In physics, chemistry and biology, diffusion denotes the mixing of two or more substances or the net motion of a substance from an area of high concentration to an area of low concentration. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties Foundations of modern biology There are five unifying principles The theory is that both of these result from the random motion of micro-scale individual agents (such as molecules) giving rise to net changes on the macro-scale. While originally formulated within the framework of the physical sciences, the concept of diffusion has been applied to phenomena such as the manner in which information is spread amongst a population. The chemistry definition of diffusion is the movement of a fluid from an area of higher concentration to an area of lower concentration.

Diffusion is an abstract topic and is often only explained as theoretical model. It is part of transport phenomena in general, and often accompanied by the much quicker convection (making it hard to observe 'pure' diffusion). The first edition of Transport Phenomena was published in 1960 two years after having been preliminarily published under the title Notes on Transport Phenomena based Convection in the most general terms refers to the movement of molecules within Fluids (i A few examples are shown below.

Why we can smell things

Why the whole spoon gets hot when its only half in the tea

Why smoke spreads to fill a whole room

The diffusion equation

Separated particles can mix by randomly 'walking around'. This process is called Brownian motion, because Robert Brown was the first to see it with his microscope. This article is about the physical phenomenon for the stochastic process see Wiener process. Robert Brown FRS ( 21 December, 1773 &ndash 10 June, 1858) was a Scottish scientist who is acknowledged as the leading botanist

To verify any microscopic model we may think up, we need to calculate its consequences and compare these to observation. Another way of arriving at a microscopic model is to write down a general equation and solve it mathematically (i. e. start from what you already know). This general equation, not refering to any microscopic model, is the diffusion equation

.

This equation is composed out of two true statements. One of these is the continuity equation

. A continuity equation is a Differential equation that describes the conservative transport of some kind of quantity

And the other Fick's law

,

where is the flux, D is the diffusion constant, and is the concentration of diffusing material. Fick's laws of diffusion describe Diffusion and can be used to solve for the diffusion coefficient D. In the various subfields of Physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks Fick's laws of diffusion describe Diffusion and can be used to solve for the diffusion coefficient D.

The continuity equation is the mathematical equivalent to a piggybank. For the song by 50 Cent see Piggy Bank (song. "Money Box" redirects here Your savings increase by the amount that you put in, they decrease by the amount you take out, no more and no less. Fick's law, on the other hand, was born as an empirical law which means that it describes observations and is not derived from any argument.

One general solution to the diffusion equation is a Gaussian one. This suggest an uncorrelated random walk as a microscopic model, completely in line with Robert Brown's observations.

Einstein relation

Einstein showed that Fick's law (empirical) can be derived by noting that the flux due to diffusion only can depend on the chemical potential, and taking this potential to be that of an ideal gas. Fick's laws of diffusion describe Diffusion and can be used to solve for the diffusion coefficient D. In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical These four properties that constitute an ideal gas can be easily remembered by the acronym RIPE which stands for - R andom Motion (molecules are in constant random motion This last step is justified because the final stage of a spreading concentration may be described as an ideal gas. The result is

,

where γ is the drag coefficient (the inverse of the mobility). In Fluid dynamics, drag (sometimes called fluid resistance) is the force that resists the movement of a Solid object through a Fluid (a The Einstein relation follows directly to be

,

which is the most general expression for the diffusion coefficient, not refering to any microscopic model. In Physics (namely in Kinetic theory) the Einstein relation (also known as Einstein–Smoluchowski relation) is a previously unexpected connection revealed

Entropy and diffusion

Low and high entropy. For any state of any system there is a number that describes how messy it is, this number is called entropy. In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Any spontaneous process will increase a system's entropy (as stated by the second law). The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which

Diffusion increases the entropy of a system. In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy This is nothing else than saying that diffusion is a spontaneous and irreversible process. Something can spread out by diffusing, but it won't spontaneously 'suck back in'.

In biology

In cell biology, diffusion is a main form of transport for necessary materials such as amino acids through cell membranes. See also List of basic cell biology topics. Cell biology (also called cellular biology or formerly cytology, from the In Chemistry, an amino acid is a Molecule containing both Amine and Carboxyl Functional groups In Biochemistry, this ^[1]

No equilibrium system

Because diffusion is a transport process of particles, the system in which it takes place is no equilibrium system (i. e. it is not at rest yet). For this reason thermodynamics and statistical mechanics are of little to no use in describing diffusion. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics However, there might occur so-called quasi-steady states where the diffusion process does not change in time. As the name suggests, this process is a fake equilibrium since the system is still evolving.

