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55-632: Taiwan Bank is a residual sedimentation of continental shelf . The undersea terrain of the Taiwan Strait used to be a valley, and had been constantly accumulating soil and sand from both sides since the Pliocene until the Holocene , when sea levels rose and remains of sands beneath the sea become oceanic bank. The Kuroshio Current and typhoon waves help push sands on the seabed to the north, but are blocked by ancient volcanic rocks and beach rocks, thus while

110-514: A concentration gradient , a change in pressure over a distance is called a pressure gradient , and a change in temperature over a distance is called a temperature gradient . The word diffusion derives from the Latin word, diffundere , which means "to spread out". A distinguishing feature of diffusion is that it depends on particle random walk , and results in mixing or mass transport without requiring directed bulk motion. Bulk motion, or bulk flow,

165-432: A fundamental law, for the operation of diffusion in a single element of space". He asserted a deep analogy between diffusion and conduction of heat or electricity, creating a formalism similar to Fourier's law for heat conduction (1822) and Ohm's law for electric current (1827). Robert Boyle demonstrated diffusion in solids in the 17th century by penetration of zinc into a copper coin. Nevertheless, diffusion in solids

220-516: A region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential . It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, as in spinodal decomposition . Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and

275-413: A sufficiently strong force to produce significant sedimentation. Settling is the process by which particulates move towards the bottom of a liquid and form a sediment . Particles that experience a force, either due to gravity or due to centrifugal motion will tend to move in a uniform manner in the direction exerted by that force. For gravity settling, this means that the particles will tend to fall to

330-553: Is In case the diffusion coefficient is independent of x {\displaystyle x} , Fick's second law can be simplified to where Δ {\displaystyle \Delta } is the Laplace operator , Fick's law describes diffusion of an admixture in a medium. The concentration of this admixture should be small and the gradient of this concentration should be also small. The driving force of diffusion in Fick's law

385-479: Is where ( J , ν ) {\displaystyle (\mathbf {J} ,{\boldsymbol {\nu }})} is the inner product and o ( ⋯ ) {\displaystyle o(\cdots )} is the little-o notation . If we use the notation of vector area Δ S = ν Δ S {\displaystyle \Delta \mathbf {S} ={\boldsymbol {\nu }}\,\Delta S} then The dimension of

440-536: Is a vector J {\displaystyle \mathbf {J} } representing the quantity and direction of transfer. Given a small area Δ S {\displaystyle \Delta S} with normal ν {\displaystyle {\boldsymbol {\nu }}} , the transfer of a physical quantity N {\displaystyle N} through the area Δ S {\displaystyle \Delta S} per time Δ t {\displaystyle \Delta t}

495-480: Is called aggradation . The rate of sedimentation is the thickness of sediment accumulated per unit time. For suspended load, this can be expressed mathematically by the Exner equation . Rates of sedimentation vary from less than 3 millimeters (0.12 in) per thousand years for pelagic sediment to several meters per thousand years in portions of major river deltas . However, long-term accumulation of sediments

550-407: Is common to all of these: a substance or collection undergoing diffusion spreads out from a point or location at which there is a higher concentration of that substance or collection. A gradient is the change in the value of a quantity; for example, concentration, pressure , or temperature with the change in another variable, usually distance . A change in concentration over a distance is called

605-461: Is determined less by rate of sedimentation than by rate of subsidence, which creates accommodation space for sediments to accumulate over geological time scales. Most sedimentation in the geologic record occurred in relative brief depositional episodes separated by long intervals of nondeposition or even erosion. In estuarine environments, settling can be influenced by the presence or absence of vegetation. Trees such as mangroves are crucial to

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660-436: Is intensity of any local source of this quantity (for example, the rate of a chemical reaction). For the diffusion equation, the no-flux boundary conditions can be formulated as ( J ( x ) , ν ( x ) ) = 0 {\displaystyle (\mathbf {J} (x),{\boldsymbol {\nu }}(x))=0} on the boundary, where ν {\displaystyle {\boldsymbol {\nu }}}

715-491: Is opposed by the diffusion of the particles. The distribution of sediment near the boundary comes into sedimentation equilibrium . Measurements of the distribution yields information on the nature of the particles. In geology , the term sedimentation is broadly applied to the entire range of processes that result in the formation of sedimentary rock, from initial formation of sediments by erosion of particles from rock outcrops, through sediment transport and settling, to

770-412: Is the j {\displaystyle j} th thermodynamic force and L i j {\displaystyle L_{ij}} is Onsager's matrix of kinetic transport coefficients . The thermodynamic forces for the transport processes were introduced by Onsager as the space gradients of the derivatives of the entropy density s {\displaystyle s} (he used

