Welcome to Diffusion Explorer

Explore the fascinating world of diffusion processes!

Diffusion Fails for Long-Distance Neural Signaling

Diffusion spreads particles passively from high to low concentration. It works over tiny distances but slows drastically over axon-scale lengths.

\(\langle x^2 \rangle = 6Dt\)

\(\langle x^2 \rangle\): mean squared displacement, \(D\): diffusion constant, \(t\): time.

Time grows with distance squared: \(t \propto x^2\). Example: to diffuse 1 mm, Na+ ions (\(D \approx 1.33 \times 10^{-9}\,\text{m}^2/\text{s}\)) take about 160 s, while an action potential traveling \(50\,\text{m/s}\) takes ~0.02 s. Diffusion alone is too slow, so neurons use electrical signals.

Time Calculator: How Long It Takes

For 3D diffusion the time to reach distance \(x\) is:

\(t_{\text{diff}} = \dfrac{x^2}{6D}\)

Distance in meters, time in seconds. The quadratic dependence shows why long-distance diffusion is impractical.

Time Calculater

Adjust distance see how time it takes to reach that distance

How Temperature, Viscosity, and Ion Size Affect \(D\)

Stokes-Einstein relation:

\(D = \dfrac{k_B T}{6 \pi \eta r}\)

  • Temperature \(T\): higher \(T\) increases \(D\) and speeds diffusion.
  • Viscosity \(\eta\): thicker media lower \(D\) and slow diffusion.
  • Ion radius \(r\): larger ions move slower, reducing \(D\).

Small ions in warm, low-viscosity fluid diffuse fastest; large ions in cold, viscous fluid diffuse slowest.

Parameter Explorer

Adjust temperature, viscosity, and ion size to see how they affect the diffusion constant D

Diffusion Graphs

The mean squared displacement (MSD) of a particle changes with time. The linear increase in MSD indicates normal diffusion, where particles move randomly and spread out at a constant rate over time.

Diffusion Time

See how diffusion time scales with distance. and The curved (non-linear) rise indicates that diffusion time scales with the square of the distance ( 𝑡 ∝ 𝑥 2 t∝x 2 ). This means that doubling the distance makes diffusion take about four times longer, highlighting how diffusion becomes very slow over large distances.

Compare Diffusion Constants

This graph compares the time required for signal transmission by diffusion and by action potentials over increasing distances. Diffusion becomes dramatically slower as distance increases, while action potentials transmit signals rapidly and efficiently with nearly linear time scaling. This highlights why biological systems rely on action potentials rather than diffusion for long-distance communication.