Fick

Fick's laws of diffusion describe the diffusion phenomenon, which is an essential concept in many fields, including physics, chemistry, and biology. Named after the German physicist Adolf Fick, these laws form the basis of our understanding of diffusion processes.

Fick's First Law

Fick's first law relates the diffusive flux to the concentration under the assumption of steady state. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). In one (spatial) dimension, the law is:

J = -D (dφ/dx)

where:

• J is the "diffusion flux," of which the dimension is amount of substance per unit area per unit time,
• φ (for ideal mixtures) is the concentration, of which the dimension is amount of substance per unit volume,
• D is the diffusion coefficient or diffusivity. Its dimension is area per unit time,
• x is the position [length].

Fick's Second Law

Fick's second law predicts how diffusion causes the concentration to change with time. It postulates that the rate at which a substance diffuses into a region or out of a region is proportional to the amount of substance present and to the amount of substance in the surrounding regions. In one (spatial) dimension, the law is:

∂φ/∂t = D ∂²φ/∂x²

where:

• t is the time,
• ∂/∂t denotes the derivative with respect to time,
• ∂²/∂x² is the second derivative with respect to position (a measure of curvature or concavity of the concentration profile).

Applications

Fick's laws are used in a wide variety of scientific and engineering disciplines, such as physics, chemistry, chemical engineering, and biomedical engineering. For example, they are used to model the diffusion of pollutants in the air, the distribution of nutrients in soil, and the time-dependent behavior of concentration gradients in solid-state physics.

See Also

• Diffusion
• Adolf Fick
• Physics
• Chemistry
• Biomedical Engineering

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