Fick's laws of diffusion in the context of Passive diffusion

In physics and engineering, permeation (also called imbuing) is the penetration of a permeate (a fluid such as a liquid, gas, or vapor) through a solid. It is directly related to the concentration gradient of the permeate, a material's intrinsic permeability, and the materials' mass diffusivity. Permeation is modeled by equations such as Fick's laws of diffusion, and can be measured using tools such as a minipermeameter.

Passive transport is a type of membrane transport that does not require energy to move substances across cell membranes. Instead of using cellular energy, like active transport, passive transport relies on the second law of thermodynamics to drive the movement of substances across cell membranes. Fundamentally, substances follow Fick's first law, and move from an area of high concentration to an area of low concentration because this movement increases the entropy of the overall system. The rate of passive transport depends on the permeability of the cell membrane, which, in turn, depends on the organization and characteristics of the membrane lipids and proteins. The four main kinds of passive transport are simple diffusion, facilitated diffusion, filtration, and/or osmosis.

Passive transport follows Fick's first law.

The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other fields, such as materials science, information theory, and biophysics. The diffusion equation is a special case of the convection–diffusion equation when bulk velocity is zero. It is equivalent to the heat equation under some circumstances.