Membrane Diffusion

Choose an example or enter the starting particle counts and exchange rate, then Start. Pause keeps the current state; Step advances 0.1 model seconds. Clear clears the experiment and keeps your inputs. Duration, random seed and an optional rotatable 3D view are under More options. Ctrl/Command + wheel zooms the 3D view.

This is an idealized model of one substance in two equally sized, well-mixed, closed compartments. Each particle switches sides independently with rate k in s⁻¹. The exact endpoint probability over Δt is (1 − exp(−2kΔt))/2. It is sampled on a fixed 0.01 s grid. Total particle count is conserved; net left→right is initial left count minus current left count. Positive means net movement to the right; negative means to the left. Particle colours indicate their original compartment, including after exchange.

The dashed curve is the expected left count: Ntotal/2 + (Nleft,0 − Nright,0)exp(−2kt)/2. A single random run fluctuates around it. At equal counts, exchange continues in both directions; there is no systematic net movement. k=0 blocks exchange. The same seed repeats the same sampled trajectory; change it for another realization. Hidden tools and pauses do not advance model time.

The diagram and channel paths are schematic, not physical molecular trajectories. k is a teaching exchange constant, not measured membrane permeability. No membrane voltage, charge, active transport, osmosis, binding or temperature dependence is modeled. OpenStax: passive transport.