Stefan flow
Encyclopedia
Stefan flow, occasionally called Stefan's flow (Slovene Stefanov tok), is a transport phenomenon concerning the movement of a chemical species
by a flowing fluid
(typically in the gas phase) that is induced to flow
by the production or removal of the species at an interface
. Any process that adds the species of interest to or removes it from the flowing fluid may cause Stefan flow, but the most common processes include evaporation
, condensation
, chemical reaction
, sublimation, ablation
, adsorption
, absorption, and desorption
. It was named after the Slovene physicist
, mathematician
, and poet
Joseph Stefan
for his early work on calculating evaporation rates.
Stefan flow is distinct from diffusion
as described by Fick's law, but diffusion almost always also occurs in multi-species systems that are experiencing Stefan flow. In systems undergoing one of the species addition or removal processes mentioned previously, the addition or removal generates a mean
flow in the flowing fluid as the fluid next to the interface is displaced by the production or removal of additional fluid by the processes occurring at the interface. The transport of the species by this mean flow is the Stefan flow. When concentration
gradient
s of the species are also present, diffusion transports the species relative to the mean flow. The total transport rate of the species is then given by a summation of the Stefan flow and diffusive contributions.
An example of Stefan flow occurs when a droplet of liquid
evaporates in air. In this case, the vapor
/air mixture
surrounding the droplet is the flowing fluid, and liquid/vapor boundary of the droplet is the interface. As heat
is absorbed by the droplet from the environment
, some of the liquid evaporates into vapor at the surface of the droplet, and flows away from the droplet as it is displaced by additional vapor evaporating from the droplet. This process causes the flowing medium to move away from the droplet at some mean speed that is dependent on the evaporation rate and other factors such as droplet size and composition. In addition to this mean flow, a concentration gradient must exist in the neighborhood of the droplet (assuming an isolated droplet) since the flowing medium is mostly air far from the droplet and mostly vapor near the droplet. This gradient causes Fickian diffusion that transports the vapor away from the droplet and the air towards it, with respect to the mean flow. Thus, in the frame
of the droplet, the flow of vapor away from the droplet is faster than for pure Stefan flow, since diffusion is working in the same direction as the mean flow. However, the flow of air away from the droplet is slower than the pure Stefan flow, since diffusion is working to transport air back towards the droplet against the Stefan flow. Such flow from evaporating droplets is important in understanding the combustion
of liquid fuels such as diesel in internal combustion engine
s, and in the design of such engines. Stefan flow from evaporating droplets and subliming ice particles also plays prominently in meteorology
as it influences the formation and dispersion of clouds and precipitation
.
Chemical species
Chemical species are atoms, molecules, molecular fragments, ions, etc., being subjected to a chemical process or to a measurement. Generally, a chemical species can be defined as an ensemble of chemically identical molecular entities that can explore the same set of molecular energy levels on a...
by a flowing fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
(typically in the gas phase) that is induced to flow
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
by the production or removal of the species at an interface
Interface (chemistry)
An interface is a surface forming a common boundary among two different phases, such as an insoluble solid and a liquid, two immiscible liquids or a liquid and an insoluble gas. The importance of the interface depends on which type of system is being treated: the bigger the quotient area/volume,...
. Any process that adds the species of interest to or removes it from the flowing fluid may cause Stefan flow, but the most common processes include evaporation
Evaporation
Evaporation is a type of vaporization of a liquid that occurs only on the surface of a liquid. The other type of vaporization is boiling, which, instead, occurs on the entire mass of the liquid....
, condensation
Condensation
Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....
, chemical reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...
, sublimation, ablation
Ablation
Ablation is removal of material from the surface of an object by vaporization, chipping, or other erosive processes. This occurs in spaceflight during ascent and atmospheric reentry, glaciology, medicine, and passive fire protection.-Spaceflight:...
, adsorption
Adsorption
Adsorption is the adhesion of atoms, ions, biomolecules or molecules of gas, liquid, or dissolved solids to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. It differs from absorption, in which a fluid permeates or is dissolved by a liquid or solid...
