Equilibrium Theory of Chromatography — Sorption Effect

Single adsorbable component + inert carrier with velocity change caused by ad/de‑sorption (isothermal, isobaric, fixed inlet velocity). Riemann problem solved analytically: envelope construction on νq vs. the mole ratio y/(1−y), velocity from the wave quadrature and shock balances. Hover a physical plane; click to pin.
Axes
RH ↔ y helper (water vapour in a carrier gas)

Physical plane — composition y

hover to explore · click to pin

Physical plane — velocity v/vF

Isotherm & construction

Breakthrough & velocity history

Column profile

Model: [1 + ν f′(y)(1−y)] ∂y/∂τ + ω ∂y/∂ξ = 0 and ν f′(y) ∂y/∂τ + ∂ω/∂ξ = 0, with ω = v/vF, ν = (1−ε)/ε (Ortner et al. 2014; Hefti et al. 2015). In inert-flow coordinates this reduces to a scalar conservation law in the mole ratio Φ = y/(1−y) with flux νf — envelopes are therefore taken on νq vs. Φ (drawn mapped back onto the isotherm). Along simple waves d ln ω/dy = νf′/(1+νf′(1−y)); across shocks ω jumps by the solute + inert balances.
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