# 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:

**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:

**INTAKE= OUTFLOW- DISAPPEARANCE BY REACTION + ACCUMULATION**

where

Intake= 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}} }**