The Stefan flow, occasionally called Stefan's flow, is a

transport phenomenon In engineering, physics, and chemistry, the study of transport phenomena concerns the exchange of mass, energy, charge, momentum and angular momentum between observed and studied systems. While it draws from fields as diverse as continuum me ...

concerning the movement of a

chemical species A chemical species is a chemical substance or ensemble composed of chemically identical molecular entities that can explore the same set of molecular energy levels on a characteristic or delineated time scale. These energy levels determine the wa ...

by a flowing fluid (typically in the

gas phase In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetiza ...

) that is induced to flow by the production or removal of the species at an

interface Interface or interfacing may refer to: Academic journals * ''Interface'' (journal), by the Electrochemical Society * '' Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Linguistics'' * '' Int ...

. 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, condensation,

chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...

, sublimation,

ablation Ablation ( la, ablatio – removal) is removal or destruction of something from an object by vaporization, chipping, erosive processes or by other means. Examples of ablative materials are described below, and include spacecraft material for a ...

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 ...

, absorption, and

desorption Desorption is the physical process where a previously adsorbed substance is released from a surface. This happens when a molecule gains enough energy to overcome the activation barrier of the bounding energy that keeps it in the surface. There ...

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

Josef Stefan Josef Stefan ( sl, Jožef Štefan; 24 March 1835 – 7 January 1893) was an ethnic Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire. Life and work Stefan was born in an outskirt village of St. Peter (Slovene: ; to ...

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 chemica ...

as described by

Fick's law Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second law which in turn is identical to the diffusion equ ...

, 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 lower end of a tube or other surface boundary, producing a hanging drop called a pendant ...

of liquid evaporates in air. In this case, the

vapor In physics, a vapor (American English) or vapour (British English and Canadian English; see spelling differences) is a substance in the gas phase at a temperature lower than its critical temperature,R. H. Petrucci, W. S. Harwood, and F. G. Her ...

/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 Environment most often refers to: __NOTOC__ * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...

, 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 a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...

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