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Dalhousie University

Dalhousie University (commonly known as Dal) is a large public research university in Nova Scotia, Canada, with three campuses in Halifax, a fourth in Bible Hill, and a second medical school campus in Saint John, New Brunswick. Dalhousie offers over 200 degree programs in 13 undergraduate, graduate, and professional faculties. The university is a member of the U15, a group of research-intensive universities in Canada.

The institution was established as Dalhousie College, a nonsectarian institution established in 1818 by the eponymous Lieutenant Governor of Nova Scotia, George Ramsay, 9th Earl of Dalhousie, with education reformer Thomas McCulloch as its first principal. However, the college did not hold its first class until 1838, with operations remaining sporadic due to financial difficulties. The college was reorganized in 1863 and renamed The Governors of Dalhousie College and University. The university formally changed its name to Dalhousie University in 1997 through the same provincial legislation that merged the institution with the Technical University of Nova Scotia.

Dalhousie's varsity teams, the Tigers, compete in the Atlantic University Sport conference of Canadian Interuniversity Sport. Dalhousie's Faculty of Agriculture varsity teams are called the Dalhousie Rams, and compete in the ACAA and CCAA. Dalhousie is a coeducational university with more than 20,000 students and 150,000 alumni around the world. The university's notable alumni include a Nobel Prize winner and 94 Rhodes Scholars.

History
Dalhousie was founded, as the Lieutenant Governor of Nova Scotia George Ramsay, 9th Earl of Dalhousie, desired a non-denominational college in Halifax. Financing largely came from customs duties collected by a previous Lieutenant Governor, John Coape Sherbrooke, during the War of 1812 occupation of Castine, Maine; Sherbrooke invested £7,000 as an initial endowment and reserved £3,000 for the physical construction of the college. The college was established in 1818 though it faltered shortly after, as Ramsay left Halifax to serve as the Governor General of British North America. The school was structured upon the principles of the University of Edinburgh, located near Ramsay's home in Scotland, where lectures were open to male students, regardless of Christian religion or nationality.

In 1821, Dalhousie College was officially incorporated by the Nova Scotia House of Assembly under the 1821 Act of Incorporation. The college did not hold its first class until 1838; operation of the college was intermittent and no degrees were awarded. In 1841, an Act of the Nova Scotia House of Assembly conferred university powers on Dalhousie.

Dalhousie's first principal was Thomas McCulloch. A Presbyterian minister and naturalist, he was the founder of Nova Scotia's second degree-granting institution (after King's College, now University of King's College), Pictou Academy in Pictou, Nova Scotia, which attracted students from PEI, Cape Breton, as well as the Caribbean due to McCulloch's views and the school's ecumenical stance.

In 1838, the board of Dalhousie College was able to convince McCulloch leave Pictou Academy and take on the floundering Dalhousie. With a reputation as an anti-papal pamphleteer and firmly against the Church of England's hold on higher education in Nova Scotia (through King's College), McCulloch carried with him from Pictou his education theory and pedagogy, “If Dalhousie College acquires usefulness and eminence, it will be not by an imitation of Oxford, but as an institution of science, and practical intelligence.” His approach to education was radical: he firmly believed that all schools "ought first to be ascertained, how far it is calculated to improve the community; and, if its general utility appear, it is, in proportion to its value and to the extent of the public funds, unquestionably entitled to the protection of Government, whether it belong to churchmen or [Presbyterian] dissenters, protestants or catholics, ought to be entirely disregarded!" He was responsible for creating a chair of natural history at Dalhousie to teach "geology, mineralogy, botany, and zoology."

Following McCulloch's death, the college fell into decline once again and was reorganized as a high school in 1848. In 1863, the college opened for a third time and was reorganized by another legislative act, which added "University" to the school's name: "The Governors of Dalhousie College and University". Dalhousie reopened with six professors and one tutor. When it awarded its first degrees in 1866, the student body consisted of 28 male students working toward degrees and 28 occasional students. Despite the reorganization and an increase in students, money continued to be a problem for the institution. In 1879, amid talks of closure due to the university's dire financial situation, George Munro, a wealthy New York publisher with Nova Scotian roots, began to donate to the university; Munro was brother-in-law to Dalhousie's Board of Governors member John Forrest. As such, Munro is credited with rescuing Dalhousie from closure. In honour of his contributions, Dalhousie observes a university holiday called George Munro Day on the first Friday of each February. The first female graduate was Margaret Florence Newcombe from Grafton, Nova Scotia, who earned a Bachelor of Arts degree in 1885.

Originally located at the space now occupied by Halifax City Hall, the college moved in 1886 to Carleton Campus and spread gradually to Studley Campus. Dalhousie grew steadily during the 20th century. From 1889 to 1962 the Halifax Conservatory was affiliated with and awarded degrees through Dalhousie. In 1920, several buildings were destroyed by fire on the campus of the University of King's College in Windsor, Nova Scotia. Through a grant from the Carnegie Foundation, King's College relocated to Halifax and entered into a partnership with Dalhousie that continues to this day.

Dalhousie expanded on 1 April,1997 when provincial legislation mandated an amalgamation with the nearby Technical University of Nova Scotia. This merger saw reorganization of faculties and departments to create the Faculty of Engineering, Faculty of Computer Science and the Faculty of Architecture and Planning. From 1997 to 2000, the Technical University of Nova Scotia operated as a constituent college of Dalhousie called Dalhousie Polytechnic of Nova Scotia (DalTech) until the collegiate system was dissolved. The legislation that merged the two schools also formally changed the name of the institution to its present form, Dalhousie University. On 1 September 2012, the Nova Scotia Agricultural College merged into Dalhousie to form a new Faculty of Agriculture, located in Bible Hill, Nova Scotia.

Campuses
Dalhousie has three campuses within the Halifax Peninsula and a fourth, the Agricultural Campus, in Bible Hill, Nova Scotia.

Studley Campus in Halifax serves as the primary campus; it houses the majority of the university's academic buildings such as faculties, athletic facilities, and the university's Student Union Building. The campus is largely surrounded by residential neighbourhoods.

Robie Street divides it from the adjacent Carleton Campus, which houses the faculties of dentistry, medicine, and other health profession departments. The campus is adjacent to two large teaching hospitals affiliated with the school: the IWK Health Centre and the Queen Elizabeth II Health Sciences Centre.

Sexton Campus in Downtown Halifax hosts the engineering, architecture and planning faculties. Sexton Campus served as the campus of the Technical University of Nova Scotia prior to amalgamation. The Agricultural Campus in Bible Hill, a suburban community of Truro, served as the campus for the Nova Scotia Agricultural College prior to its merger with Dalhousie in 2011. The university presently operates the largest academic library system in Atlantic Canada, and hosts the headquarters for the Ocean Tracking Network.

The buildings at Dalhousie vary in age from Hart House, which was completed in 1864, to the Collaborative Health Education Building, completed in 2015. The original building of Dalhousie University was completed in 1824 on Halifax's Grand Parade. It was demolished in 1885 when the university outgrew the premises, and the City of Halifax sought possession of the entire Grand Parade. Halifax City Hall presently occupies the site of the original Dalhousie College.

Libraries and museums
The university has five libraries. The largest, Killam Memorial Library, opened in 1971 and claims to be the largest academic library in Atlantic Canada. The W. K. Kellogg Health Science Library provides services largely for the faculties of dentistry, medicine, and other health professions. The Sexton Design & Technology Library is located within Sexton Campus. Its collection largely serves those in the faculties of engineering, architecture and planning, and houses the university's rare books collection. The Sir James Dunn Law Library holds the university's collection of common law materials, legal periodicals, as well as books on international law, health law, and environmental law. MacRae Library is located at the university's Agricultural Campus, and has the largest collection of agricultural resource material in Atlantic Canada. The Dalhousie University Archives houses official records of, or relating to, or people/activities connected with Dalhousie University and its founding institutions. The archives also houses material related to theatre, business and labour in Nova Scotia. The collection consists of manuscripts, texts, photographs, audio-visual material, microfilm, music, and artifacts. The university's first library, Macdonald Memorial Library, was built after alumni raised funds on the death of professor Charles Macdonald, who had left the university $2,000 to buy books in English literature on his death in 1901.

The biology department operates the Thomas McCulloch Museum in its Life Sciences Centre (LSC). The most notable of the museum's exhibits include its preserved birds collection. Other collections include its Lorenzen ceramic mushrooms, its coral and shell collection, and its butterfly and insect collection. The museum's namesake Thomas McCulloch was a Scottish Presbyterian minister who served as Dalhousie's first president and created the Audubon mounted bird collection which is now housed at the museum.

The Dalhousie Art Gallery is both a public gallery and an academic support unit housed since 1971 on the lowest level of the Dalhousie Arts Centre. Admission is free of charge. It is host to a permanent collection of over 1000 works. Some of the outdoor sculptures around the campus are part of this collection, such as the distinctive Marine Venus which has sat in the median of University Avenue since 1969. A notable exhibition from the Dalhousie Art Gallery includes "Archives of the Future" (March – April 2016) exploring the relationship between art creation and commerce with work by artists Zachary Gough, Dawn Georg, Sharlene Bamboat, Katie Vida and Dana Claxton.

