Percolation (from

Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...

''percolare'', "to filter" or "trickle through"), in

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...

chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...

and materials science, refers to the movement and

filtering Filter, filtering or filters may refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component tha ...

of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.

Background

During the last decades,

percolation theory In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnecte ...

, the mathematical study of percolation, has brought new understanding and techniques to a broad range of topics in physics, materials science,

complex network In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real ...

epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decisions and evi ...

, and other fields. For example, in

geology Geology () is a branch of natural science concerned with Earth and other Astronomical object, astronomical objects, the features or rock (geology), rocks of which it is composed, and the processes by which they change over time. Modern geology ...

, percolation refers to filtration of water through soil and permeable rocks. The water flows to recharge the

groundwater Groundwater is the water present beneath Earth's surface in rock and Pore space in soil, soil pore spaces and in the fractures of stratum, rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit ...

in the

water table The water table is the upper surface of the zone of saturation. The zone of saturation is where the pores and fractures of the ground are saturated with water. It can also be simply explained as the depth below which the ground is saturated. T ...

and

aquifer An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials ( gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characte ...

s. In places where infiltration basins or septic drain fields are planned to dispose of substantial amounts of water, a percolation test is needed beforehand to determine whether the intended structure is likely to succeed or fail. In two dimensional square lattice percolation is defined as follows. A site is "occupied" with probability p or "empty" (in which case its edges are removed) with probability 1 – p; the corresponding problem is called site percolation, see Fig. 2. Percolation typically exhibits universality.

Statistical physics Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approxim ...

concepts such as scaling theory, renormalization,

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states ...

, critical phenomena and

fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as ill ...

s are used to characterize percolation properties.

Combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

is commonly employed to study percolation thresholds. Due to the complexity involved in obtaining exact results from analytical models of percolation, computer simulations are typically used. The current fastest algorithm for percolation was published in 2000 by

Mark Newman Mark Newman is an English-American physicist and Anatol Rapoport Distinguished University Professor of Physics at the University of Michigan, as well as an external faculty member of the Santa Fe Institute. He is known for his fundamental contri ...

and Robert Ziff.

Examples

* Coffee percolation (see Fig. 1), where the solvent is water, the permeable substance is the coffee grounds, and the soluble constituents are the chemical compounds that give coffee its color, taste, and aroma. * Movement of weathered material down on a slope under the earth's surface. * Cracking of trees with the presence of two conditions, sunlight and pressure. * Collapse and robustness of biological virus shells to random subunit removal (experimentally-verified fragmentation of viruses). * Transport in porous media. * Spread of diseases. * Surface roughening. * Dental percolation, increase rate of decay under crowns because of a conducive environment for strep mutants and lactobacillus * Potential sites for septic systems are tested by the " perc test". Example/theory: A hole (usually 6–10 inches in diameter) is dug in the ground surface (usually 12–24" deep). Water is filled in to the hole, and the time is measured for a drop of one inch in the water surface. If the water surface quickly drops, as usually seen in poorly-graded sands, then it is a potentially good place for a septic " leach field". If the hydraulic conductivity of the site is low (usually in clayey and loamy soils), then the site is undesirable.

Background

Examples

See also

References

Further reading