In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion.

• In the study of transport phenomena (heat transfer, mass transfer and fluid dynamics), flux is defined as the amount that flows through a unit area per unit time. The first edition of Transport Phenomena was published in 1960 two years after having been preliminarily published under the title Notes on Transport Phenomena based In thermal physics, heat transfer is the passage of Thermal energy from a hot to a colder body Mass transfer is the phrase commonly used in engineering for physical processes that involve molecular and convective transport of Atoms and Molecules Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion ^[1] Flux in this definition is a vector.
• In the field of electromagnetism, flux is usually the integral of a vector quantity over a finite surface. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space The result of this integration is a scalar quantity. In Physics, a scalar is a simple Physical quantity that is not changed by Coordinate system rotations or translations (in Newtonian mechanics or ^[2] The magnetic flux is thus the integral of the magnetic vector field B over a surface, and the electric flux is defined similarly. Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic Using this definition, the flux of the Poynting vector over a specified surface is the rate at which electromagnetic energy flows through that surface. In Physics, the Poynting vector can be thought of as representing the Energy Flux (in W/m2 of an Electromagnetic field. Confusingly, the Poynting vector is sometimes called the power flux, which is an example of the first usage of flux, above. ^[3] It has units of watts per square metre (Wm^-2)

One could argue, based on the work of James Clerk Maxwell^[4], that the transport definition precedes the more recent way the term is used in electromagnetism. The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. M^2 redirects here For other uses see M². CM2 redirects here James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. The specific quote from Maxwell is "In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface. The result of this operation is called the surface integral of the flux. In Mathematics, a surface integral is a Definite integral taken over a Surface (which may be a curved set in Space) it can be thought It represents the quantity which passes through the surface".

In addition to these common mathematical definitions, there are many more loose usages found in fields such as biology.

Transport phenomena

Flux definition and theorems

Flux is surface bombardment rate. There are many fluxes used in the study of transport phenomena. Each type of flux has its own distinct unit of measurement along with distinct physical constants. Six of the most common forms of flux from the transport literature are defined as:

1. Momentum flux, the rate of transfer of momentum across a unit area (N·s·m^-2·s^-1). In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product (Newton's law of viscosity,)
2. Heat flux, the rate of heat flow across a unit area (J·m^-2·s^-1). Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature (Fourier's law of convection)^[5] (This definition of heat flux fits Maxwell's original definition. Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter from a region of higher Temperature to a region of lower ^[4])
3. Chemical flux, the rate of movement of molecules across a unit area (mol·m^-2·s^-1). (Fick's law of diffusion)
4. Volumetric flux, the rate of volume flow across a unit area (m³·m^-2·s^-1). Fick's laws of diffusion describe Diffusion and can be used to solve for the diffusion coefficient D. The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically (Darcy's law of groundwater flow)
5. Mass flux, the rate of mass flow across a unit area (kg·m^-2·s^-1). In Fluid dynamics, Darcy's law is a phenomologically derived Constitutive equation that describes the flow of a Fluid through a Porous medium Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object (Either an alternate form of Fick's law that includes the molecular mass, or an alternate form of Darcy's law that includes the density)
6. Radiative flux, the amount of energy moving in the form of photons at a certain distance from the source per steradian per second (J·m^-2·s^-1). In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena The steradian (symbol sr) is the SI unit of Solid angle. It is used to describe two-dimensional angular spans in three- Dimensional space Used in astronomy to determine the magnitude and spectral class of a star. Also acts as a generalization of heat flux, which is equal to the radiative flux when restricted to the infrared spectrum.
7. Energy flux, the rate of transfer of energy through a unit area (J·m^-2·s^-1). In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός The radiative flux and heat flux are specific cases of energy flux.

These fluxes are vectors at each point in space, and have a definite magnitude and direction. Also, one can take the divergence of any of these fluxes to determine the accumulation rate of the quantity in a control volume around a given point in space. In Vector calculus, the divergence is an Operator that measures the magnitude of a Vector field &rsquos source or sink at a given point the For incompressible flow, the divergence of the volume flux is zero. In Fluid mechanics or more generally Continuum mechanics, an incompressible flow is Solid or Fluid flow in which the Divergence of

Chemical diffusion

Flux, or diffusion, for gaseous molecules can be related to the function:

where:

• N is the total number of gaseous particles,
• k is Boltzmann's constant,
• T is the relative temperature in kelvins,
• σ_ab is the mean free path between the molecules a and b. The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics

Chemical molar flux of a component A in an isothermal, isobaric system is also defined in Ficks's first law as:

where:

• D_AB is the molecular diffusion coefficient (m²/s) of component A diffusing through component B,
• c_A is the concentration (mol/m³) of species A. An isothermal process is a Thermodynamic process in which the Temperature of the System stays Constant: &Delta T = 0 System (from Latin systēma, in turn from Greek systēma is a set of interacting or interdependent Entities, real or abstract Fick's laws of diffusion describe Diffusion and can be used to solve for the diffusion coefficient D. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this ^[6]