Sustainability
Dalhousie University is actively involved in sustainability issues and has received a number of sustainability awards and recognition for academic programs, university operations, and research. In 2022, Dalhousie received a GOLD rating from AASHE STARS (Version 2.2) In 2009, the university signed the University and College Presidents' Climate Change Statement of Action for Canada to reduce emissions of greenhouse gases. Dalhousie is also a signatory of UNEP's International Declaration on Cleaner Production. In 1999, the university signed the Talloires Declaration, which committed Dalhousie and other higher education institutions to developing, creating, supporting, and maintaining sustainability.

In 2008, the College of Sustainability, the Office of Sustainability, and the Dalhousie Student Union Sustainability Office were formed. During 2008, the President's Advisory Council on Sustainability was also created. The council meets quarterly to discuss pan-university sustainability issues. Dalhousie's College of Sustainability offers an undergraduate Major in Environment, Sustainability and Society (ESS) integrating with seven bachelor's degrees and 40 subjects across five faculties.

Administration
University governance is conducted through the Board of Governors and the Senate, both of which were given much of their present power in the Unofficial Consolidation of an Act for the Regulation and Support of Dalhousie College in Chapter 24 of the Acts of 1863. This statute replaced ones from 1820, 1823, 1838, 1841 and 1848, and has since been supplemented 11 times, most recently in 1995. The Board is responsible for conduct, management, and control of the university and of its property, revenues, business, and affairs. Board members, known as Governors of the Board, include the university's chancellor, president, and 25 other members. Members include people from within the university community such as four approved representatives from Dalhousie Student Union, and those in the surrounding community, such as the Mayor of Halifax. The Senate is responsible for the university's academics, including standards for admission and qualifications for degrees, diplomas, and certificates. The Senate consists of 73 positions granted to the various faculty representatives, academic administrators, and student representatives.

The president acts as the chief executive officer and is responsible to the Board of Governors and to the Senate for the supervision of administrative and academic works. Kim Brooks is the 13th president of the university, and has served since August 2023. Thomas McCulloch served as the first president when the office was created in 1838. John Forrest was the longest-serving president, holding the office from 1885 to 1911.

Affiliated institutions
University of King's College is a post-secondary institution in Halifax affiliated with Dalhousie. The institution's campus is located adjacent to Dalhousie's Studley campus. Established in 1789, it was the first post-secondary institution in English Canada and the oldest English-speaking Commonwealth university outside the United Kingdom. The University of King's College was formerly an independent institution located in Windsor, Nova Scotia, until 1920, when a fire ravaged its campus. To continue operation, the University of King's College accepted a generous grant from the Carnegie Foundation, although the terms of the grant required that it move to Halifax and enter into association with Dalhousie. Under the agreement, King's agreed to pay the salaries of a number of Dalhousie professors, who in turn were to help in the management and academic life of the college.

Students at King's have access to all of the amenities at Dalhousie, and academic programs at King's would fold into the College of Arts and Sciences at Dalhousie according to the agreement. Presently, students of both institutions are allowed to switch between the two throughout their enrolment. In spite of the shared academic programs and facilities, the University of King's College maintains its own scholarships, bursaries, athletics programs, and student residences.

Finances
The university completed the 2017–18 year with revenues of $697.354 million and expenses of $664.274 million, yielding a surplus of $33.08 million. The largest source of revenue for the university was provincial operational grants, followed by tuition fees. The total endowment revenue reported in fiscal 2017–2018 was $481.372 million.

Diversity
The university has attempted to increase the representation of under-represented groups at Dalhousie through inclusive recruitment strategies. There have been several Dalhousie University scandals related to discrimination at the university.

Academics
Dalhousie is a publicly funded research university, and a member of the Association of Universities and Colleges of Canada, as well as the U15. , there were 20,970 students enrolled at the university. Dalhousie offers more than 4,000 courses and over 200 degree programs in 13 undergraduate, graduate, and professional faculties. The requirements for admission differ between students from Nova Scotia, students from other provinces in Canada, and international students due to lack of uniformity in marking schemes. The requirements for admission also differ depending on the program. In 2011, the secondary school average for incoming first-year undergraduate students was 85 percent.

Canadian students may apply for financial aid such as the Nova Scotia Student Assistance Program and Canada Student Loans and Grants through the federal and provincial governments. Financial aid may also be provided in the form of loans, grants, bursaries, scholarships, fellowships, debt reduction, interest relief, and work programs. The university's registrar provides scholarships for its students in order to provide financial assistance, or to reward academic merits or performances in another fields, such as community involvement and leadership.

Reputation
The 2022 Academic Ranking of World Universities ranked Dalhousie University 301–400 in the world and 13–17 in Canada. The 2023 QS World University Rankings ranked the university 308th in the world, and twelfth in Canada. The 2023 Times Higher Education World University Rankings placed Dalhousie 301–350 in the world. In the 2022–23 U.S. News & World Report Best Global University Ranking, the university placed 314th in the world, and 11th in Canada. In terms of national rankings, Maclean's ranked Dalhousie seventh in their 2023 Medical-Doctoral university rankings. Dalhousie was ranked in spite of having opted out – along with several other universities in Canada – of participating in Maclean's graduate survey since 2006.

Dalhousie also placed in a number of rankings that evaluated the employment prospects of its graduates. In the Times Higher Education's 2022 global employability ranking, Dalhousie placed 186th in the world, and eighth in Canada. In QS's 2020 graduate employability ranking, the university ranked 301–500 in the world, and 10–16 in Canada.

Research
In 2018, Research Infosource ranked Dalhousie as 15th on their list for top 50 research universities in Canada, with a sponsored research income (external sources of funding) of $150.038 million in 2017. In the same year, Dalhousie's faculty averaged a sponsored research income of $130,000, while its graduate students averaged a sponsored research income of $44,600. In 2003 and 2004, The Scientist placed Dalhousie among the top five places in the world outside the United States for postdoctoral work and conducting scientific research. In 2007 Dalhousie topped the list of The Scientist's "Best Places to Work in Academia". The annual list divides research and academic institutions into American and international lists; Dalhousie University ranked first in the international category. According to a survey conducted by The Scientist, Dalhousie was the best non-commercial scientific institute in which to work in Canada. Dalhousie's research performance has been noted in several bibliometric university rankings, which use citation analysis to evaluate the impact a university has on academic publications. In 2019, the Performance Ranking of Scientific Papers for World Universities ranked Dalhousie 301st in the world, tied for 12th in Canada with the University of Manitoba; whereas the University Ranking by Academic Performance 2018–19 rankings placed the university 302nd in the world, and 13th in Canada.

Marine research at Dalhousie has become a large focus of the university, with many of the university's faculty members involved in some form of marine research. Notably, Dalhousie is the headquarters of the Ocean Tracking Network, a research effort using implanted acoustic transmitters to study fish migration patterns. Dalhousie houses a number of marine research pools, a wet laboratory, and a benthic flume, which are collectively known as the Aquatron laboratory. Dalhousie is one of the founding members of the Halifax Marine Research Institute, founded on 2 June 2011. The institute, which is a partnership between a number of private industries, government, and post-secondary institutions, was designed to help increase the scale, quality, internationalization and impact of marine research in the region. In 2011, the university, along with WWF-Canada, created the Conservation Legacy For Oceans, which aimed at providing scholarships, funding, curriculum development, and work placements for students and academics dedicated to marine research, law, management, and policy making. In 2016, Dalhousie partnered with Memorial University of Newfoundland and the University of Prince Edward Island to form a collaborative research organization known as The Ocean Frontier Institute.

Many of Dalhousie's faculties and departments focus on marine research. The Faculty of Engineering operates the Ocean Research Centre Atlantic, which is dedicated to research and tests in naval and off-shore engineering. Schulich School of Law also operates the Marine & Environmental Law Institute, which carries out research and conducts consultancy activities for governmental and non-governmental organizations. The school's Department of Political Science similarly operates the Centre for Foreign Policy Studies, which is primarily concerned with the fields of Canadian and American foreign, security, and defence policy, including maritime security policy.

Student life
The student body of Dalhousie is currently represented by two student unions; the Dalhousie Student Union, which represents the general student population, and the Dalhousie Association for Graduate Students, which represents the interests of graduate students specifically. As of 2011, there were three sororities and three fraternities. They operate as non-accredited organizations and are not recognized by the Dalhousie Student Union.

The main student newspaper, The Dalhousie Gazette, claims to be the oldest student-run newspaper in North America. The newspaper's offices are in the Student Union building. The radio station began as a radio club in 1964 and operated as CKDU in 1975; it began FM broadcasting in 1985. CKDU acquired its present frequency 88.1 in 2006 and upgraded its transmitting power.

In 2021 and 2022, controversies arose around alcohol consumption at unsanctioned student gatherings on campus, specifically 'homecoming' in early October. Halifax Police urged the university to play a more active role in the issue.

