Uptake Curves — Diffusion in Bidisperse Adsorbents

Predicts a gravimetric uptake experiment: a step change of sorbate fraction y₀→y₁ in an inert carrier at constant total pressure, single component, isothermal spheres. Choose micropore (crystal) diffusion, macropore diffusion, the full bidisperse (macro + micro) model, or an LDF lumped model. Darken’s thermodynamic correction available for micropore diffusion. Equilibrium at the outer surface; symmetry at both centres.

Transport model T (K) P (bar) y₀ initial (–) y₁ final (–) Darken correction D_μΓ(q), Γ = d ln p/d ln q

Isotherm q = f(y) (mol/kg)

Micropore (crystal)

D_μ0 (m²/s) r_c (μm)

Macropore (particle)

D_m molecular (m²/s) D_K Knudsen (m²/s) τ_p tortuosity (–) ε_p porosity (–) ρ_p (kg/m³) R_p (μm)

LDF

k (1/s) Glueckauf k = 15 D_μ0/r_c²

Knudsen helper · numerics

Pore radius r_pore (nm) Molar mass M (g/mol)

Crystal cells N_c Particle cells N_p Time steps K t_end (s, blank = auto)

Isotherm & step

drag the state markers

Intracrystalline profile q(r)

Intraparticle profile

Uptake (m_t − m₀)/(m_∞ − m₀)

Micropore: ∂q/∂t = r⁻²∂/∂r(r²D_μ(q)∂q/∂r) with D_μ = D_μ0Γ(q), Γ = d ln p/d ln q · Macropore: ε_p∂c/∂t + ρ_p∂q̄/∂t = R⁻²∂/∂R(R²D_e∂c/∂R), D_e = ε_pD_pore/τ_p, 1/D_pore = 1/D_m + 1/D_K (Bosanquet) · Bidisperse couples both scales (Ruckenstein-type); LDF: dq̄/dt = k(q* − q̄). Conservative finite volumes + L-stable TR-BDF2, validated against exact series solutions (see README).
Works offline — single file, share freely. Built by Arvind Rajendran with Claude Code · v1.0 · August 2026 · educational & research use · no warranty — use at your own risk
Runs entirely in your browser, no data collected · © 2026 · CC BY 4.0 · Part of the Research Apps suite →