This flux has units of mol·m⁻²·s⁻¹, and fits Maxwell's original definition of flux. ^[4]

Note: ("nabla") denotes the del operator. Nabla is the Symbol \nabla The name comes from the Greek word for a Hebrew Harp, which had a similar shape &nablaDel

Quantum mechanics

Main article: Probability current

In quantum mechanics, particles of mass m in the state ψ(r,t) have a probability density defined as

So the probability of finding a particle in a unit of volume, say d³x, is

Then the number of particles passing through a perpendicular unit of area per unit time is

This is sometimes referred to as the "flux density". In Quantum mechanics, the probability current (sometimes called probability flux) is a concept describing the flow of Probability density. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons ^[7]

Electromagnetism

Flux definition and theorems

An example of the second definition of flux is the magnitude of a river's current, that is, the amount of water that flows through a cross-section of the river each second. The amount of sunlight that lands on a patch of ground each second is also a kind of flux.

To better understand the concept of flux in Electromagnetism, imagine a butterfly net. The amount of air moving through the net at any given instant in time is the flux. If the wind speed is high, then the flux through the net is large. If the net is made bigger, then the flux would be larger even though the wind speed is the same. For the most air to move through the net, the opening of the net must be facing the direction the wind is blowing. If the net opening is parallel to the wind, then no wind will be moving through the net. (These examples are not very good because they rely on a transport process and as stated in the introduction, transport flux is defined differently than E+M flux. ) Perhaps the best way to think of flux abstractly is "How much stuff goes through your thing", where the stuff is a field and the thing is the imaginary surface.

The flux visualized. The rings show the surface boundaries. The red arrows stand for the flow of charges, fluid particles, subatomic particles, photons, etc. The number of arrows that pass through each ring is the flux.

As a mathematical concept, flux is represented by the surface integral of a vector field,

where:

• E is a vector field of Electric Force,
• dA is the vector area of the surface S, directed as the surface normal,
• Φ_f  is the resulting flux. In Mathematics, a surface integral is a Definite integral taken over a Surface (which may be a curved set in Space) it can be thought In Mathematics a vector field is a construction in Vector calculus which associates a vector to every point in a (locally Euclidean space. In Geometry, for a finite planar surface of scalar Area S the vector area \mathbf{S} is defined as a vector

The surface has to be orientable, i. A surface S in the Euclidean space R 3 is orientable if a two-dimensional figure (for example) cannot be moved around the surface and back e. two sides can be distinguished: the surface does not fold back onto itself. Also, the surface has to be actually oriented, i. e. we use a convention as to flowing which way is counted positive; flowing backward is then counted negative.

The surface normal is directed accordingly, usually by the right-hand rule. For the related yet different principle relating to electromagnetic coils see Right hand grip rule.

Conversely, one can consider the flux the more fundamental quantity and call the vector field the flux density.

Often a vector field is drawn by curves (field lines) following the "flow"; the magnitude of the vector field is then the line density, and the flux through a surface is the number of lines. Lines originate from areas of positive divergence (sources) and end at areas of negative divergence (sinks). In Vector calculus, the divergence is an Operator that measures the magnitude of a Vector field &rsquos source or sink at a given point the

See also the image at right: the number of red arrows passing through a unit area is the flux density, the curve encircling the red arrows denotes the boundary of the surface, and the orientation of the arrows with respect to the surface denotes the sign of the inner product of the vector field with the surface normals. In Mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object In Mathematics, an inner product space is a Vector space with the additional Structure of inner product.

If the surface encloses a 3D region, usually the surface is oriented such that the outflux is counted positive; the opposite is the influx.

The divergence theorem states that the net outflux through a closed surface, in other words the net outflux from a 3D region, is found by adding the local net outflow from each point in the region (which is expressed by the divergence). In Vector calculus, the divergence theorem, also known as Gauss&rsquos theorem ( Carl Friedrich Gauss) Ostrogradsky&rsquos theorem ( Mikhail In Vector calculus, the divergence is an Operator that measures the magnitude of a Vector field &rsquos source or sink at a given point the

If the surface is not closed, it has an oriented curve as boundary. Stokes' theorem states that the flux of the curl of a vector field is the line integral of the vector field over this boundary. In Differential geometry, Stokes' theorem is a statement about the integration of Differential forms which generalizes several Theorems from cURL is a Command line tool for transferring files with URL syntax. In Mathematics, a line integral (sometimes called a path integral or curve integral) is an Integral where the function to be integrated This path integral is also called circulation, especially in fluid dynamics. In Fluid dynamics, circulation is the Line integral around a closed curve of the Fluid Velocity. Thus the curl is the circulation density.

We can apply the flux and these theorems to many disciplines in which we see currents, forces, etc. , applied through areas.

