What is a Diffusion Coefficient?

The diffusion coefficient (D) is a fundamental physical constant that quantifies how quickly a substance moves through another via random thermal motion. In liquid phases, this is most commonly described by the Stokes-Einstein equation. This value is critical for chemical engineers, biologists, and material scientists who need to predict how molecules will spread in a given medium over time.

How to Use the Diffusion Coefficient Calculator

To use this tool, you need three primary inputs. First, enter the Temperature. Higher temperatures increase kinetic energy, leading to a higher diffusion rate. Second, provide the Dynamic Viscosity of the solvent (fluid). For example, water at room temperature has a viscosity of approximately 0.89 mPa·s. Finally, enter the Particle Radius of the diffusing molecule. Larger particles experience more drag and therefore move more slowly.

The Stokes-Einstein Equation

This calculator utilizes the Stokes-Einstein relation: D = (k_B × T) / (6 × π × η × r). Where k_B is the Boltzmann constant (1.38 × 10⁻²³ J/K), T is the absolute temperature in Kelvin, η is the dynamic viscosity, and r is the hydrodynamic radius of the particle. This model assumes the particles are spherical and moving through a continuous fluid at a low Reynolds number.

Frequently Asked Questions (FAQs)

Q: Why does temperature affect diffusion?
A: As temperature rises, the thermal energy of molecules increases, causing them to vibrate and move faster, which directly increases the diffusion coefficient.

Q: Can this be used for gases?
A: While the general concept of diffusion applies to gases, the Stokes-Einstein equation is specifically designed for spherical particles in liquids. Gas diffusion usually follows Chapman-Enskog theory.

Q: What are the typical units for D?
A: In the SI system, it is measured in square meters per second (m²/s), though cm²/s is also commonly used in laboratory settings.