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Percolation

Percolation is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Percolation rather than just read about it. In short: In physics, chemistry, and materials science, percolation (from Latin percolare 'to filter, trickle through', coined in the 1840s by Edward Loysel) refers to the movement and filtering of fluids through porous materials. It is not described by Darcy's law.

Percolation — main illustration
Percolation — illustration

Key takeaways

  • Percolation belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Percolation to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Percolation from memory before moving on to harder problems.

Reference excerpt

In physics, chemistry, and materials science, percolation (from Latin percolare 'to filter, trickle through', coined in the 1840s by Edward Loysel) refers to the movement and filtering of fluids through porous materials. It is not 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

Origins In Western Europe, percolation was a process formally invented in the early nineteenth century, particularly in researching methods of extraction for apothecary and pharmaceutical substances. Important contributions were made by Jöns Jacob Berzelius, the Count of Real, Pierre-François-Guillaume Boullay, who generally referred to the process as "displacement." In 1845, Edward Loysel coined the term and popularised it with his coffee machine.

Recent history During the last decades, percolation theory, the mathematical study of percolation, has brought new understanding and techniques to a broad range of topics in physics, materials science, complex networks, epidemiology, and other fields. For example, in geology, percolation refers to filtration of water through soil and permeable rocks. The water flows to recharge the groundwater in the water table and aquifers. 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 concepts such as scaling theory, renormalization, phase transition, critical phenomena and fractals are used to characterize percolation properties. Combinatorics 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 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.

See also

References

Further reading Kesten, Harry; "What is percolation?", in Notices of the AMS, May 2006. Sahimi, Muhammad; Applications of Percolation Theory, Taylor & Francis, 1994. ISBN 0-7484-0075-3 (cloth), ISBN 0-7484-0076-1 (paper). Grimmett, Geoffrey; Percolation (2. ed). Springer Verlag, 1999. Stauffer, Dietrich; and Aharony, Ammon; Introduction to Percolation Theory, Taylor & Francis, 1994, revised second edition, ISBN 9780748402533. Kirkpatrick, Scott; "Percolation and Conduction", in Reviews of Modern Physics, 45, 574, 1973. Rodrigues, Edouard; Remarkable properties of pawns on a hexboard Archived 2021-12-09 at the Wayback Machine Bollobás, Béla; Riordan, Oliver; Percolation, Cambridge University Press, 2006, ISBN 0521872324. Grimmett, Geoffrey; Percolation, Springer, 1999

Illustrations

Percolation: In coffee percolation, soluble compounds leave the coffee grounds and join the water to form coffee. Insoluble compounds (and granulates) remain within the coffee filter.
In coffee percolation, soluble compounds leave the coffee grounds and join the water to form coffee. Insoluble compounds (and granulates) remain within the coffee filter.
Percolation: Percolation in a square lattice.
Percolation in a square lattice.

Worked examples

Example 1 — a first encounter with Percolation

Start with the simplest possible case. Write down what Percolation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Percolation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Percolation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Percolation

In research
Percolation appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Percolation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Percolation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Combinatorics, Systems theory, so understanding it makes those chapters shorter.
In everyday life
Look for Percolation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Percolation in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Percolation means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Percolation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Percolation in simple terms?

In physics, chemistry, and materials science, percolation (from Latin percolare 'to filter, trickle through', coined in the 1840s by Edward Loysel) refers to the movement and filtering of fluids through porous materials. It is not described by Darcy's law.

Why does Percolation matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Percolation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Percolation.

Tags

  • Combinatorics
  • Systems theory

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