Capillary Isoelectric Focusing — Drift-Diffusion Field Map

Field & Gradient

Electric field 15 kV/cm

pH gradient width 7.0 pH

Diffusion / temperature 4

Proteins (by pI)

Live Readouts

Focusing time

0.0 s

Off-gradient bands

0 / 5

Worst-pair resolution R_s

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How this 2D model differs from the 3D version

The 3D version tracks each protein as hundreds of discrete particles doing a biased random walk (a Lagrangian Monte-Carlo model). This 2D version instead solves the concentration field directly: for every species it evolves a continuous density c(x,t) along the capillary with an explicit finite-volume drift-diffusion (advection-diffusion) equation on a fixed grid — the Eulerian, PDE-based counterpart used throughout real electrophoresis and chromatography modelling.

∂c/∂t = −∂(v·c)/∂x + D·∂²c/∂x²
v(x) = μ·E · tanh[k·(pI − pH(x))]

The vertical axis of the main panel is a kymograph — space (left–right) versus time (top, now, scrolling down into the past) — so you watch each species' whole concentration field sharpen into a band and hold position, rather than watching individual dots settle. The strip below is the instantaneous concentration profile, the continuum equivalent of a detector trace.

Electric field — scales the drift velocity v(x); higher field steepens the restoring flow toward each pI and narrows the steady-state band.
pH gradient width — narrowing it steepens dpH/dx, sharpening resolution, but any protein whose pI falls outside the covered range never finds a sign change in v(x) and its concentration field piles up against the nearest no-flux boundary instead.
Diffusion / temperature — the D·∂²c/∂x² term; near a pI the band relaxes to a Gaussian with steady-state variance σ² = D/γ, γ = μE·k·(dpH/dx) — more diffusion (heat) widens σ, more field narrows it.
Resolution R_s uses the same definition as the 3D model, R_s = Δx / [2(σ₁+σ₂)], computed from the field's own mean and variance (its statistical moments) rather than particle positions.

Anode · low pH Cathode · high pH

← position along capillary →
time increases downward ↓