Biomod/2013/NanoUANL/Reactor

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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:

E + S \leftrightarrow ES \rightarrow E^0 + P

with a reaction rate of:

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

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

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

Image: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:

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

where NAr represents molar flux. For NBr we obtain:

\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:

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:

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

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

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:

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:

λL = λbam

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


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}

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