Clubs and societies
In addition to the efforts made by the Dalhousie Student Union (DSU) Council, Dalhousie students have created and participated in over 320 clubs/societies. The Management Society, for example, is a group of students in the Faculty of Management who group together to enhance the experience of students in that faculty by hosting events, providing assistance and giving back. Until 25 July 2016, Dalhousie offered a website named "Tiger Society" which listed all current clubs and societies that were available for students to join. Through this website, students could request to join a society. Dalhousie also holds a Society Fair at the beginning of each fall and winter semester, in which all societies are given the opportunity to display their purpose/efforts and recruit new members. Student societies partake in a range of activities from simple gatherings, study groups, bake sales, intramural sports teams, to organizing larger scale fundraising events.

Athletics
Dalhousie's sports teams are called the Tigers. The Tigers varsity teams participate primarily in the Atlantic University Sport (AUS) of U Sports. There are teams for basketball, hockey, soccer, swimming, track and field, cross country running, and volleyball. The Tigers garnered a number of championships in the first decade of the 20th century, winning 63 AUS championships and two U Sports championships. More than 2,500 students participate in competitive clubs, intramural sport leagues, and tournaments. Opportunities are offered at multiple skill levels across a variety of sports. Dalhousie has six competitive sports clubs and 17 recreational clubs. Dalhousie's Agricultural Campus operates its own varsity team, called the Dalhousie Rams. The Rams varsity team participates in the Atlantic Collegiate Athletic Association, a member of the Canadian Collegiate Athletic Association. The Rams varsity teams include badminton, basketball, rugby, soccer, volleyball, and woodsmen.

Dalhousie has a number of athletic facilities open to varsity teams and students. Dalplex is the largest main fitness and recreational facility. It houses a large fieldhouse, an Olympic-sized swimming pool, an indoor running track, weight rooms, courts and other facilities. Wickwire Field, with a seating capacity of up to 1,200, is the university's main outdoor field and is host to the varsity football, soccer, field hockey, lacrosse and rugby teams. Other sporting facilities include the Studley Gymnasium, and the Sexton Gymnasium and field. The Memorial Arena, home to the varsity hockey team, was demolished in 2012. The school is working to build a new arena jointly with nearby Saint Mary's University, whose facility is also aging. The Agricultural Campus has one athletic facility, the Langille Athletic Centre. As of 2010, through the efforts of alumni and devoted volunteers, the Dalhousie Football Club was reinstated. Playing in the Atlantic Football League (AFL), the team operates on donations from alumni. The team plays its home games at Wickwire Field.

Seal
The Dalhousie seal is based on the heraldic achievement of the Clan Ramsay of Scotland, of which founder George Ramsay was clan head. The heraldic achievement consists of five parts: shield, coronet, crest, supporters, and motto. One major difference between the Ramsay coat of arms and the university seal is that the Ramsay seal features a griffin and greyhound, and the Dalhousie seal has two dragons supporting the eagle-adorned shield. Initially, the Ramsay coat of arms was used to identify Dalhousie, but the seal has evolved with the amalgamations the university has undergone. The seal was originally silver-coloured, but in 1950, the university's Board of Governors changed it to gold to match the university's colours, gold and black. These colours were adopted in 1887, after the rugby team led the debate about college colours for football jerseys. The shield and eagle of Dalhousie's seal have been used as the logo since 1987, with the present incarnation in use since 2003, which includes the tagline "inspiring minds".

Motto and song
The university motto Ora et Labora translates from Latin as "pray and work"; it adopted in 1870 from the Earl of Dalhousie's motto to replace the university's original one, which the administration believed did not convey confidence. The original motto was Forsan (Latin for "perhaps"), and first appeared in the first Dalhousie Gazette of 1869. It was from Virgil's epic poem Aeneid, Book 1, line 203, Forsan et haec olim meminisse iuvabit, which translates as "Perhaps the time may come when these [difficulties] will be sweet to remember." In 2020, students and staff representatives sought to remove the inherently religious tone of the current motto and return to the first.

Among the school's songs is the "Carmina Dalhousiana", written in Halifax in 1882. A Dalhousie University songbook was compiled by Charles B. Weikel in 1904.

Notable alumni
Dalhousie graduates have found success in a variety of fields, serving as heads of a diverse array of public and private institutions. Dalhousie University has over 130,000 alumni. Throughout Dalhousie's history, faculty, alumni, and former students have played prominent roles in many fields, and include 91 Rhodes Scholars.

Dalhousie has also educated Nobel laureates. Astrophysicist and Dalhousie alumni Arthur B. McDonald (BSc 1964, MSc 1965) received the 2015 Nobel Prize in Physics for identifying neutrino change identities and mass. McDonald was also previously awarded the Herzberg Prize and the Benjamin Franklin Prize in physics. Other notable graduates of Dalhousie includes Donald O. Hebb, who helped advance the field of neuropsychology, Kathryn D. Sullivan, the first American woman to walk in space and Jeff Dahn, one of the world's foremost researchers in lithium battery chemistry and aging. E. Elizabeth Patton, elected as a Fellow of the Royal Society of Edinburgh (2021) and Personal Chair in Melanoma Genetics and Drug Discovery, MRC Human Genetics Unit, Edinburgh.

Notable politicians who have attended Dalhousie include three Prime Ministers of Canada, R. B. Bennett, Joe Clark, and Brian Mulroney. Eight graduates have served as Lieutenant Governors: John Crosbie, Myra Freeman, Clarence Gosse, John Keiller MacKay, Henry Poole MacKeen, John Robert Nicholson, Fabian O'Dea, and Albert Walsh. Twelve graduates have served as provincial premiers: Allan Blakeney, John Buchanan, Alex Campbell, Amor De Cosmos, Darrell Dexter, Joe Ghiz, John Hamm, Angus Lewis Macdonald, Russell MacLellan, Gerald Regan, Robert Stanfield, Clyde Wells, and Danny Williams. The first woman appointed to the Supreme Court of Canada, Bertha Wilson, was a graduate from Dalhousie Law School.

Other notable alumni from the Dalhousie include Lucy Maud Montgomery, an author that wrote a series of novels, including Anne of Green Gables. Prominent business leaders who studied at Dalhousie include Jamie Baillie, former CEO of Credit Union Atlantic, Graham Day, former CEO of British Shipbuilders, Sean Durfy, former CEO of WestJet, and Charles Peter McColough, former president and CEO of Xerox.

title: Dalhousie University


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Molecular diffusion

Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random motion of the molecules. The result of diffusion is a gradual mixing of material such that the distribution of molecules is uniform. Since the molecules are still in motion, but an equilibrium has been established, the result of molecular diffusion is called a "dynamic equilibrium". In a phase with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually result in complete mixing.

Consider two systems; S1 and S2 at the same temperature and capable of exchanging particles. If there is a change in the potential energy of a system; for example μ1>μ2 (μ is Chemical potential) an energy flow will occur from S1 to S2, because nature always prefers low energy and maximum entropy.

Molecular diffusion is typically described mathematically using Fick's laws of diffusion.

Applications
Diffusion is of fundamental importance in many disciplines of physics, chemistry, and biology. Some example applications of diffusion:
 * Sintering to produce solid materials (powder metallurgy, production of ceramics)
 * Chemical reactor design
 * Catalyst design in chemical industry
 * Steel can be diffused (e.g., with carbon or nitrogen) to modify its properties
 * Doping during production of semiconductors.

Significance
Diffusion is part of the transport phenomena. Of mass transport mechanisms, molecular diffusion is known as a slower one.

Biology
In cell biology, diffusion is a main form of transport for necessary materials such as amino acids within cells. Diffusion of solvents, such as water, through a semipermeable membrane is classified as osmosis.

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.

Tracer, self- and chemical diffusion
Fundamentally, two types of diffusion are distinguished:
 * Tracer diffusion and Self-diffusion, which is a spontaneous mixing of molecules taking place in the absence of concentration (or chemical potential) gradient. This type of diffusion can be followed using isotopic tracers, hence the name. The tracer diffusion is usually assumed to be identical to self-diffusion (assuming no significant isotopic effect). This diffusion can take place under equilibrium. An excellent method for the measurement of self-diffusion coefficients is pulsed field gradient (PFG) NMR, where no isotopic tracers are needed. In a so-called NMR spin echo experiment this technique uses the nuclear spin precession phase, allowing to distinguish chemically and physically completely identical species e.g. in the liquid phase, as for example water molecules within liquid water. The self-diffusion coefficient of water has been experimentally determined with high accuracy and thus serves often as a reference value for measurements on other liquids. The self-diffusion coefficient of neat water is: 2.299·10−9 m2·s−1 at 25 °C and 1.261·10−9 m2·s−1 at 4 °C.
 * Chemical diffusion occurs in a presence of concentration (or chemical potential) gradient and it results in net transport of mass. This is the process described by the diffusion equation. This diffusion is always a non-equilibrium process, increases the system entropy, and brings the system closer to equilibrium.

The diffusion coefficients for these two types of diffusion are generally different because the diffusion coefficient for chemical diffusion is binary and it includes the effects due to the correlation of the movement of the different diffusing species.

