The Stefan flow, occasionally called Stefan's flow, is a transport phenomenon concerning the movement of a

chemical species Chemical species are a specific form of chemical substance or chemically identical molecular entities that have the same molecular energy level at a specified timescale. These entities are classified through bonding types and relative abundance of ...

by a flowing

fluid In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...

(typically in the

gas phase In the physical sciences, a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a ...

) 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 the Stefan flow, but the most common processes include

evaporation Evaporation is a type of vaporization that occurs on the Interface (chemistry), surface of a liquid as it changes into the gas phase. A high concentration of the evaporating substance in the surrounding gas significantly slows down evapora ...

condensation Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor ...

chemical reaction A chemical reaction is a process that leads to the chemistry, chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an Gibbs free energy, ...

, sublimation,

ablation Ablation ( – removal) is the removal or destruction of something from an object by vaporization, chipping, erosion, erosive processes, or by other means. Examples of ablative materials are described below, including spacecraft material for as ...

adsorption Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which a ...

, absorption, and

desorption Desorption is the physical process where Adsorption, adsorbed atoms or molecules are released from a surface into the surrounding vacuum or fluid. This occurs when a molecule gains enough energy to overcome the activation barrier and the binding e ...

. It was named after the Slovenian physicist, mathematician, and poet

Josef Stefan Josef Stefan (; 24 March 1835 – 7 January 1893) was a Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire. Life and work Stefan was born in the village of St. Peter (Slovene: ) on the outskirts of Klagenfurt) to A ...

for his early work on calculating evaporation rates. The Stefan flow is distinct from

diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...

as described by

Fick's law Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second ...

, but diffusion almost always also occurs in multi-species systems that are experiencing the Stefan flow.Counter example? 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 gradients 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 the Stefan flow occurs when a

droplet A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the end of a tube or other surface boundary, producing a hanging drop called a pendant drop. Dro ...

of liquid evaporates in air. In this case, the

vapor In physics, a vapor (American English) or vapour (Commonwealth English; American and British English spelling differences#-our, -or, see spelling differences) is a substance in the gas phase at a temperature lower than its critical temperature,R ...

/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 A frame is often a structural system that supports other components of a physical construction and/or steel frame that limits the construction's extent. Frame and FRAME may also refer to: Physical objects In building construction *Framing (con ...

of the droplet, the flow of vapor away from the droplet is faster than for the 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 engines, and in the design of such engines. The Stefan flow from evaporating droplets and subliming ice particles also plays prominently in

meteorology Meteorology is the scientific study of the Earth's atmosphere and short-term atmospheric phenomena (i.e. weather), with a focus on weather forecasting. It has applications in the military, aviation, energy production, transport, agricultur ...

as it influences the formation and dispersion of clouds and precipitation.

References

{{Reflist * C. T. Bowman, ''Course Notes on Combustion'', 2004, Stanford University course reference material for ME 371: Fundamentals of Combustion. * C. T. Bowman, ''Course Notes on Combustion'', 2005, Stanford University course reference material for ME 372: Combustion Applications. Transport phenomena Flow regimes