825-528: Is the antigradient of concentration, − ∇ n {\displaystyle -\nabla n} . In 1931, Lars Onsager included the multicomponent transport processes in the general context of linear non-equilibrium thermodynamics. For multi-component transport, where J i {\displaystyle \mathbf {J} _{i}} is the flux of the i {\displaystyle i} th physical quantity (component), X j {\displaystyle X_{j}}

880-435: Is the characteristic of advection . The term convection is used to describe the combination of both transport phenomena . If a diffusion process can be described by Fick's laws , it is called a normal diffusion (or Fickian diffusion); Otherwise, it is called an anomalous diffusion (or non-Fickian diffusion). When talking about the extent of diffusion, two length scales are used in two different scenarios: "Bulk flow"

935-420: Is the falling of suspended particles through the liquid, whereas sedimentation is the final result of the settling process. In geology , sedimentation is the deposition of sediments which results in the formation of sedimentary rock . The term is broadly applied to the entire range of processes that result in the formation of sedimentary rock, from initial erosion through sediment transport and settling to

990-415: Is the movement/flow of an entire body due to a pressure gradient (for example, water coming out of a tap). "Diffusion" is the gradual movement/dispersion of concentration within a body with no net movement of matter. An example of a process where both bulk motion and diffusion occur is human breathing. First, there is a "bulk flow" process. The lungs are located in the thoracic cavity , which expands as

1045-434: Is the normal to the boundary at point x {\displaystyle x} . Fick's first law: The diffusion flux, J {\displaystyle \mathbf {J} } , is proportional to the negative gradient of spatial concentration, n ( x , t ) {\displaystyle n(x,t)} : where D is the diffusion coefficient . The corresponding diffusion equation (Fick's second law)

1100-458: Is universally recognized that atomic defects are necessary to mediate diffusion in crystals. Henry Eyring , with co-authors, applied his theory of absolute reaction rates to Frenkel's quasichemical model of diffusion. The analogy between reaction kinetics and diffusion leads to various nonlinear versions of Fick's law. Each model of diffusion expresses the diffusion flux with the use of concentrations, densities and their derivatives. Flux

1155-480: Is used to model the stellar atmospheres of chemically peculiar stars . Diffusion of the elements is critical in understanding the surface composition of degenerate white dwarf stars and their evolution over time. In the scope of time, diffusion in solids was used long before the theory of diffusion was created. For example, Pliny the Elder had previously described the cementation process , which produces steel from

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1210-457: The i {\displaystyle i} th component. The corresponding driving forces are the space vectors where T is the absolute temperature and μ i {\displaystyle \mu _{i}} is the chemical potential of the i {\displaystyle i} th component. It should be stressed that the separate diffusion equations describe the mixing or mass transport without bulk motion. Therefore,

1265-454: The Boltzmann equation , which has served mathematics and physics with a source of transport process ideas and concerns for more than 140 years. In 1920–1921, George de Hevesy measured self-diffusion using radioisotopes . He studied self-diffusion of radioactive isotopes of lead in the liquid and solid lead. Yakov Frenkel (sometimes, Jakov/Jacob Frenkel) proposed, and elaborated in 1926,

1320-491: The Brownian motion and the atomistic backgrounds of diffusion were developed by Albert Einstein . The concept of diffusion is typically applied to any subject matter involving random walks in ensembles of individuals. In chemistry and materials science , diffusion also refers to the movement of fluid molecules in porous solids. Different types of diffusion are distinguished in porous solids. Molecular diffusion occurs when

1375-548: The Little Ice Age when the sea level dropped, Taiwan Bank might have been inhabitable by humans. Thus, they think the island marked Dongning on the map Kunyu Wanguo Quantu published in year 1602 could in fact be Taiwan Bank instead of the Taiwan Island. Due to rich construction grade sand deposits on Taiwan Bank, many mainland Chinese ships have tried to gather sands from the area in recent years, due to restrictions by

1430-446: The attenuation of waves or currents, promoting the settlement of suspended particles. An undesired increased transport and sedimentation of suspended material is called siltation , and it is a major source of pollution in waterways in some parts of the world. High sedimentation rates can be a result of poor land management and a high frequency of flooding events. If not managed properly, it can be detrimental to fragile ecosystems on

1485-450: The blood in the body. Third, there is another "bulk flow" process. The pumping action of the heart then transports the blood around the body. As the left ventricle of the heart contracts, the volume decreases, which increases the pressure in the ventricle. This creates a pressure gradient between the heart and the capillaries, and blood moves through blood vessels by bulk flow down the pressure gradient. There are two ways to introduce

1540-472: The kinetic coefficients L i j {\displaystyle L_{ij}} should be symmetric ( Onsager reciprocal relations ) and positive definite ( for the entropy growth ). The transport equations are Here, all the indexes i , j , k = 0, 1, 2, ... are related to the internal energy (0) and various components. The expression in the square brackets is the matrix D i k {\displaystyle D_{ik}} of