Non-equilibrium system
Because chemical diffusion is a net transport process, the system in which it takes place is not an equilibrium system (i.e. it is not at rest yet). Many results in classical thermodynamics are not easily applied to non-equilibrium systems. However, there sometimes occur so-called quasi-steady states, where the diffusion process does not change in time, where classical results may locally apply. As the name suggests, this process is a not a true equilibrium since the system is still evolving.

Non-equilibrium fluid systems can be successfully modeled with Landau-Lifshitz fluctuating hydrodynamics. In this theoretical framework, diffusion is due to fluctuations whose dimensions range from the molecular scale to the macroscopic scale.

Chemical diffusion increases the entropy of a system, i.e. diffusion is a spontaneous and irreversible process. Particles can spread out by diffusion, but will not spontaneously re-order themselves (absent changes to the system, assuming no creation of new chemical bonds, and absent external forces acting on the particle).

Concentration dependent "collective" diffusion
Collective diffusion is the diffusion of a large number of particles, most often within a solvent.

Contrary to brownian motion, which is the diffusion of a single particle, interactions between particles may have to be considered, unless the particles form an ideal mix with their solvent (ideal mix conditions correspond to the case where the interactions between the solvent and particles are identical to the interactions between particles and the interactions between solvent molecules; in this case, the particles do not interact when inside the solvent).

In case of an ideal mix, the particle diffusion equation holds true and the diffusion coefficient D the speed of diffusion in the particle diffusion equation is independent of particle concentration. In other cases, resulting interactions between particles within the solvent will account for the following effects:
 * the diffusion coefficient D in the particle diffusion equation becomes dependent of concentration. For an attractive interaction between particles, the diffusion coefficient tends to decrease as concentration increases. For a repulsive interaction between particles, the diffusion coefficient tends to increase as concentration increases.
 * In the case of an attractive interaction between particles, particles exhibit a tendency to coalesce and form clusters if their concentration lies above a certain threshold. This is equivalent to a precipitation chemical reaction (and if the considered diffusing particles are chemical molecules in solution, then it is a precipitation).

Molecular diffusion of gases
Transport of material in stagnant fluid or across streamlines of a fluid in a laminar flow occurs by molecular diffusion. Two adjacent compartments separated by a partition, containing pure gases A or B may be envisaged. Random movement of all molecules occurs so that after a period molecules are found remote from their original positions. If the partition is removed, some molecules of A move towards the region occupied by B, their number depends on the number of molecules at the region considered. Concurrently, molecules of B diffuse toward regimens formerly occupied by pure A. Finally, complete mixing occurs. Before this point in time, a gradual variation in the concentration of A occurs along an axis, designated x, which joins the original compartments. This variation, expressed mathematically as -dCA/dx, where CA is the concentration of A. The negative sign arises because the concentration of A decreases as the distance x increases. Similarly, the variation in the concentration of gas B is -dCB/dx. The rate of diffusion of A, NA, depend on concentration gradient and the average velocity with which the molecules of A moves in the x direction. This relationship is expressed by Fick's Law

 * $$N_{A}= -D_{AB} \frac{dC_{A}}{dx}$$  (only applicable for no bulk motion)

where D is the diffusivity of A through B, proportional to the average molecular velocity and, therefore dependent on the temperature and pressure of gases. The rate of diffusion NA, is usually expressed as the number of moles diffusing across unit area in unit time. As with the basic equation of heat transfer, this indicates that the rate of force is directly proportional to the driving force, which is the concentration gradient. This basic equation applies to a number of situations. Restricting discussion exclusively to steady state conditions, in which neither dCA/dx or dCB/dx change with time, equimolecular counterdiffusion is considered first.

Equimolecular counterdiffusion
If no bulk flow occurs in an element of length dx, the rates of diffusion of two ideal gases (of similar molar volume) A and B must be equal and opposite, that is $$N_A=-N_B$$. The partial pressure of A changes by dPA over the distance dx. Similarly, the partial pressure of B changes dPB. As there is no difference in total pressure across the element (no bulk flow), we have

 * $$ \frac{dP_A}{dx}=-\frac{dP_B}{dx}$$.

For an ideal gas the partial pressure is related to the molar concentration by the relation
 * $$     P_{A}V=n_{A}RT$$

where nA is the number of moles of gas A in a volume V. As the molar concentration CA is equal to nA/ V therefore
 * $$     P_{A}=C_{A}RT$$

Consequently, for gas A,

 * $$ N_{A}=-D_{AB} \frac{1}{RT} \frac{dP_{A}}{dx} $$

where DAB is the diffusivity of A in B. Similarly,

 * $$ N_{B}=-D_{BA} \frac{1}{RT} \frac{dP_{B}}{dx}=D_{AB} \frac{1}{RT}\frac{dP_{A}}{dx}$$

Considering that dPA/dx=-dPB/dx, it therefore proves that DAB=DBA=D. If the partial pressure of A at x1 is PA 1 and x2 is PA 2, integration of above equation,

 * $$ N_{A}=-\frac{D}{RT} \frac{(P_{A2}-P_{A1})}{x_{2}-x_{1}}$$

A similar equation may be derived for the counterdiffusion of gas B.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Molecular diffusion


text:
Talk:Molecular diffusion

Definition
Diffusion is not limited to molecules, from a general (mathematical formulation) point-of-view a lot of processes are diffusive. What diffusion is or not is, is best to discuss by means of maths because that is the most accurate and objective way to write down things with. Things like "diffusion is the movement of molecules from high to low chemical potential/concentration, sometimes against the concentration gradient!" I would like to see in it's own section, i.e. not stated as general fact in the first few lines of this article.145.94.65.212 (talk) 07:08, 1 October 2008 (UTC)

 * Diffusion "in general" and the mathematical formulation already have their own articles. Other "diffusive processes" also have their respective articles, e.g., Momentum diffusion. I feel this article should contain itself to a physical phenomenon of molecular diffusion of mass, that does exist, and try to explain it in an accessible language.

 * Alternatively, I think a new article should be considered, like Molecular diffusion of mass. Then this article (Diffusion) changed to represent what it is actually about because right now it does not seem clear at all. Stan J. Klimas (talk) 14:22, 13 October 2008 (UTC)

 * I would like to add that Fourier's brilliant mathematics did not lead him to understand diffusion first, though Fourier was clearly one of the first to describe heat transfer from a mathematical perspective. But he was describing conduction.  It was all Fick, who saw the relevance of the mathematics describing heat and momentum transfer in describing mass transfer.  The thermal conductivity in Fourier's equations of transport can simply be replaced with a diffusion coefficient to describe mass transfer, I know this is a small thing, but I think Adolf Fick was a genius in his work, and I think the discovery of diffusion should be placed on him soley.  Sure on a molecular level, the stretching of bonds is relevant for heat transfer, but I see this as thermodynamics...not mass transfer.Biotechscientist (talk) 03:04, 19 November 2010 (UTC)

Mathematics
It is to specialistic for the general reader looking up diffusion.145.116.1.3 (talk) 07:45, 5 June 2008 (UTC)

Exactly, there seems to be a problem with the management of this page, I tried to put in a general definition in the introduction (see revision of early september) and it disappears; in its place childish statements like "Einstein was clever".

Also there is a problem of definition. I come from a physical chemistry research background where diffusion is only used in the sense of the movement of molecules due to their thermal energy within chemical systems. The transfer of heat may follow the same maths but is not diffusion (to me). I am willing to have a physicist clarify this, but there still needs to be a separate page. The example of the spoon getting hot is confusing and I believe wrong. Manikato (talk) 03:22, 30 September 2008 (UTC)

I would like to keep the page on diffusion general, to fit all the different (natural) processes that show the same behaviour. To me (physicist), diffusion is not restricted to particles/molecules alone, since there can be diffusion of heat, or diffusion of wave function in quantum mechanics (for example). 145.94.65.212 (talk) 19:23, 1 October 2008 (UTC)

General discussion
Diffusion is the movement from a high to low concentration along the concentration gradient. In ternary solutions particles can be tranported from low to high concentrations. Joao

This can happen in binary alloys, too Olof
 * Agreed. Molecular diffusion occurs in solids as well as liquids and gases; even pure, unalloyed metals exhibit molecular diffusion. 99.133.144.210 (talk) 01:56, 29 July 2011 (UTC)

Diffusion as noted in the last paragraph generally implies a dilution or mixing of the medium. Hence I'm not totally happy by a contrast with radiation as this is itself a diffusion mechanism. Indeed the reference to heat through a window is indeed diffusion by radiation. Rjstott

Heat through a window was a bad example. Maybe heat through a window at nighttime was what I was thinking. Perhaps heat through an oven door is a better example. However, I think its correct to say radiation and diffusion are completely different transport phenomena: in heat transport by radiation, photons get emitted by thermal activation and carry the energy until the photons are absorbed somewhere else. heat transport by diffusion is governed by the thermal conductivity of the material and the temperature gradient. Olof

Way back in school, there were three heat transport mechanisms, conduction, convection and radiation. I believe that heat can be diffused by any of these three. Light is an electromagnetic radiation and diffusion is often associated with light too. Perhaps an example based on light diffusion might work better? Rjstott

You are right about the three mechanisms: Radiation is when photons carry the energy from one place to another. Heat disappears from a material when the photon gets created, and reappears at the place where the photon gets absorbed. The key part there is that the material needs to be hot enough so that it can thermally activate a photon creation, as when a metal is 'red hot'. Of course, at lower temperatures, the photons are lower energy and there is some radiative heat transport. Convection is when, for example, the hot air next to the oven rises to the ceiling, and the air that used to be near the ceiling moves to.... and so on. It is only applicable to fluids. Conduction is when heat diffuses through a material, and it is the only one of the three mechanisms which is strictly a diffusion. By this I mean that the mathematical equation which is used to model the heat flow is the diffusion equation. Olof

I was also thinking of adding a section on computer graphics diffusion: the process whereby an image is blurred by an image editing program also follows the same math. Olof

I think the 'in biology' section is completely wrong. Amino acids cannot diffuse across a cell membrane, they must be transported across by specific sodium-dependent transport proteins. Moreover, the citation is not very good - many introductory textbooks are notoriously wrong. —Preceding unsigned comment added by 128.61.94.19 (talk) 02:24, 24 October 2008 (UTC)

Disambiguation
I hate it when one page is used for two topics. Something needs to be done! Either create a page for Diffusion (physics) and Diffusion (anthropology) or kill the anthropology on the diffusion page.

