- Stefan flow
Stefan flow, occasionally called Stefan's flow (Slovene "Stefanov tok"), is a
transport phenomena concerning the movement of achemical species by a flowingfluid (typically in thegas phase ) that is induced toflow 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 includeevaporation ,condensation ,chemical reaction ,sublimation ,ablation ,adsorption ,absorption , anddesorption . It was named after the Slovenephysicist ,mathematician , andpoet Joseph Stefan for his early work on calculating evaporation rates.Stefan flow is distinct from
diffusion as described byFick'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 amean 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. Whenconcentration 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 ofliquid evaporates in air. In this case, thevapor /airmixture surrounding the droplet is the flowing fluid, and liquid/vapor boundary of the droplet is the interface. Asheat 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 thecombustion ofliquid fuel s such asdiesel ininternal combustion engine s, and in the design of such engines. Stefan flow from evaporating droplets and subliming ice particles also plays prominently inmeteorology as it influences the formation and dispersion ofclouds and precipitation.References
* 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.
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