Diffusion Calculators

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Diffusion is the passive movement of molecules from regions of high concentration to regions of low concentration, driven by thermal (Brownian) motion — without requiring energy input. It is the dominant mechanism for short-range molecular transport in biological systems: oxygen and CO₂ exchange across alveoli and capillaries, neurotransmitter diffusion across synapses, and nutrient uptake by small cells all rely on diffusion. Fick's laws of diffusion quantify the rate of diffusion in terms of concentration gradients, diffusion coefficients, and path lengths. The limits of diffusion explain many features of biological design, including cell size constraints and the need for circulatory systems in large organisms.

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Fick's First Law of Diffusion

J = −D × (dC/dx)

where J is the diffusion flux (mol/m²/s), D is the diffusion coefficient (m²/s), and dC/dx is the concentration gradient. The negative sign indicates flux is in the direction of decreasing concentration. Higher D (smaller molecule, lower viscosity, higher temperature) and steeper gradients produce faster diffusion.

Fick's Second Law

∂C/∂t = D × ∂²C/∂x²

Describes how concentration changes over time at any point, as diffusion flattens concentration gradients. The characteristic diffusion distance: x ≈ √(2Dt) — the distance diffused scales with the square root of time. Diffusing 10 μm takes milliseconds; 1 mm takes hours; 1 cm takes days. This explains why diffusion alone cannot supply nutrients to large organisms.

Diffusion Coefficients in Biology

Typical D values in aqueous solution: O₂: 2 × 10⁻⁹ m²/s; glucose: 7 × 10⁻¹⁰ m²/s; proteins (albumin): ~6 × 10⁻¹¹ m²/s. Membrane diffusion is orders of magnitude slower due to the hydrophobic core — only nonpolar, small molecules diffuse freely. Ion channels, transporters, and pumps facilitate membrane crossing for polar solutes and ions.

Facilitated Diffusion

Facilitated diffusion uses membrane transport proteins (channels or carriers) to move molecules down their concentration gradient without ATP. Unlike simple diffusion, it is saturable (limited by transporter number) and can be specific for one molecule type. Glucose enters cells via GLUT transporters; ions cross through specific ion channels.

Glossary

Diffusion Coefficient (D)
A constant describing the rate at which a molecule diffuses through a medium; depends on molecular size, temperature, and solvent viscosity; units of m²/s.
Fick's First Law
J = −D × (dC/dx); flux is proportional to the concentration gradient and the diffusion coefficient; fundamental to understanding passive molecular transport.
Facilitated Diffusion
Passive transport of molecules across a membrane via specific protein channels or carriers; moves substances down their concentration gradient without ATP; saturable and specific.

Frequently Asked Questions

Fick's first law states that diffusion flux (J) is proportional to the concentration gradient: J = −D × (dC/dx), where D is the diffusion coefficient and dC/dx is the change in concentration over distance. The negative sign means molecules flow from high to low concentration. A steeper gradient or a larger diffusion coefficient (smaller molecule, lower viscosity, higher temperature) produces faster diffusion. This law applies to steady-state conditions where the concentration gradient is constant.

Diffusion distance scales with the square root of time: x ≈ √(2Dt). For oxygen in water (D ≈ 2 × 10⁻⁹ m²/s), diffusing 10 μm takes about 25 milliseconds — fine for single cells. Diffusing 1 mm takes about 250 seconds; 1 cm takes about 7 hours. Cells more than ~100–200 μm from a supply surface would starve or suffocate before nutrients arrived. This is why organisms larger than ~1 mm have evolved circulatory systems to deliver nutrients convectively, with diffusion serving only the final few micrometers.

Simple diffusion moves molecules directly through the lipid bilayer down their concentration gradient — no proteins required. Only small, nonpolar molecules (O₂, CO₂, steroid hormones) diffuse simply. Facilitated diffusion uses membrane transport proteins (channels or carriers) to move polar or charged molecules down their gradient. Unlike simple diffusion, facilitated diffusion is saturable (limited by transporter number), specific (one protein handles one or a few similar molecules), and can be inhibited by competing molecules.

Diffusion rate increases with: larger concentration gradient (steeper dC/dx), smaller molecular size (D increases), higher temperature (increases kinetic energy and D), lower viscosity (D increases), and shorter diffusion distance. In biological membranes, permeability (P = K × D / thickness, where K is partition coefficient) summarizes how easily a molecule crosses. For ions and polar molecules, permeability is determined mainly by available transporter proteins rather than the physical diffusion coefficient.