Osmosis= diffusion of water not general diffusion surely. Equally my GCSE biology teacher could have been lying to me...

 * I agree the osmosis reference should be removed, and I did so. Danrs 18:45, 15 August 2007 (UTC)

Types of diffusion in separate pages
I just made a major change to the layout of the page. Since there were alot different types (and sub-types) of diffusion listed inthe article, I grouped them all in one section and moved the relevant information to separate pages on the particular types of diffusion. Hope that made the page a bit clearer than before. Cheers Karol 18:01, 15 September 2005 (UTC)

Diffusion and Turbulence
I think diffusion is not connected to turbulence, the example of smoke dissipating into the air is a bad example since it involves convection. I have removed the parts accordingly. Lirnup 20:28, 28 September 2005 (UTC)
 * Good work catching that. Also, diffusion isn't quite the same thing as Brownian motion, no? Karol 06:06, 29 September 2005 (UTC)
 * As I understand it, in the case of diffusion the particles move one by one by brownian motion, but I'm not really an expert on that. Lirnup 06:21, 29 September 2005 (UTC)
 * Sure, in the case of the diffusion of particles, but that is only one type of diffusion since not only particles diffuse. There is also the subtle difference that BM is a description of the stochastic motion of single particles in itself, whereas diffusion is more a dsecription of a process, in which there is a net transport and flux of the diffusing quantity (related to some kind of gradient). Karol 14:37, 29 September 2005 (UTC)
 * Yes, the brownian motion thing came in only to make a kind of juxtaposition. We better take this out there Lirnup 10:28, 4 October 2005 (UTC)

Good point on the diffusion not being connected to turbulence, some sort of convection would really be necessary as I would consider the velocity of diffusion occurring within some characteristic length to not be able to obtain Reynolds numbers normally associated with turbulence. I consider the dissipation of smoke a laminar flowBiotechscientist (talk) 02:37, 19 November 2010 (UTC)
 * To some extent there is a false dichotomy between convection and diffusion, insofar as "shear induced dispersion" is a coherent concept used to quantify effective diffusivities, see e.g. Taylor dispersion. The key is to establish the scale (in time and space) of the motion of interest- turbulent mixing is an effective diffusion on scales much larger than the scale of the turbulent eddies; for the typically encountered situations the fractal nature of turbulence means that no scale can be found on which it only adds to an effective diffusion, but some media have upper cutoff lengthscales for the turbulent motion. That smoke example was bad and should stay deleted, but convection and diffusion are not always mutually exclusive, and frequently what is called convection on a small scale leads to diffusion on a large scale. 99.133.144.210 (talk) 02:13, 29 July 2011 (UTC)

A redlink story
At 11h04 today (31 october 2005), I added a link to collective diffusion in this article. At 11h06, or 2 minutes later, this link was deleted by user:Karol Langner, on the basis that I should first create the collective diffusion article (I created this article "only" at 11h17). So Karol, a question: are you going to delete all the red links that have existed for more than 2 minutes in this encyclopedia, or should I conclude that you are specifically after my edits? ThorinMuglindir 12:32, 31 October 2005 (UTC)

OK sorry Karol I was a bit upset when I dscovered you had canceled my edit. Now, admit the real reason why you canceled it is because it conflicted with yours, and having to cope with those 2 text boxes is a mess. So that you thought that since your edit as big and mine was just a link, it wouldn't be much of a deal for me to add it back... I prefer that to you being specifically after my edits. ThorinMuglindir 14:27, 31 October 2005 (UTC)

BTW in hopes that you'd visit it quickly, I added a red link to the following page:
 * Talk:Degrees of freedom (physics and chemistry) ThorinMuglindir 14:27, 31 October 2005 (UTC)
 * I wasn't even aware that it was your edit, and deleted the red link, because it didn't add anything to that list. And I didn't look at the time, so I also didn't get that the page would be created soon. In any case, I'm not stalking you. Sorry. My bad. Karol 15:01, 31 October 2005 (UTC)

 * OK no problem. Your edits you do appear sound to me btw. We'd better get across as clearly as possible that diffusion is a very general phenomenon.ThorinMuglindir 16:21, 31 October 2005 (UTC)

Diffusion (mathematics)
I find this page only gives the physical view. There is also the mathematical term of a diffusion (process). Of course these concepts are related, but it's not the same. LARS 18:58, 19 November 2005 (UTC)

 * The mathematical term--and the other uses of diffusion--are in analogy to the mathematical models for the physical process, no? You can discuss the diffusion equation or a random walk without reference to the physical process, but then there are already articles on those topics.  I added a statement about the analogies in the intro. Danrs 18:53, 15 August 2007 (UTC)

Giant animation
Somebody might want to remove the giant animated GIF from this page. Just sayin'.

 * What's your screen resolution? You might want to increase it... — 0918 BRIAN • 2006-04-3 07:37

 * It's distracting and irritating, and the size contributes to this. My screen resolution is higher than average, yet I still find the image too big; I have a higher resolution because I want a greater density of information.  It really doesn't take a 12x12 square of pixels to represent a particle.  The image should be reduced to half size, and possibly slowed down (most of the animation shows random motion - the reader currently needs to watch the loop several times to catch the three seconds or so of diffusion). --Will 152.78.191.84 12:16, 14 June 2006 (UTC)

Why does diffusion happen faster in warmer systems?
Isn't it because warmer systems have more energy and higher energy molecules move fast? too bad i don't have a reference for that Tsinoyboi 16:16, 21 September 2006 (UTC)

Examples of diffusion
The example of the sugar cube in WATER is wrong, unless we could guarantee that water is completely still. Otherwise there will be some transport due to convection, and it is also likely that the "sugar water" neat the sugar cube will sink to the bottom of the glass due to its higher density and the gravitational force. —The preceding unsigned comment was added by 201.231.152.118 (talk • contribs).

 * I have removed the examples listed as not being examples of diffusion, because the statement implies that they do not really contribute to the article. Perhaps they could be reworded so they can be included in the article. For instance, I would still think diffusion plays an important role (in addition to convection). Perheps this could be reworded to reflect the role of diffusion?--GregRM 21:57, 19 July 2006 (UTC)

Could it be convection and diffusion? i'm finding in my chemistry textbook that convection in an isolated system such as a closed flask are examples. Maybe the difference is that it be closed and a room has too much outside energy such as people or light. Tsinoyboi 17:14, 21 September 2006 (UTC)

Removed section
The following are NOT examples of diffusion:
 * A gas distributes itself over a room by diffusion
 * A sugar cube in a glass of water that is not stirred will dissolve slowly and the sugar molecules will distribute over the water by diffusion
 * Ink in a beaker of water is an example of diffusion. In the end, the ink particles spread evenly throughout the mass of water

According to my textbook, Chemistry & Chemical Reactivity, 6th edition, Thomson Brooks/Cole ISBN 0-495-01013-8, cover seen here http://www.newtexts.com/newtexts/book.cfm?book_id=3038, those count as diffusion that ultimately they become scattered. It says so on page It's supposed to be closed containers so they can be closed systems, it's just that those systems are open to other sources of energy to affect the rate system. Rate doesn't mean it's not diffusion. Warmer molecules will just mix faster. Being open systems, heat may be introduced like windows or people in a room, or escape like water evaporating from a beaker. The listed items are still molecules diffusion.

