# Biomod/2013/NanoUANL/Reactor

(Difference between revisions)
 Revision as of 01:16, 12 October 2013 (view source) (New page: == 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 ty...)← Previous diff Revision as of 01:45, 12 October 2013 (view source)Next diff → Line 1: Line 1: - == What is a reactor? == == What is a reactor? == Line 23: Line 22: Mass balance was presented as such: Mass balance was presented as such: - INPUT = OUTPUT - DISAPPEARANCE BY REACTION + ACCUMULATION + '''INTAKE= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION + ''' where where - Input = F0 + Intake= F0 - Output = F0(1-XS) + + Outflow= F0(1-XS) + Disappearance = V(-rS Disappearance = V(-rS + Accumulation = $\tfrac{d[P]}{dt}$ 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: + + $F_A=4\pi r_1^2N_{Ar}|_{r=r1}= + \frac{4\pi cD_{AB}}{1/r_1=1/r_2} + \ln\frac{x_{B2}}{x_{B1}} + +$

## 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:

INTAKE= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION

where

Intake= 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.

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:

$F_A=4\pi r_1^2N_{Ar}|_{r=r1}= \frac{4\pi cD_{AB}}{1/r_1=1/r_2} \ln\frac{x_{B2}}{x_{B1}}$