Diffusion

Diffusion is the phenomenon of random motion causing a system to decay towards uniform conditions. 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—a smooth decrease in concentration from high to low—will form between the two regions. As time progresses, the gradient will grow increasingly shallow until the concentrations are equalized.

Diffusion is a spontaneous process (more familiarly known as a "passive" form of transport, rather than "active"); 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.^[1]

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.

Diffusion can also be described using discrete quantities (the diffusion equation has derivatives and thus applies to continuous quantities). A common model of discrete diffusion is the random walk. A random walk model is connected to the diffusion equation by considering an infinite number of random walkers starting from a non-uniform configuration, where the evolution of the concentration is described by the diffusion equation.

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
• Gaseous diffusion, used for isotope separation
• Heat flow
• Itō diffusion
• Knudsen diffusion
• Momentum diffusion, ex. the diffusion of the hydrodynamic velocity field
• Osmosis
• Photon diffusion
• Reverse diffusion
• Self-diffusion
• Thermal diffusion

Diffusion displacement

The diffusion displacement can be described by the following formula

where is the dimensions of the system and can be one, two or three. is the diffusion coefficient of the particles and is time. For the three-dimensional systems the above equation will be:

Diffusion in biological systems

Diffusion plays a variety of roles in biological organisms. In addition to simple diffusion of molecules within or across cells, cells contain a variety of channels or pores that allow facilitated diffusion of selected molecules between the inside and outside of the cell. Charged molecules such as ions cannot simply diffuse, as net motion of charges causes a change in the potential which opposes further motion. The interplay of facilitated diffusion and electrostatics leads cells to have a resting potential which is nonzero.

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.

An Experiment to Demonstrate Diffusion
Requirements:

             1 Wide glass tube
             2 Corks
             3 Cotton wool soaked in  Ammonia solution
             4 Red litmus paper

Procedure: Cork the two ends of the wide glass tube. Plug the wet cotton wool with one of the corks and hang the litmus papers with a thread within the tube.

Observation: The red litmus papers turn blue.

Interpretation: The ammonia molecules by diffusion travels from higher concentration which is the cotton wool to lower concentration which is 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.

References

1. ^ Biddle, Verne, and Gregory Parker. Chemistry: Precision and Design. Pensacola: A Beka Book, 2000. p109.

See also

External links

• Some pictures that display diffusion and osmosis
• An animation describing diffusion.
• A tutorial on the theory behind and solution of the Diffusion Equation.