However, in a quiescent medium, gas could distribute evenly across across a room, and the dissolving of sugar will distribute sugar within the water, and the ink particles distributing is diffusion again. I think the word NOT should have been simply removed. Wiki editors, I am new to this, but removing content that is worthwhile to the general public, and relevant, I think you should correct the inaccuracies, and not just remove content. I know about my little section of the world, but so do other people, even if it is the other way around.Biotechscientist (talk) 02:47, 19 November 2010 (UTC)

Removed examples
Theses have nothing to do with diffusion, they are examples of active transport, require energy and specialized transporters/engulfing machinery:
 * 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

Besides Pinocytosis is an intake of small droplets of liquid not lipids, phagocytosis has nothing to do with transporting glucose, it's engulfing of solid particles by cell membranes, read their articles for more info.Enemyunknown (talk) 13:24, 12 December 2008 (UTC)

Diffusion and Thermodynamics
Diffusion and Thermodynamics are definitely related but can you say that diffusion occurs as a result of the second law of thermodynamics? isn't it more that The second law of thermodynamics works because of diffusion of heat? Tsinoyboi 16:15, 21 September 2006 (UTC)

Also, i found on Thermodynamic equilibrium, "diffusive equilibrium" is used but there's no page for it. Tsinoyboi 16:34, 21 September 2006 (UTC)

hmm, i guess in Chemical potential, it states that entropy remains unchanged at equilibrium, but then again how is chemical potential related to diffusion? I still stand by diffusion as a result of the second law is incorrect. Tsinoyboi 16:34, 21 September 2006 (UTC)

I changed the third paragraph of nature of diffusion. I even cited my source --Tsinoyboi 07:28, 29 September 2006 (UTC)

Chemical potential gradients are what cause diffusion. This is why diffusion of, for example, matter, does not have to occur 'down a concentration gradient' - it will go in any direction which reduces the chemical potential. If this weren't true, we couldn't get spinodal decomposition. Mike 17:07, 17 May 2007 (UTC)

I re-added a sentence about the chemical potential gradient's importance to diffusion, and in particular up-hill diffusion. I think it is of great importance to be aware that diffusion in reality is NOT an effect of concentration gradients but of the interactions between individual atoms/molecules, and how these prefer to stick together or to spread out, to minimize the system energy.(Johnsarelli (talk) 12:12, 4 August 2008 (UTC))

Example Animation is Convection not Diffusion
The example animation on the page shows a clear example of convection and bulk flow; the higher-density dye sinks in the glass of liquid (with turbulent fluid flow); barely any of the visible mixing is due to diffusion. After all, diffusion constants for small molecules tend to be a few hundred microns squared per second, meaning that it would take millions of seconds (weeks) for diffusion to equilibrate the dye concentration in the glass.

Does anyone want to keep that graphic as an example of "mixing that isn't diffusion"? Otherwise, even though it looks cool, I'll just delete it. Ichoran 04:29, 15 October 2006 (UTC)

You are right. http://en.wikipedia.org/wiki/Image:Diffusion.gif must be deleted from the diffusion or edited. -V.I. 17 November 2006

WHY?????? goddammit, quit deleting my edit...Will987654321 06:08, 1 December 2006 (UTC)will987654321

Because it is NOT diffusion -V.I.

I agree that the illustration is NOT an example of diffusion in the Fickian sense that this article is referring to. It is an example of convection. The time it would take to see Fickian diffusion at that scale is BIG. I think that the animation is very misleading and should be removed. When I get some time I will make a simulation of Fickian diffusion. -ZBS

 * I agree with the point that convection is not diffusion and doesn't belong here. A quibble about the use of "Fickian": usually it's used to contrast with other (non-Fickian) forms of diffusion, for example in complex systems, or where the flux depends on the magnitude of the concentration (in addition to the concentration gradient).  It's a little odd to use Fickian to contrast with convection, which is not diffusion at all.  Also, see Fick's law section below.  Danrs 19:04, 15 August 2007 (UTC)

Fick's law
The introduction implied that Fick's law and Fourier's law were alternate names of the diffusion equation. Fick's law is used to derive the diffusion equation, but is not identical to it. Also, I think the important aspect of Fick's law is not that it labels the diffusing substance as mass (as opposed heat), which was implied, but that the net transport is proportional to the concentration gradient. There are other possibilities for purely diffusive systems! I tried to clarify this in the introduction. Danrs 20:04, 15 August 2007 (UTC)

Spontaneous Process
See my comment in the Spontaneous Process talk page.

A section for the shmucks
Is it possible for us to add a section into the article where this process is explained simply? I'm staring at the screen and cringing when I read this - maybe I just have unnaturally low intelligence. The Last Melon 01:53, 26 June 2007 (UTC)

I've tried to make the introductory paragraph more accessible to non-experts. Ichoran 19:03, 17 July 2007 (UTC)

 * Unfortunately, the introductory paragraph was edited to say that diffusion *is* the movement of particles, rather than that this is an *example*. I'm restoring the more general (i.e. more accurate) text.  If there is a compelling reason to do otherwise, please mention the reasoning here!  128.177.16.8 19:10, 3 October 2007 (UTC)

Concentration gradient
"A concentration gradient is the difference between the high concentration and the low concentration. It also determines how fast diffusion occurs."

Isn't it more like the concentration gradient is a measure of how fast the diffusion is? // habj 21:17, 3 August 2007 (UTC)

 * No. The diffusion coefficient is the measure of how fast the diffusion is. The concentration gradient is the result of the initial condition, which diffusion tends to erase.

 * Both sentences from the quoted text have problems. The gradient is the difference between the high and low concentration _divided by the distance_.  Also, it's the flux through a surface that is affected by the concentration gradient, not diffusion.  Simple diffusion occurs independent of concentration and can be measured even in a uniform concentration field.  For instance, the motions of particles in a well-mixed solution can be measured (e.g. using a microscope), and assuming pure diffusion their mean squared displacement will increase linearly in time (a dynamical hallmark of diffusion), with the constant of proportionality giving the diffusion coefficient, as described in the "Diffusion displacement" section.  Danrs 22:16, 13 August 2007 (UTC)

Thermal diffusion ≠ Heat flow
Thermal diffusion ≠ Heat flow. Currently Thermal diffusion redirects here, and then this article sends it off to "Heat flow", which redirects to Heat transfer). This is not the best understanding of Thermal diffusion as in the OED or most places. — DIV (128.250.204.118 06:03, 21 September 2007 (UTC))

Diffusion experiments
The diffusion experiment with ammonia and cotton wool seems a little suspect to me. Won't the rapid evaporation of ammonia increase the local pressure and thus cause slight bulk flow within the tube? Wouldn't stabbing gelatin with a needle with ink be a better experiment? The key to doing a good experiment that demonstrates diffusion is to choose a system where non-diffusive flow is greatly retarded by viscosity or somesuch. Ichoran 19:55, 3 October 2007 (UTC)

This etymology is complete nonsense.
The term diffusion is derived from the Latin verb husionere which means "to break" but can also mean "leave way"

There is no such word "husionere" in Latin. In fact, I can only assume this is vandalism, since it doesn't bear even a passing resemblance to reality.

http://www.m-w.com/

diffuse
 * Etymology: Middle English, from Latin diffusus, past participle of diffundere to spread out, from dis- + fundere to pour

dis-
 * Etymology: Middle English dis-, des-, from Anglo-French & Latin; Anglo-French des-, dis-, from Latin dis-, literally, apart;

http://archives.nd.edu/latgramm.htm

diffusilis -e [capable of spreading, elastic]

fusus (1) -a -um partic. from fundo; q.v.

fundo (1) fundere fudi fusum: of liquids [to pour, pour out]; of metals, [to melt, cast]. Transf., [to pour out, shower, give abundantly]; [to squander]; 'se fundere', [to rush, stream]; of sounds, [to utter]; with emphasis on distribution, [to spread, extend, scatter]; milit., [to rout, defeat, scatter, put to flight]. Hence partic. fusus -a -um, [spread out, extended]; 'crines', [flowing free]; of speech, [diffuse]; adv. fuse, [widely, copiously].

Proving once again that an encyclopedia predicated on popular consensus... sucks.

--75.63.48.18 (talk) 08:02, 8 January 2008 (UTC)
 * A quick google search shows that husionere has now successfully diffused around on the net. These usages may now be used as a citation to refute your proposed etymology. 178.38.117.134 (talk) 13:13, 13 April 2014 (UTC)

Proposed move to Molecular diffusion
I proposed to move this article to Molecular diffusion.

Reason: to better define the scope of the article. "Diffusion" is a large and complex topic.

 * For "diffusion in general", there is already an article Diffusion (disambiguation).
 * For specific types of diffusion, there are already multiple English Wikipedia articles, as listed on the above disambiguation page. If any specific diffusion-related topic is missing, a new article can be added.

The obviously central yet missing article is that on the molecular diffusion of mass.

Under the current title, the basic definitions are disputed. The article does not appear to develop into a useful one, despite an overall large number of edits.

