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

## 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:

${\displaystyle E+S\leftrightarrow ES\rightarrow E^{0}+P}$

with a reaction rate of:

${\displaystyle {\frac {d[ES]}{dt}}=k_{1}[E][S]-k_{-1}[ES]-k_{2}[ES]}$

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 = ${\displaystyle {\tfrac {d[P]}{dt}}}$

F0 = F0(1-XS) - V(-rS) + ${\displaystyle {\tfrac {d[P]}{dt}}}$

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:

${\displaystyle {\frac {d}{dr}}(r^{2}N_{Ar})=0}$

where NAr represents molar flux. For NBr we obtain:

${\displaystyle {\frac {d}{dr}}(r^{2}{\frac {cD_{AB}}{1-x_{A}}}{\frac {dx_{A}}{dr}})=0}$

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

${\displaystyle F_{A}=4\pi r_{1}^{2}N_{Ar}|_{r=r1}={\frac {4\pi cD_{AB}}{1/r_{1}=1/r_{2}}}\ln {\frac {x_{B2}}{x_{B1}}}}$

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:

$\displaystyle D_{AB}°= \frac{RT}{F^2} \frac{\lambda^o_+\lambda^o_-}{\lambda^o_++\lambda^o_-} \frac{|Z_-|+|Z_+|}{|Z_+Z_-|}$

where

• 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

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

${\displaystyle T_{b}=\mathbf {198} +\sum _{k}N_{k}(tbk)}$

in which Nk is the number of times that the contribution occurs in the compound.

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

${\displaystyle T_{c}=T_{b}{\Bigg [}\mathbf {0.584} +\mathbf {0.965} {\bigg \{}\sum _{k}N_{k}(tck){\bigg \}}-{\bigg \{}\sum _{k}N_{k}(tck){\bigg \}}^{2}{\Bigg ]}^{-1}}$

Joback Method Contributions (C1 Prausnitz)

[TABLA]

Conductivity was determined by the Sastri method:

${\displaystyle \lambda _{L}=\lambda _{b}a^{m}}$

where λL = thermic conductivity of the liquid [ W/(m·K)] λb = thermic conductivity at normal boiling point Tbr= T/Tc = reduced temperature Tc = critical temperature, K

${\displaystyle m=1-{\bigg (}{\frac {1-T_{r}}{1-T_{br}}}{\bigg )}^{n}}$

a=0.16 n=0.2

Contribución de Sastri (Tabla 10.5. Prausnitz 5a)

[TABLA]

Silver density

{pendiente}