, absorption, and desorption
Desorption
Desorption is a phenomenon whereby a substance is released from or through a surface. The process is the opposite of sorption . This occurs in a system being in the state of sorption equilibrium between bulk phase and an adsorbing surface...
. It was named after the Slovene physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, and poet
Poet
A poet is a person who writes poetry. A poet's work can be literal, meaning that his work is derived from a specific event, or metaphorical, meaning that his work can take on many meanings and forms. Poets have existed since antiquity, in nearly all languages, and have produced works that vary...
Joseph Stefan
Joseph Stefan
Joseph Stefan was a physicist, mathematician, and poet of Slovene mother tongue and Austrian citizenship.- Life and work :...
for his early work on calculating evaporation rates.
Stefan flow is distinct from diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
as described by Fick's law, but diffusion almost always also occurs in multi-species systems that are experiencing Stefan flow. In systems undergoing one of the species addition or removal processes mentioned previously, the addition or removal generates a mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
flow in the flowing fluid as the fluid next to the interface is displaced by the production or removal of additional fluid by the processes occurring at the interface. The transport of the species by this mean flow is the Stefan flow. When concentration
Concentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...
gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
s of the species are also present, diffusion transports the species relative to the mean flow. The total transport rate of the species is then given by a summation of the Stefan flow and diffusive contributions.
An example of Stefan flow occurs when a droplet of liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
evaporates in air. In this case, the vapor
Vapor
A vapor or vapour is a substance in the gas phase at a temperature lower than its critical point....
/air mixture
Mixture
In chemistry, a mixture is a material system made up by two or more different substances which are mixed together but are not combined chemically...
surrounding the droplet is the flowing fluid, and liquid/vapor boundary of the droplet is the interface. As heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
is absorbed by the droplet from the environment
Environment (systems)
In science and engineering, a system is the part of the universe that is being studied, while the environment is the remainder of the universe that lies outside the boundaries of the system. It is also known as the surroundings, and in thermodynamics, as the reservoir...
, some of the liquid evaporates into vapor at the surface of the droplet, and flows away from the droplet as it is displaced by additional vapor evaporating from the droplet. This process causes the flowing medium to move away from the droplet at some mean speed that is dependent on the evaporation rate and other factors such as droplet size and composition. In addition to this mean flow, a concentration gradient must exist in the neighborhood of the droplet (assuming an isolated droplet) since the flowing medium is mostly air far from the droplet and mostly vapor near the droplet. This gradient causes Fickian diffusion that transports the vapor away from the droplet and the air towards it, with respect to the mean flow. Thus, in the frame
Frame of reference
A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...
of the droplet, the flow of vapor away from the droplet is faster than for pure Stefan flow, since diffusion is working in the same direction as the mean flow. However, the flow of air away from the droplet is slower than the pure Stefan flow, since diffusion is working to transport air back towards the droplet against the Stefan flow. Such flow from evaporating droplets is important in understanding the combustion
Combustion
Combustion or burning is the sequence of exothermic chemical reactions between a fuel and an oxidant accompanied by the production of heat and conversion of chemical species. The release of heat can result in the production of light in the form of either glowing or a flame...
of liquid fuels such as diesel in internal combustion engine
Internal combustion engine
The internal combustion engine is an engine in which the combustion of a fuel occurs with an oxidizer in a combustion chamber. In an internal combustion engine, the expansion of the high-temperature and high -pressure gases produced by combustion apply direct force to some component of the engine...
s, and in the design of such engines. Stefan flow from evaporating droplets and subliming ice particles also plays prominently in meteorology
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...
as it influences the formation and dispersion of clouds and precipitation
Precipitation (meteorology)
In meteorology, precipitation In meteorology, precipitation In meteorology, precipitation (also known as one of the classes of hydrometeors, which are atmospheric water phenomena is any product of the condensation of atmospheric water vapor that falls under gravity. The main forms of precipitation...
.