Diffusion
Diffusion is the spontaneous net movement of particles from an area of high concentration to an area of low concentration in a given volume of fluid (either liquid or gas) down the concentration gradient. For example, diffusing molecules will move randomly between areas of high and low concentration but because there are more molecules in the high concentration region, more molecules will leave the high concentration region than the low concentration one.  Therefore, there will be a net movement of molecules from high to low concentration.  Initially, a concentration gradient leaves a smooth decrease in concentration from high to low which will form between the two regions.  As time progresses, the gradient will grow increasingly shallow until the concentrations are equalized.
Diffusion is a part of your body cells, a spontaneous process. It is simply the statistical outcome of random motion.  Diffusion increases entropy, decreasing Gibbs free energy, and therefore is thermodynamically favorable. Diffusion operates within the boundaries of the Second Law of Thermodynamics because it demonstrates nature's tendency to wind down, as evidenced by increasing entropy.
The diffusion equation provides a mathematical description of diffusion.  This equation is derived from Fick's law, which states that the net movement of diffusing substance per unit area of section (the flux) is proportional to the concentration gradient (how steeply the concentration changes in space), and is toward lower concentration.  (Thus if the concentration is uniform there will be no net motion.) The constant of proportionality is the diffusion coefficient, which depends on the diffusing species and the material through which diffusion occurs. Fick's law is an assumption that may not hold for a given diffusive system (e.g., the diffusion may depend on concentration in addition to concentration gradient), in which case the motion would not be described by the normal (simple, Fickian) diffusion equation.  An analogous statement of Fick's law, for heat instead of concentration, is Fourier's law.
The mechanism of diffusion is "Brownian motion" whereby a molecule makes a random walk about a central location since by kinetic theory the mean velocity of a particle is zero if it is not subject to any external forces. Due to collisions with neighboring molecules the motion of the particle is characterized by a mean free path which tends to confine the particle. But since there is no potential field acting to restore a particle to its original position, it is still free to move about the vessel or liquid in which it is located. The Laplacian in the diffusion equation indicates that the dispersion of the particles is second order effect, i.e., due to changes in the concentration gradient.
Diffusion is often important in systems experiencing an applied force.  In a conducting material, the net motion of electrons in an electrical field quickly reaches a terminal velocity (resulting in a steady current described by Ohm's law) because of the thermal (diffusive) motions of atoms.   The Einstein relation relates the diffusion coefficient to the mobility of particles.
In cell biology, diffusion is a main form of transport within cells and across cell membranes.

# Types of diffusion
The spreading of any quantity that can be described by the diffusion equation or a random walk model (e.g. concentration, heat, momentum, ideas, price) can be called diffusion.  Some of the most important examples are listed below.
- Atomic diffusion
- Brownian motion, for example of a single particle in a solvent
- Collective diffusion, the diffusion of a large number of (possibly interacting) particles
- Effusion of a gas through small holes.
- Electron diffusion, resulting in electric current
- Facilitated diffusion, present in some organisms.
- Gaseous diffusion, used for isotope separation
- Heat flow
- Ito diffusion
- Knudsen diffusion
- Momentum diffusion, ex. the diffusion of the hydrodynamic velocity field
- Osmosis is the diffusion of water through a cell membrane.
- Photon diffusion
- Reverse diffusion
- Self-diffusion
- Surface diffusion
Metabolism and respiration rely in part upon diffusion in addition to bulk or active processes.  For example, in the alveoli of mammalian lungs, due to differences in partial pressures across the alveolar-capillary membrane, oxygen diffuses into the blood and carbon dioxide diffuses out.  Lungs contain a large surface area to facilitate this gas exchange process.

# An experiment to demonstrate diffusion
Diffusion is easy to observe, but care must be taken to avoid a mixture of diffusion and other transport processes.
It can be demonstrated with a wide glass tube, two corks, some cotton wool soaked in ammonia solution and some red litmus paper. By corking the two ends of the wide glass tube and plugging the wet cotton wool with one of the corks, and the litmus paper can be hung with a thread within the tube. It will be observed that the red litmus papers turn blue.
This is because the ammonia molecules travel by diffusion from the higher concentration in the cotton wool to the lower concentration in the rest of the glass tube. As the ammonia solution is alkaline, the red litmus papers turn blue. By changing the concentration of ammonia, the rate of color change of the litmus papers can be changed.