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

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This equation defines the nanoreactor inflow; a similar analysis yields the reactor outflow. | 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>: | The ionic silver diffusion coefficient in function to the solution is described by Nerst's equation (1888)<sup>1</sup>: | ||

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

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in which ''N<sub>k</sub>'' is the number of times that the contribution occurs in the compound. | 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: | Using a similar approach, also by Joback, we estimated the critical temperature: | ||

Line 99: | Line 105: | ||

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

</math> | </math> | ||

+ | |||

+ | Tabla .- Joback Method Contributions (C1 Prausnitz) | ||

+ | |||

+ | [TABLA] | ||

+ | |||

+ | ---- | ||

+ | |||

+ | Conductivity was determined by the Sastri method: | ||

+ | |||

+ | <math>\lambda_L=\lambda_ba^m</math> | ||

+ | |||

+ | where | ||

+ | λ<sub>L</sub> = thermic conductivity of the liquid [ W/(m·K)] | ||

+ | λ<sub>b</sub> = thermic conductivity at normal boiling point | ||

+ | ''T<sub>br</sub>''= ''T/T<sub>c</sub>'' = reduced temperature | ||

+ | ''T<sub>c</sub>'' = critical temperature, K | ||

+ | |||

+ | |||

+ | <math>m=1-\bigg(\frac{1-T_r}{1-T_{br}}\bigg)^n</math> |

## Revision as of 22:46, 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

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

**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 T_b=\mathbf{198} + \sum_{k} N_k(tbk)}**

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:

**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 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} }**

Tabla .- Joback Method Contributions (C1 Prausnitz)

[TABLA]

Conductivity was determined by the Sastri method:

**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 \lambda_L=\lambda_ba^m}**

where
λ_{L} = thermic conductivity of the liquid [ W/(m·K)]
λ_{b} = thermic conductivity at normal boiling point
*T _{br}*=

*T/T*= reduced temperature

_{c}*T*= critical temperature, K

_{c}

**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 m=1-\bigg(\frac{1-T_r}{1-T_{br}}\bigg)^n}**