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
• Ellusion of a gas through small holes. Atomic Diffusion is a process whereby the random thermally-activated hopping of Atoms in a Solid results in the net transport of atoms This article is about the physical phenomenon for the stochastic process see Wiener process. Collective diffusion is the Diffusion of a large number of particles most often within a Solvent.
• Electronic diffusion, resulting in electric current
• Facilitated diffusion, present in some organisms. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. Facilitated diffusion (or facilitated transport) is a process of Diffusion, a form of Passive transport facilitated by Transport proteins The
• Gaseous diffusion, used for isotope separation
• Heat flow
• Itō diffusion
• Knudsen diffusion
• Momentum diffusion, ex. Gaseous diffusion is a technology used to produce Enriched uranium by forcing gaseous Uranium hexafluoride, UF6 through semi-permeable membranes Isotope separation is the process of concentrating specific Isotopes of a Chemical element by removing other isotopes for example separating Natural uranium In thermal physics, heat transfer is the passage of Thermal energy from a hot to a colder body In Mathematics &mdash specifically in stochastic analysis &mdash an Itō diffusion is a solution to a specific type of Stochastic differential equation Knudsen diffusion is a means of Diffusion that occurs in a long pore with a narrow diameter (2–50nm because molecules frequently collide with the pore wall Momentum diffusion refers to the Diffusion, or spread of Momentum between particles ( Atoms or Molecules of Matter, usually in the the diffusion of the hydrodynamic velocity field
• Osmosis is the diffusion of water through a cell membrane. Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion Osmosis is the Diffusion of a solvent (frequently water through a semi-permeable membrane, from a solution of low solute concentration (high water potential
• Photon diffusion
• Reverse diffusion
• Rotational diffusion
• Self-diffusion
• Surface diffusion
• Active transport, pumping material across a cell membrane
• Pinocytosis, "cell drinking" intake of small droplets of lipids
• Phagocytosis, carrier proteins are used to transport glucose

Metabolism and respiration rely in part upon diffusion in addition to bulk or active processes. Photon diffusion refers to a situation where Photons travel through a material with a high Optical depth and very short Mean free path. Reverse diffusion refers to a situation where the transport of particles ( Atoms or Molecules in a medium occurs towards regions of lower concentration gradients opposite Rotational diffusion is a process by which the Equilibrium statistical distribution of the overall orientation of particles or molecules is maintained or restored According to IUPAC definition self-diffusion coefficient is the Diffusion coefficient D_i^* of species i when the Chemical potential Surface diffusion is a general process involving the motion of Adatoms Molecules and atomic clusters ( Adparticles) at solid material Surfaces Active transport is the mediated process of moving particles across Biological membrane against the concentration gradient In Cellular biology, pinocytosis ("cell-drinking" "bulk-phase pinocytosis" "non-specific non-adsorptive pinocytosis" "fluid endocytosis" Phagocytosis is the cellular process of engulfing solid particles by the Cell membrane to form an internal Phagosome, or "food vacuole 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. An alveolus (plural alveoli, from Latin alveolus, "little cavity" is an anatomical structure that has the form of a hollow cavity Mammals ( class Mammalia) are a class of Vertebrate Animals characterized by the presence of Sweat glands, including sweat glands lung is the essential Respiration organ in air-breathing Animals including most Tetrapods a few Fish and a few Snails The most primitive Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single 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 phenomena.

It can be demonstrated with a wide glass tubed paper, two corks, some cotton wool soaked in ammonia solution and some red litmus paper. Cotton is a soft staple Fibre that grows around the seeds of the cotton plant ( Gossypium sp Wool is the fiber derived from the specialized skin cells called follicles of animals in the Caprinae family principally sheep, but the hair of certain species RollerCoaster Tycoon 3 is a simulation and strategy Computer game that simulates Amusement park management Ammonia is a compound with the formula N[[hydrogen H3]] It is normally encountered as a Gas with a characteristic pungent Odor Litmus is a Water - Soluble mixture of different Dyes Extracted from Lichens, especially Roccella tinctoria. By corking the two ends of the wide glass tube and plugging the wet cotton wool with one of the corks, and 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.

References

• Einstein, Albert (1956). Investigations on the Theory of the Brownian Movement. Dover. ISBN 0-486-60304-0.  

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.
• NetLogo Simulation Model for Educational Use (Java Applet)