Stefan flow

Last updated February 24, 2019

The Stefan flow, occasionally called Stefan's flow, 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 the Stefan flow, but the most common processes include evaporation, condensation, chemical reaction, sublimation, ablation, adsorption, absorption, and desorption. It was named after the Austrian physicist, mathematician, and poet Josef Stefan for his early work on calculating evaporation rates.

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. The term is applied equally to a set of chemically identical atomic or molecular structural units in a solid array.

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress, or external force. Fluids are a phase of matter and include liquids, gases and plasmas. They are substances with zero shear modulus, or, in simpler terms, substances which cannot resist any shear force applied to them.

In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation,

The 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 the Stefan flow. [1] 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.

Diffusion Statistical movement of molecules or atoms from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical potential)

Diffusion is the net movement of molecules or atoms from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in chemical potential of the diffusing species.

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

In physics a vapor or vapour is a substance in the gas phase at a temperature lower than its critical temperature, which means that the vapor can be condensed to a liquid by increasing the pressure on it without reducing the temperature. A vapor is different from an aerosol. An aerosol is a suspension of tiny particles of liquid, solid, or both within a gas.

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 or neighborhood, and in thermodynamics, as the reservoir. Depending on the type of system, it may interact with the environment by exchanging mass, energy, linear momentum, angular momentum, electric charge, or other conserved properties. In some disciplines, such as information theory, information may also be exchanged. The environment is ignored in analysis of the system, except in regard to these interactions.

In physics, a frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements.

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Evaporation type of vaporization of a liquid that occurs from its surface; surface phenomenon

Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase. The surrounding gas must not be saturated with the evaporating substance. When the molecules of the liquid collide, they transfer energy to each other based on how they collide with each other. When a molecule near the surface absorbs enough energy to overcome the vapor pressure, it will escape and enter the surrounding air as a gas. When evaporation occurs, the energy removed from the vaporized liquid will reduce the temperature of the liquid, resulting in evaporative cooling.

Mass transfer is the net movement of mass from one location, usually meaning stream, phase, fraction or component, to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration, and distillation. Mass transfer is used by different scientific disciplines for different processes and mechanisms. The phrase is commonly used in engineering for physical processes that involve diffusive and convective transport of chemical species within physical systems.

Convection is the heat transfer due to the bulk movement of molecules within fluids such as gases and liquids, including molten rock (rheid). Convection includes sub-mechanisms of advection, and diffusion.

Spray drying is a method of producing a dry powder from a liquid or slurry by rapidly drying with a hot gas. This is the preferred method of drying of many thermally-sensitive materials such as foods and pharmaceuticals. A consistent particle size distribution is a reason for spray drying some industrial products such as catalysts. Air is the heated drying medium; however, if the liquid is a flammable solvent such as ethanol or the product is oxygen-sensitive then nitrogen is used.

Heat transfer exchange of thermal energy between physical systems

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

A heat pipe is a heat-transfer device that combines the principles of both thermal conductivity and phase transition to effectively transfer heat between two solid interfaces.

The Marangoni effect is the mass transfer along an interface between two fluids due to a gradient of the surface tension. In the case of temperature dependence, this phenomenon may be called thermo-capillary convection.

Thermosiphon is a method of passive heat exchange, based on natural convection, which circulates a fluid without the necessity of a mechanical pump. Thermosiphoning is used for circulation of liquids and volatile gases in heating and cooling applications such as heat pumps, water heaters, boilers and furnaces. Thermosiphoning also occurs across air temperature gradients such as those utilized in a wood fire chimney or solar chimney.

Drying is a mass transfer process consisting of the removal of water or another solvent by evaporation from a solid, semi-solid or liquid. This process is often used as a final production step before selling or packaging products. To be considered "dried", the final product must be solid, in the form of a continuous sheet, long pieces, particles or powder. A source of heat and an agent to remove the vapor produced by the process are often involved. In bioproducts like food, grains, and pharmaceuticals like vaccines, the solvent to be removed is almost invariably water. Desiccation may be synonymous with drying or considered an extreme form of drying.

An evaporator is a device in a process used to turn the liquid form of a chemical substance such as water into its gaseous-form/vapor. The liquid is evaporated, or vaporized, into a gas form of the targeted substance in that process.

