SecTheory.Edm#

SecTheory.Edm.py

EDM - Equilibrium Dispersive Model

based on the paper 2022, Jamil Ur Rehman,: ANALYSIS OF EQUILIBRIUM DISPERSIVE MODEL OF LIQUID CHROMATOGRAPHY CONSIDERING A QUADRATIC-TYPE ADSORPTION ISOTHERM

class Edm(z=30, L=30, a=1.5, b=0.5, u=1.2, e=0.4, Dz=0.02, cinit=0, cinj=1.0, c0=0.0001, tinj=2.0)#

Bases: object

Parameters:

a (float) – Henry coefficient = K_SEC × (Vp/V0), where K_SEC ∈ [0,1] is the Ogston partition coefficient and Vp/V0 is the pore-to-void volume ratio. For a fully accessible small molecule: a = 1 × (Vp/V0). Determined from peak retention (gam2 ≈ a for small c0).
b (float) – Langmuir nonlinearity. b < 0 → fronting (aggregation in SEC); b > 0 → tailing (secondary adsorption); b = 0 → linear isotherm. Note: b = 0 causes ZeroDivisionError (lam = 0 → U = 2/(lam*Pe) fails).
e (float) –

Mobile-phase fraction of the accessible volume:
e = V0 / (V0 + Vp)

where V0 = interstitial void volume, Vp = pore volume. Solid bead volume is entirely outside the EDM mass balance. NOT the standard chromatographic total porosity ε_T = (V0+Vp)/V_column. The phase ratio F = (1-e)/e = Vp/V0 directly. Default e=0.4 → F=1.5. In the 2D column simulation (ColumnSimulation.py, rs=0.0381, ~42 grains) the measured volumes give Vp/V0 ≈ 0.88 → e ≈ 0.53.
u (float) – Mobile-phase velocity (column lengths per time unit).
Dz (float) – Axial dispersion coefficient.
cinj (float) – Injected concentration.
c0 (float) – Reference concentration for linearising the isotherm (keep small).

edm_func(t, u, a, b, e, Dz, cinj, cinit=0, c0=0.0001, tinj=2.0, L=30, z=30)#

SecTheory.Edm