Exponential growth with fixed coefficient

Definition

This law changes the concentration of a class depending on an other class concentration (or eventually itself), and two fix coefficients \(k\) and\(\alpha_k\) as shown here:

\(\frac{dC_i}{dt}=k C_j^{\alpha_k}\)

Classic use

Numerous solutes have a first-order kinetics with an equation similar to :

\(\frac{dC_{Ni}}{dt}= - k_{Ni} C_{Ni}\)

where \(k_{Ni}\) is the reaction constant (which is the inverse of a time). For instance, bacteriological oxygen demand (DBO_5$$), has a constant around 0.3 days ^-1 . This degradation models the process of water auto-purification in streams.

Specifications

• Law’s ID : 201
• Number of acting classes : 2
• Number of parameters : : 2

Acting classes : - \(C_i\) : the class modified by the law - \(C_j\) : the parameter class of the law

Parameters : - \(k\) : reaction constant - \(\alpha_k\) : reaction order