1595-464: The lithification of the sediments. However, the strict geological definition of sedimentation is the mechanical deposition of sediment particles from an initial suspension in air or water. Sedimentation may pertain to objects of various sizes, ranging from large rocks in flowing water, to suspensions of dust and pollen particles, to cellular suspensions, to solutions of single molecules such as proteins and peptides . Even small molecules supply

1650-462: The lithification of the sediments. However, the term is more particularly applied to the deposition of sediments, and in the strictest sense, it applies only to the mechanical deposition of sediment particles from an initial suspension in air or water. Sedimentation results in the formation of depositional landforms and the rocks that constitute the sedimentary record . The building up of land surfaces by sedimentation, particularly in river valleys,

1705-540: The Chinese government against gathering sand from Chinese rivers and coastal areas. Sedimentation Sedimentation is the deposition of sediments . It takes place when particles in suspension settle out of the fluid in which they are entrained and come to rest against a barrier. This is due to their motion through the fluid in response to the forces acting on them: these forces can be due to gravity , centrifugal acceleration , or electromagnetism . Settling

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1760-452: The alveoli and the blood in the capillaries that surround the alveoli. Oxygen then moves by diffusion, down the concentration gradient, into the blood. The other consequence of the air arriving in alveoli is that the concentration of carbon dioxide in the alveoli decreases. This creates a concentration gradient for carbon dioxide to diffuse from the blood into the alveoli, as fresh air has a very low concentration of carbon dioxide compared to

1815-399: The bottom of the vessel, forming sludge or slurry at the vessel base. Settling is an important operation in many applications, such as mining , wastewater and drinking water treatment, biological science, space propellant reignition, Classification of sedimentation: When particles settling from a suspension reach a hard boundary, the concentration of particles at the boundary

1870-426: The cell, the probability that oxygen molecules will enter the cell is higher than the probability that oxygen molecules will leave the cell. Therefore, the "net" movement of oxygen molecules (the difference between the number of molecules either entering or leaving the cell) is into the cell. In other words, there is a net movement of oxygen molecules down the concentration gradient. In astronomy , atomic diffusion

1925-402: The collision with another molecule is more likely than the collision with the pore walls. Under such conditions, the diffusivity is similar to that in a non-confined space and is proportional to the mean free path. Knudsen diffusion occurs when the pore diameter is comparable to or smaller than the mean free path of the molecule diffusing through the pore. Under this condition, the collision with

1980-416: The concept of the mean free path . In the same year, James Clerk Maxwell developed the first atomistic theory of transport processes in gases. The modern atomistic theory of diffusion and Brownian motion was developed by Albert Einstein , Marian Smoluchowski and Jean-Baptiste Perrin . Ludwig Boltzmann , in the development of the atomistic backgrounds of the macroscopic transport processes , introduced

2035-482: The corresponding mathematical models are used in several fields beyond physics, such as statistics , probability theory , information theory , neural networks , finance , and marketing . The concept of diffusion is widely used in many fields, including physics ( particle diffusion ), chemistry , biology , sociology , economics , statistics , data science , and finance (diffusion of people, ideas, data and price values). The central idea of diffusion, however,

2090-462: The diffusing particles. In molecular diffusion , the moving molecules in a gas, liquid, or solid are self-propelled by kinetic energy. Random walk of small particles in suspension in a fluid was discovered in 1827 by Robert Brown , who found that minute particle suspended in a liquid medium and just large enough to be visible under an optical microscope exhibit a rapid and continually irregular motion of particles known as Brownian movement. The theory of

2145-400: The diffusion flux is proportional to the negative gradient of concentrations. It goes from regions of higher concentration to regions of lower concentration. Sometime later, various generalizations of Fick's laws were developed in the frame of thermodynamics and non-equilibrium thermodynamics . From the atomistic point of view , diffusion is considered as a result of the random walk of

2200-595: The diffusion ( i , k  > 0), thermodiffusion ( i  > 0, k  = 0 or k  > 0, i  = 0) and thermal conductivity ( i = k = 0 ) coefficients. Under isothermal conditions T  = constant. The relevant thermodynamic potential is the free energy (or the free entropy ). The thermodynamic driving forces for the isothermal diffusion are antigradients of chemical potentials, − ( 1 / T ) ∇ μ j {\displaystyle -(1/T)\,\nabla \mu _{j}} , and

2255-397: The diffusion flux is [flux] = [quantity]/([time]·[area]). The diffusing physical quantity N {\displaystyle N} may be the number of particles, mass, energy, electric charge, or any other scalar extensive quantity . For its density, n {\displaystyle n} , the diffusion equation has the form where W {\displaystyle W}