Maxwell's equations

The flux of electric and magnetic field lines is frequently discussed in electrostatics. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical This is because in Maxwell's equations in integral form involve integrals like above for electric and magnetic fields. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric

For instance, Gauss's law states that the flux of the electric field out of a closed surface is proportional to the electric charge enclosed in the surface (regardless of how that charge is distributed). Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. The constant of proportionality is the reciprocal of the permittivity of free space. Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability

Its integral form is:

where:

• is the electric field,
• is the area of a differential square on the surface A with an outward facing surface normal defining its direction,
• is the charge enclosed by the surface,
• is the permittivity of free space
• is the integral over the surface A. Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability

Either or is called the electric flux.

Faraday's law of induction in integral form is:

where:

• is an infinitesimal element (differential) of the contour C (i. Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of In mathematics and more specifically in Differential calculus, the term differential has several interrelated meanings e. a vector with magnitude equal to the length of the infinitesimal line element, and direction equal to the direction of the contour C). Infinitesimals (from a 17th century Modern Latin coinage infinitesimus, originally referring to the " Infinite[[ th]]" member of a series have A contour line (also Level set, isopleth, isoline, isogram or isarithm) of a function of two

The magnetic field is denoted by . In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Its flux is called the magnetic flux. Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic The time-rate of change of the magnetic flux through a loop of wire is minus the electromotive force created in that wire. Electromotive force ( emf, \mathcal{E} is a term used to characterize electrical devices such as Voltaic cells thermoelectric devices electrical The direction is such that if current is allowed to pass through the wire, the electromotive force will cause a current which "opposes" the change in magnetic field by itself producing a magnetic field opposite to the change. This is the basis for inductors and many electric generators. An inductor is a passive electrical component designed to provide Inductance in a circuit In Electricity generation, an electrical generator is a device that converts Mechanical energy to Electrical energy, generally using Electromagnetic

Poynting vector

The flux of the Poynting vector through a surface is the electromagnetic power, or energy per unit time, passing through that surface. In Physics, the Poynting vector can be thought of as representing the Energy Flux (in W/m2 of an Electromagnetic field. In Physics, power (symbol P) is the rate at which work is performed or energy is transmitted or the amount of energy required or expended for In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of This is commonly used in analysis of electromagnetic radiation, but has application to other electromagnetic systems as well. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter.

Biology

In general, 'flux' in biology relates to movement of a substance between compartments. Foundations of modern biology There are five unifying principles There are several cases where the concept of 'flux' is important.

• The movement of molecules across a membrane: in this case, flux is defined by the rate of diffusion or transport of a substance across a permeable membrane. Diffusion is the net movement of particles (typically molecules from an area of high concentration to an area of low concentration by uncoordinated random movement MembraneA biological membrane or biomembrane is an enclosing or separating Amphipathic layer that acts as a barrier within or around a cell. Except in the case of active transport, net flux is directly proportional to the concentration difference across the membrane, the surface area of the membrane, and the membrane permeability constant. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance Surface area is the measure of how much exposed Area an object has A semipermeable membrane, also termed a selectively-permeable membrane, a partially-permeable membrane or a differentially-permeable membrane, is a membrane
• In ecology, flux is often considered at the ecosystem level - for instance, accurate determination of carbon fluxes using techniques like eddy covariance (at a regional and global level) is essential for modeling the causes and consequences of global warming. Ecology (from Greek grc οἶκος oikos, "house(hold" and grc -λογία -logia) is the scientific study of An ecosystem is a natural unit consisting of all plants animals and micro-organisms( Biotic factors in an area functioning together with all of the non-living physical ( Carbon dioxide forms approximately 004% of the Earth's atmosphere. The eddy covariance ( eddy correlation, eddy flux) technique is a prime atmospheric flux measurement technique to measure and calculate vertical turbulent fluxes Global warming is the increase in the average measured temperature of the
• Metabolic flux refers to the rate of flow of metabolites along a metabolic pathway, or even through a single enzyme. Flux, or metabolic flux is the rate of turnover of Molecules through a Metabolic pathway or an Enzyme. In Biochemistry, a metabolic pathway is a series of chemical reactions occurring within a cell. Enzymes are Biomolecules that catalyze ( ie increase the rates of Chemical reactions Almost all enzymes are Proteins A calculation may also be made of carbon (or other elements, e. g. nitrogen) flux. It is dependent on a number of factors, including: enzyme concentration; the concentration of precursor, product, and intermediate metabolites; post-translational modification of enzymes; and the presence of metabolic activators or repressors. Posttranslational modification (PTM is the chemical modification of a Protein after its translation. Metabolic control analysis and flux balance analysis provide frameworks for understanding metabolic fluxes and their constraints. Metabolic control analysis (MCA is a mathematical framework for describing metabolic, signaling and genetic pathways. Introduction Flux balance analysis ( FBA) has been shown to be a very useful technique for analysis of metabolic capabilities of cellular

See also

References

Further reading

• Stauffer, P. H. (2006). "Flux Flummoxed: A Proposal for Consistent Usage". Ground Water 44 (2): 125–128. doi:10.1111/j.1745-6584.2006.00197.x. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.