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:
[math]\displaystyle{ E + S \leftrightarrow ES \rightarrow E^0 + P }[/math]
with a reaction rate of:
[math]\displaystyle{ \frac{d[ES]}{dt}=k_1[E][S]-k_{-1}[ES]-k_2[ES] }[/math]
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 = [math]\displaystyle{ \tfrac{d[P]}{dt} }[/math]
F0 = F0(1-XS) - V(-rS) + [math]\displaystyle{ \tfrac{d[P]}{dt} }[/math]
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:
[math]\displaystyle{ \frac{d}{dr}(r^2N_{Ar})=0 }[/math]
where NAr represents molar flux. For NBr we obtain:
[math]\displaystyle{ \frac{d}{dr}(r^2\frac{cD_{AB}}{1-x_A}\frac{dx_A}{dr})=0 }[/math]
At a constant temperature the product (cDAB) is equally constant and xA=1-xB, the equation can be integrated into the following expression:
[math]\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}} }[/math]
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:
[math]\displaystyle{ D_{AB}°= \frac{RT}{F^2} \frac{\lambda^o_+\lambda^o_-}{\lambda^o_++\lambda^o_-} \frac{|Z_-|+|Z_+|}{|Z_+Z_-|} }[/math]
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