Cheers. Stan J. Klimas (talk) 21:32, 22 October 2008 (UTC)
 * Complete Tohd8BohaithuGh1 (talk) 19:22, 23 October 2008 (UTC)

Example diffusion speeds
The article gives a few examples for typical diffusion speeds such as "In gas: 100 mm per minute". Diffusion is inherently something that is described by the square of length per time unit and these examples (which suggest that 100 mm per 60 seconds equals about 1.5 mm per second) are misleading. Han-Kwang (t) 09:14, 2 February 2009 (UTC)
 * Yes, this is much clearer. Yet, perhaps the examples should be even more clarified or removed altogether because they can confuse. Not sure. Stan J. Klimas (talk) 23:03, 2 February 2009 (UTC)

See also section
The See also section is now rather long with 13 entries. Would it be better to shorten this and rely on the Diffusion Category to aid further navigation? --Art Carlson (talk) 11:35, 9 March 2009 (UTC)

Suggested merge of diffusion equilibrium into this article
I just suggested that the page Diffusion equilibrium be merged into this one. There is only a small amount of material on that page, and this article already has a section on non-equlibrium systems, so it seems like it would fit here. Shanata (talk) 21:29, 20 October 2009 (UTC)

Diffusion page figure: Carrier diffusion in instrinsic semiconductors
The animation on carrier diffusion in an intrinsic semiconductor bar is inaccurate. The greater hole concentration relative to electron concentration is attributed to the higher diffusion coefficient of electrons in most semiconductors. While this is true for most values of electron and hole diffusion coefficients, under this configuration the photogenerated electrons and holes actually diffuse at the same rate, i.e. they should be in equal concentration for each position in the bar. The reason for this is the formation of an electric field between the electrons and holes as the electrons attempt to diffuse more rapidly. This electric field drives the electrons back towards the holes and vice versa as any concentration mismatch develops. Because of the induced drift, the carriers actually diffuse at the same rate, otherwise known as ambipolar diffusion. This phenomenon is not a good example to show since it fundamentally involves both diffusion and drift. I would suggest changing to an example not involving the diffusion of charged particles due to this complication, so that it is more accurate.

Diffusion vs convection
[moved here from private talk page:]

In October of 2010 I edited the diffusion page with the example of spraying cologne. Agreed, maybe I should have been more specific about the transport phenomena occuring, but the edit you have made of this example is clearly incorrect. When the cologne leaves the nozzle of the sprayer convective flow will be dominating; however as the cologne "cloud" increases its volume it will eventually reduce its velocity to zero at which point it will be at atmospheric pressure. Please note, this phase of transport is primarily driven by pressure and is therefore the convective regime of this process; however there will still be a concentration gradient between the cologne cloud and the room air(so long as the room is sufficiently large enough to accomodate the cologne cloud at atmospheric pressure and temperature). Transport will then continue via brownian motion, ie diffusion, until the cologne is eventually distributed throughout the room. This process will occur in the presence of no other gradients (pressure, temperture, electromagentic) because of the random motion of the molecules. Or it could be looked at as, it will always occur because the system with a cologne cloud and air is more ordered than a system where the cologne molecules evenly distributed throughout the room. This is to say the process is entropically driven. Since entropy always increases the process will occur spontaneously at any temperature above 0 kelvin. Another way of looking at it, is that the pressure driven flow is an enthalpic process where diffusion is an entropic process.

Please make the appropriate changes to the page. The ink droplet example is also incorrect for similiar reasons. I am not fixing the page because I did not break it.

If you did not make the described changes I apologize. — Preceding unsigned comment added by Anwilson6 (talk • contribs) 17:52, 14 April 2011 (UTC)

 * Eau-de-Cologne in air and ink-in-water are popular examples for mass transport because they are vivid real-life cases known to everybody. In real life, however, these tracers spread in space because of convection, period. All you say is correct in some hypothetical limit of air or water being perfectly at rest, with walls being at perfectly homogeneous and constant temperature - but in this case, diffusion takes extremely long, and you have lost any connection to the real-life situation that originally motivated the choice of these examples. -- Marie Poise (talk) 09:17, 18 April 2011 (UTC)

 * First, please show me the SIMPLE equation that you use to show that the flux of cologne can ONLY be by convection. I want your general equation and assumptions.  Convection is a bulk property.  It is either forced or natural (as with density gradients).  If I just opened the bottle of cologne up, there would be ZERO velocity due to convection.  I have not applied a force and natural convective flow is absent.  This is the same for the drop dye aside from the original movement into the water.  Additionally, you have described diffusion as EXTREMELY SLOW/LONG TIME.  Are you kidding me?  Diffusion of a gas in a gas is THE FASTEST of any molecule in a medium.

 * I would use the Nernst-Planck equation. Is there an electric field being applied?  No.  Is there a velocity of the bulk cologne?  Sure.  Is there a concentration gradient?  Yes.  Explain to me then how both aren't occurring simultaneously?  Regardless of the first persons entropic/enthalpic point, which is valid, you have given ZERO points to validate your claims in this post and the diffusion wikipage.  I BEG YOU, assuming you are educated or in the process of a obtaining a degree, to bring your Diffusion Wikipedia page post to a reputable professor of chemical engineering or mechanical engineering and have them explain to you the fundamental mass flux process.  — Preceding unsigned comment added by JC44567 (talk • contribs) 02:48, 22 April 2011 (UTC)

Major Rewrite Proposal
Diffusion vs convection [moved here from private talk page:] In October of 2010 I edited the diffusion page with the example of spraying cologne. Agreed, maybe I should have been more specific about the transport phenomena occuring, but the edit you have made of this example is clearly incorrect. When the cologne leaves the nozzle of the sprayer convective flow will be dominating; however as the cologne "cloud" increases its volume it will eventually reduce its velocity to zero at which point it will be at atmospheric pressure. Please note, this phase of transport is primarily driven by pressure and is therefore the convective regime of this process; however there will still be a concentration gradient between the cologne cloud and the room air(so long as the room is sufficiently large enough to accomodate the cologne cloud at atmospheric pressure and temperature). Transport will then continue via brownian motion, ie diffusion, until the cologne is eventually distributed throughout the room. This process will occur in the presence of no other gradients (pressure, temperture, electromagentic) because of the random motion of the molecules. Or it could be looked at as, it will always occur because the system with a cologne cloud and air is more ordered than a system where the cologne molecules evenly distributed throughout the room. This is to say the process is entropically driven. Since entropy always increases the process will occur spontaneously at any temperature above 0 kelvin. Another way of looking at it, is that the pressure driven flow is an enthalpic process where diffusion is an entropic process. Please make the appropriate changes to the page. The ink droplet example is also incorrect for similiar reasons. I am not fixing the page because I did not break it. If you did not make the described changes I apologize. — Preceding unsigned comment added by Anwilson6 (talk • contribs) 17:52, 14 April 2011 (UTC) Eau-de-Cologne in air and ink-in-water are popular examples for mass transport because they are vivid real-life cases known to everybody. In real life, however, these tracers spread in space because of convection, period. All you say is correct in some hypothetical limit of air or water being perfectly at rest, with walls being at perfectly homogeneous and constant temperature - but in this case, diffusion takes extremely long, and you have lost any connection to the real-life situation that originally motivated the choice of these examples. -- Marie Poise (talk) 09:17, 18 April 2011 (UTC) First, please show me the SIMPLE equation that you use to show that the flux of cologne can ONLY be by convection. I want your general equation and assumptions. Convection is a bulk property. It is either forced or natural (as with density gradients). If I just opened the bottle of cologne up, there would be ZERO velocity due to convection. I have not applied a force and natural convective flow is absent. This is the same for the drop dye aside from the original movement into the water. Additionally, you have described diffusion as EXTREMELY SLOW/LONG TIME. Are you kidding me? Diffusion of a gas in a gas is THE FASTEST of any molecule in a medium. I would use the Nernst-Planck equation. Is there an electric field being applied? No. Is there a velocity of the bulk cologne? Sure. Is there a concentration gradient? Yes. Explain to me then how both aren't occurring simultaneously? Regardless of the first persons entropic/enthalpic point, which is valid, you have given ZERO points to validate your claims in this post and the diffusion wikipage. I BEG YOU, assuming you are educated or in the process of a obtaining a degree, to bring your Diffusion Wikipedia page post to a reputable professor of chemical engineering or mechanical engineering and have them explain to you the fundamental mass flux process. — Preceding unsigned comment added by JC44567 (talk • contribs) 02:48, 22 April 2011 (UTC

This page needs major work. I wouldn't mind doing it, but I'd like to know if I have the community's approval first, since I'm new to this.

First, and my main gripe, it conflates the relaxation of concentration gradients with the motion of individual particles, which makes it difficult to choose a point of view from which to explain things. I'd like to separate out the continuum concepts of concentration field relaxation from the idea of random molecular motion. That way the thermodynamics and continuum mechanics ideas, like convective mixing, shear-induced dispersion, chemical potential gradients, etc, could be focused on in one article while activated hopping, collisions, and so forth can be focused on in the other. The commonly observed phenomenon, chemical or concentration diffusion, should be detailed separately from its underlying mechanism, particle diffusion, to avoid information overload for people only interested in one or the other. Each one will retain references to the other, but in less confusing mix than right now.

Second, there are numerous misleading statements, starting from the first sentence where it is implied that solids don't undergo diffusion. I'll try to clean these up, using standard engineering and physical chemistry texts like Bird Stewart and Lightfoot and Atkins as terminology references.

Third, there's too much left out. I'll fill in a bit of the history, some additional phenomenology comparing liquid, gas, and solid phase diffusion, some discussion of mathematical methods for dealing with it, e.g. grid-based and meshfree advection-diffusion PDE solvers, stochastic schemes for individual particle trajectories like Brownian and Stokesian dynamics, and so on. I'd also like to flesh out the equilibrium vs. non-equilibrium, linear vs. nonlinear, and frequency-dependent vs frequency independent cases, but I'll wait on that till linear response theory is a respectable page of its own.