The Marangoni number (Ma) is the dimensionless number that balances thermal transport via flow (convection) due to a gradient in surface tension, with thermal diffusion. The number is named after Italian scientist Carlo Marangoni, although its use dates from the 1950s and it was neither discovered nor used by Carlo Marangoni. The most common application is to a layer of liquid, such as water, when there is a temperature difference $across this layer. This could be due to the liquid evaporating or being heated from below. There is a surface tension at the surface of a liquid that depends on temperature, typically as the temperature increases the surface tension decreases. Thus if due to a small fluctuation temperature, one part of the surface is hotter than another, there will be flow from the hotter part to the colder part, driven by this difference in surface tension, this flow is called the Marangoni effect. This flow will transport thermal energy, and the Marangoni number compares the rate at which thermal energy is transported by this flow to the rate at which thermal energy diffuses.$

Transpiration is the process of water movement through a plant and its evaporation from aerial parts, such as leaves, stems and flowers. Water is necessary for plants but only a small amount of water taken up by the roots is used for growth and metabolism. The remaining 97–99.5% is lost by transpiration and guttation. Leaf surfaces are dotted with pores called stomata, and in most plants they are more numerous on the undersides of the foliage. The stomata are bordered by guard cells and their stomatal accessory cells that open and close the pore. Transpiration occurs through the stomatal apertures, and can be thought of as a necessary "cost" associated with the opening of the stomata to allow the diffusion of carbon dioxide gas from the air for photosynthesis. Transpiration also cools plants, changes osmotic pressure of cells, and enables mass flow of mineral nutrients and water from roots to shoots. Two major factors influence the rate of water flow from the soil to the roots: the hydraulic conductivity of the soil and the magnitude of the pressure gradient through the soil. Both of these factors influence the rate of bulk flow of water moving from the roots to the stomatal pores in the leaves via the xylem.

The vapor–liquid–solid method (VLS) is a mechanism for the growth of one-dimensional structures, such as nanowires, from chemical vapor deposition. The growth of a crystal through direct adsorption of a gas phase on to a solid surface is generally very slow. The VLS mechanism circumvents this by introducing a catalytic liquid alloy phase which can rapidly adsorb a vapor to supersaturation levels, and from which crystal growth can subsequently occur from nucleated seeds at the liquid–solid interface. The physical characteristics of nanowires grown in this manner depend, in a controllable way, upon the size and physical properties of the liquid alloy.

Laser drilling is the process of creating thru-holes, referred to as “popped” holes or “percussion drilled” holes, by repeatedly pulsing focused laser energy on a material. The diameter of these holes can be as small as 0.002”. If larger holes are required, the laser is moved around the circumference of the “popped” hole until the desired diameter is created; this technique is called “trepanning”.

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 mechanics and thermodynamics, it places a heavy emphasis on the commonalities between the topics covered. Mass, momentum, and heat transport all share a very similar mathematical framework, and the parallels between them are exploited in the study of transport phenomena to draw deep mathematical connections that often provide very useful tools in the analysis of one field that are directly derived from the others.

The vaporizing droplet problem is a challenging issue in fluid dynamics. It is part of many engineering situations involving the transport and computation of sprays: fuel injection, spray painting, aerosol spray, flashing releases… In most of these engineering situations there is a relative motion between the droplet and the surrounding gas. The gas flow over the droplet has many features of the gas flow over a rigid sphere: pressure gradient, viscous boundary layer, wake. In addition to these common flow features one can also mention the internal liquid circulation phenomenon driven by surface-shear forces and the boundary layer blowing effect.

Membrane technology covers all engineering approaches for the transport of substances between two fractions with the help of permeable membranes. In general, mechanical separation processes for separating gaseous or liquid streams use membrane technology.

In thermodynamics, explosive boiling or phase explosion is a method whereby a superheated metastable liquid undergoes an explosive liquid-vapor phase transition into a stable two-phase state because of a massive homogeneous nucleation of vapor bubbles. This concept was pioneered by M. M. Martynyuk in 1976 and then later advanced by Fucke and Seydel.

A climbing/falling film plate evaporator is a specialized type of evaporator in which a thin film of liquid is passed over a rising and falling plate to allow the evaporation process to occur. It is an extension of the falling film evaporator, and has application in any field where the liquid to be evaporated cannot withstand extended exposure to high temperatures, such as the concentration of fruit juices.

In chemical engineering, a Stefan tube is a device that was devised by Josef Stefan in 1874. It is often used for measuring diffusion coefficients. It comprises a vertical tube, over the top of which a gas flows and at the bottom of which is a pool of volatile liquid that is maintained in a constant-temperature bath. The liquid in the pool evaporates, diffuses through the gas above it in the tube, and is carried away by the gas flow over the tube mouth at the top. One then measures the fall in the level of the liquid in the tube.

References

↑ Counter example?

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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[1] Counter example?