Kinetic Theory

Rate Theory Models¶

In contrast to the stochastic models, there are models derived from the following differential equation known as the transport-dispersive equation (or the convection-diffusion equation).

where:

• $C$ is the solute concentration in the mobile phase,

• $C^*$ is the concentration in the stationary phase,

• $u$ is the linear velocity of the mobile phase,

• $D$ is the axial dispersion coefficient,

• $k$ is the rate constant for exchange between phases,

• $x$ is the position along the column,

• $t$ is time.

These models are often classified into the following three according to the levels of simplification.

Simply in set inclusion notation:

Equilibrium Dispersive Model¶

Rate theory models are usually computed numerically because the differential equation can be solved analytically only in special cases. However, for EDM, Ur Rehman et al. (2021) solved it analytically under applicable conditions, which we use as an additional constraint to improve the decomposition.