That's what I'd like to do. If there are objections, please let me know. Also, I'm not a professor, just a grad student, and I'm not going to want to proofread everything, so it's a sure bet that I'll confuse some terms. Help me out if you see any mistakes. — Preceding unsigned comment added by ChE Fundamentalist (talk • contribs) 05:43, 29 July 2011 (UTC)

 * So you're making a second article? What were you planning to call it? Would this article ("molecular diffusion") be the continuum or the microscopic one? Also, for people coming in with no background knowledge, which page would you want them to view first? (i.e., one of the two pages should presumably have a broader and simpler introduction and overview encompassing both the micro and macro aspects, which are after all related).
 * I'm not an expert and I hope you can educate me...but I always assumed that the word "diffusion" referred only to the process described by random molecular motion that leads to Fick's laws. Therefore, shear-induced dispersion and convective mixing are not within the topic of diffusion (except maybe in the category "small-scale processes that lead to Fick's equations on a larger scale", or the more general topic "mass transport phenomena"). If that's true, I'm not convinced there's enough continuum stuff for a dedicated article (on top of the Fick's laws article). For example, if you want to talk about PDE-solving methods, it seems to me that you should make a new article numerical solution of the convection-diffusion equation, because the topic is self-contained and specialized. (Or add to convection-diffusion equation.) :-) --Steve (talk) 13:49, 29 July 2011 (UTC)

 * I was planning to call the new one "chemical diffusion" and to focus it on continuum processes, while modifying this one to focus more on the microscopic. Do you have any other suggestions for how to handle it? "Molecular diffusion" bothers me in particular, but "Particle diffusion" isn't much better... ideally I could make it general enough to include diffusion of microstructure defects in inhomogenous materials, too, since things like hydronium ions don't really diffuse as molecules but as charge defects, but I can't think of a name that works for it. Any ideas?
 * I would want chemical diffusion to be viewed first in most cases, since it will be more related to the lay interpretation of diffusion as mixing. The introductions will both refer to one another since they are so closely related. Does that sound good?
 * I think "The process described by random molecular motion that leads to Fick's laws" is a great one-sentence summary of what's usually taught about diffusion in school, after you've learned it and if you understand how to read PDEs. However, I also think it's a pretty narrow description and it's not intuitive for people less familiar with the equations. First, it leaves out the role of chemical potential gradients, and second Fick's law is just a basic linear constitutive equation which isn't really fundamental except in the sense linear approximations have been pretty fundamental to the mathematization of physics in general. I'd rather emphasize the non-mathematical, general aspects of diffusion, like the fact that it's a spontaneous and irreversible relaxation of a higher-energy state to a lower-energy state with a rate that depends on the chemistry of the underlying material. From that thermodynamic perspective, there's a lot that can be said just on the continuum level.
 * For the shear-induced dispersion part, I was planning to have a "Role of diffusion in general mixing processes" which describes how convection leads to sharpened chemical gradients, which accelerates diffusion (among other things). I'd agree that that should go in mass transport except that the debates in the talk page here about what is convection and what is diffusion convinced me it would be worth addressing directly. Does that still sound unreasonable?
 * I agree that a detailed discussion of the numerical methods is inappropriate for this page, and if the convection-diffusion equation weren't such a special case, I'd stick everything in that article or the one you suggested making. I am planning to have a "Mathematical Descriptions of Chemical Diffusion" section which will link to articles on all the various PDEs, integral equations, and so forth that come up when you're trying to model it. That's where I was planning to mention the numerical methods, but I think you're probably right that they don't fit there. I'll leave them for the mathematical model pages, like "convection-diffusion equation." Thanks for the suggestion! ChE Fundamentalist (talk) 19:36, 31 July 2011 (UTC)

Welcome, ChE Fundamentalist! There is definitely lot of work to be done. If you are new to Wikipedia, I just suggest you start by small improvements here and there before you attack the major restructuring the diffusion articles definitely deserve. If you need help, feel free to contact me on my talk page. Again: welcome! -- Marie Poise (talk)

 * Thank you for the welcome, Marie. I'm drafting my changes in a separate document, and I'll be sure to get a bit of practice by editing some of the pages I plan to reference before I actually implement any major changes here. ChE Fundamentalist (talk)

I've gotten a bit of experience wikifying, cleaning up typos, and writing big sections on articles, so now I'm planning to return to this. I've come up with a layout, and I'd like to know what anyone watching this thinks.

First, I'm going to go ahead with the separation into Molecular diffusion and Chemical diffusion. Chemical diffusion should be the first one that viewers come across if they're just interested in the mixing process, but both should have disambiguation notices just below the titles. Is there a tool I could use to sort links from other pages to these and make sure each link goes to the right one?

In the Chemical diffusion article, my planned layout is the following:

 * 1) Key Concepts
 * 2) It is a dissipative relaxation process.
 * 3) Chemical potential gradients drive it.
 * 4) In most applications, it can be described as a local, linear, continuum process (said less technically).
 * 5) Characteristics of Chemical Diffusion
 * 6) Advection vs diffusion vs convection
 * 7) Fickian vs. anomalous diffusion
 * 8) Nonlinear vs. linear diffusion (collective vs independent motion)
 * 9) Tracer vs. chemical diffusion (both do belong in this article)
 * 10) Diffusion in Chemical Engineering and Chemistry
 * 11) Definition of diffusion constants and their calculation
 * 12) Fick's law, Maxwell-Stefan, etc
 * 13) Chapman-Enskog, Arrhenius dependence, etc.
 * 14) Application
 * 15) Purely diffusive mass transport processes i.e. membrane separation, gaseous diffusion enrichment of uranium
 * 16) Mass transport processes combining advection and diffusion, i.e. chromatography, mixing, most reactors
 * 17) Coupling of mass transport with other transport phenomena, esp heat transport
 * 18) Modeling
 * 19) Generalized correlations for mass transport, dim'less nos and engineering examples.
 * 20) Continuum equations, i.e. Smoluchowski and linear advection-diffusion

And then the Molecular diffusion page will have the following layout:

 * 1) Key Concepts
 * 2) Random processes in the statistical sense rather than nondeterministic sense
 * 3) Self-similarity and the scaling law  ~ t
 * 4) The idea of long-time, or asymptotic, behavior
 * 5) Phenomenology of Diffusion
 * 6) Mechanisms of Diffusion
 * 7) Elementary deterministic, predictable steps
 * 8) Quantum hopping
 * 9) Ballistic motion
 * 10) Overdamped motion
 * 11) Topological remodeling
 * 12) Randomization
 * 13) Internal nonlinearity (i.e. collisions)
 * 14) Random external forcing (i.e. Brownian motion)
 * 15) Statistical Mechanics of Diffusion
 * 16) Mathematical definitions
 * 17) Definition of the long-time diffusion coefficient
 * 18) Definition of the time-dependent diffusion kernel
 * 19) General Theory
 * 20) Fluctuation-dissipation theorem
 * 21) Onsager regression hypothesis
 * 22) Large Deviation Function
 * 23) Computational models
 * 24) Molecular dynamics
 * 25) Brownian and Stokesian dynamics (overdamped dynamics in general)
 * 26) Kinetic Monte Carlo and Lattice Boltzmann

I'm not trying to make this go straight from start-class to good article status; I know there are things I've left out that should be covered in these articles. If there are any that you think I've left out that simply must be in any remotely acceptable version of these articles, please wait for me to finish this and then add them yourself or type them up on this talk page so I can copy and paste them in. On the other hand, if you have any objections to the general structure that I'm proposing, please let me know immediately so I can consider changing it. ChE Fundamentalist (talk) 18:49, 21 August 2011 (UTC)

 * I am not convinced that the article should be split. It depends too much on your perspective whether the division in chemical vs molecular makes sense or not. In the end, people who do not grasp the distinction will mess thinks up by duplicating contents &c. From my editing experience, I would recommend to have one comprehensive article, covering chemical and physical, macroscopic and microscopic aspects of diffusion, but leaving out all technical details, which should go into specialised articles. At the beginning of each section, a link would point to one of them. This is also the best way to avoid duplication of contents between overview and specialist articles. -- Marie Poise (talk) 15:49, 9 January 2012 (UTC)

Molecular diffusion in solids
There is also molecular diffusion in solids. This is the origin of aging processes in many solid materials. I would therefore suggest to remove the "(liquid or gas)" in the first sentence "Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero." — Preceding unsigned comment added by 128.176.210.208 (talk) 17:14, 10 September 2019 (UTC)

Introductory sentence
Hey authors, I only had a quick view on this article and I find that already the introductory sentence "Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero." misses some precision. To my knowledge and according to the definition in many basic textbooks in physics, diffusion is the mixing process resulting from random motion, not the random motion itself. The random motion of the fluid particles is rather termed thermal motion. It seems I cannot edit the introductory section. Please help! Thanks (Pelicanelson (talk) 10:53, 10 September 2020 (UTC)).

title: Talk:Molecular diffusion