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2310-496: The element iron (Fe) through carbon diffusion. Another example is well known for many centuries, the diffusion of colors of stained glass or earthenware and Chinese ceramics . In modern science, the first systematic experimental study of diffusion was performed by Thomas Graham . He studied diffusion in gases, and the main phenomenon was described by him in 1831–1833: "...gases of different nature, when brought into contact, do not arrange themselves according to their density,

2365-409: The first step in external respiration. This expansion leads to an increase in volume of the alveoli in the lungs, which causes a decrease in pressure in the alveoli. This creates a pressure gradient between the air outside the body at relatively high pressure and the alveoli at relatively low pressure. The air moves down the pressure gradient through the airways of the lungs and into the alveoli until

2420-541: The heaviest undermost, and the lighter uppermost, but they spontaneously diffuse, mutually and equally, through each other, and so remain in the intimate state of mixture for any length of time." The measurements of Graham contributed to James Clerk Maxwell deriving, in 1867, the coefficient of diffusion for CO 2 in the air. The error rate is less than 5%. In 1855, Adolf Fick , the 26-year-old anatomy demonstrator from Zürich, proposed his law of diffusion . He used Graham's research, stating his goal as "the development of

2475-472: The idea of diffusion in crystals through local defects (vacancies and interstitial atoms). He concluded, the diffusion process in condensed matter is an ensemble of elementary jumps and quasichemical interactions of particles and defects. He introduced several mechanisms of diffusion and found rate constants from experimental data. Sometime later, Carl Wagner and Walter H. Schottky developed Frenkel's ideas about mechanisms of diffusion further. Presently, it

2530-401: The matrix of diffusion coefficients is ( i,k  > 0). There is intrinsic arbitrariness in the definition of the thermodynamic forces and kinetic coefficients because they are not measurable separately and only their combinations ∑ j L i j X j {\textstyle \sum _{j}L_{ij}X_{j}} can be measured. For example, in

2585-433: The notion of diffusion : either a phenomenological approach starting with Fick's laws of diffusion and their mathematical consequences, or a physical and atomistic one, by considering the random walk of the diffusing particles . In the phenomenological approach, diffusion is the movement of a substance from a region of high concentration to a region of low concentration without bulk motion . According to Fick's laws,

2640-404: The pore walls becomes gradually more likely and the diffusivity is lower. Finally there is configurational diffusion, which happens if the molecules have comparable size to that of the pore. Under this condition, the diffusivity is much lower compared to molecular diffusion and small differences in the kinetic diameter of the molecule cause large differences in diffusivity . Biologists often use

2695-399: The pressure of the air and that in the alveoli are equal, that is, the movement of air by bulk flow stops once there is no longer a pressure gradient. Second, there is a "diffusion" process. The air arriving in the alveoli has a higher concentration of oxygen than the "stale" air in the alveoli. The increase in oxygen concentration creates a concentration gradient for oxygen between the air in

2750-406: The receiving end, such as coral reefs. Climate change also affects siltation rates. In chemistry, sedimentation has been used to measure the size of large molecules ( macromolecule ), where the force of gravity is augmented with centrifugal force in an ultracentrifuge . Diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from

2805-421: The sands are constantly moving, they would not be transported to weaker current areas further away. On the other hand, south-flowing currents and waves caused by northeasterly trade wind transport sand on the bank to the south. These forces in both directions cancel out each other's reached relative stability and equilibrium, forming sand waves and dunes under the sea. Some academics have hypothesized that during

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2860-407: The term "force" in quotation marks or "driving force"): where n i {\displaystyle n_{i}} are the "thermodynamic coordinates". For the heat and mass transfer one can take n 0 = u {\displaystyle n_{0}=u} (the density of internal energy) and n i {\displaystyle n_{i}} is the concentration of

2915-421: The terms "net movement" or "net diffusion" to describe the movement of ions or molecules by diffusion. For example, oxygen can diffuse through cell membranes so long as there is a higher concentration of oxygen outside the cell. However, because the movement of molecules is random, occasionally oxygen molecules move out of the cell (against the concentration gradient). Because there are more oxygen molecules outside

2970-444: The terms with variation of the total pressure are neglected. It is possible for diffusion of small admixtures and for small gradients. For the linear Onsager equations, we must take the thermodynamic forces in the linear approximation near equilibrium: where the derivatives of s {\displaystyle s} are calculated at equilibrium n ∗ {\displaystyle n^{*}} . The matrix of

3025-450: Was not systematically studied until the second part of the 19th century. William Chandler Roberts-Austen , the well-known British metallurgist and former assistant of Thomas Graham studied systematically solid state diffusion on the example of gold in lead in 1896. : "... My long connection with Graham's researches made it almost a duty to attempt to extend his work on liquid diffusion to metals." In 1858, Rudolf Clausius introduced

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