# 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:

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:

Tabla .- Joback Method Contributions (C1 Prausnitz)

[TABLA]

Conductivity was determined by the Sastri method:

λ_{L} = λ_{b}*a*^{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}