ||

+ | |||

+ | Using a similar approach, also by Joback, we estimated the critical temperature: | ||

+ | |||

+ | <math>T_c=T_b\Bigg[ | ||

+ | \mathbf{0.584}+\mathbf{0.965} | ||

+ | \bigg\{\sum_{k} N_k(tck) \bigg\} - | ||

+ | \bigg\{\sum_{k} N_k(tck) \bigg\}^2 | ||

+ | \Bigg]^{-1} | ||

+ | </math> |

## Revision as of 02:37, 12 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:

with a reaction rate of:

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 =

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

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:

where N_{Ar} represents molar flux. For N_{Br} we obtain:

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:

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}:

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

Via Joback's method, we obtain the normal boiling temperature:

in which *N _{k}* is the number of times that the contribution occurs in the compound.

Using a similar approach, also by Joback, we estimated the critical temperature: