Marangoni effect
Encyclopedia
The Marangoni effect is the mass transfer along an interface
between two fluids due to surface tension
gradient
. In the case of temperature dependence, this phenomenon may be called thermo-capillary convection (or Bénard–Marangoni convection).
" by physicist James Thomson
(Lord Kelvin
's brother) in 1855. The general effect is named after Italian
physicist Carlo Marangoni
, who studied it for his doctoral dissertation at the University of Pavia
and published his results in 1865. The most complete early treatment of the subject is due to Willard Gibbs.
Since a liquid with a high surface tension
pulls more strongly on the surrounding liquid than one with a low surface tension, the presence of a gradient
in surface tension
will naturally cause the liquid to flow away from regions of low surface tension. The surface tension
gradient can be caused by concentration gradient or by a temperature gradient (surface tension is a function of temperature).
As an example, wine
may exhibit a visible effect called "tears
", as shown in the photograph. The effect is a consequence of the fact that alcohol has a lower surface tension
than water. If alcohol is mixed with water inhomogeneously, a region with a lower concentration of alcohol (greater surface tension) will pull on the surrounding fluid more strongly than a region with a higher alcohol concentration (lower surface tension). The result is that the liquid tends to flow away from regions with higher alcohol concentrationalong the tension gradient. This can also be easily demonstrated by spreading a thin film of water on a smooth surface and then allowing a drop of alcohol to fall on the center of the film. The liquid will rush out of the region where the drop of alcohol fell.
The Marangoni number
, a dimensionless value, can be used to characterize the relative effects of surface tension and viscous forces.
A very detailed mathematical treatment of this from the point of view of the Navier–Stokes equations and the equations of thermodynamics
can be found in the first third of Subrahmanyan Chandrasekhar's
Hydrodynamic and Hydromagnetic Stability, originally published in 1961 by Oxford, and republished by Dover in 1981.
in a system with a temperature gradient along a fluid/fluid interface is usually much stronger than the Marangoni effect. Many experiments (ESA MASER 1-3) have been conducted under microgravity conditions aboard sounding rockets to observe the Marangoni effect without the influence of gravity.
The effect of the Marangoni effect on heat transfer in the presence of gas bubbles on the heating surface (e.g., in subcooled nucleate boiling) has long been ignored, but it is currently a topic of ongoing research interest because of its potential fundamental importance to the understanding of heat transfer in boiling.
s: the Marangoni effect stabilizes soap films. Another instance of the Marangoni effect appears in the behavior of convection cells, the so-called Bénard cells.
One important application of the Marangoni effect is the use for drying silicon
wafers
after a wet processing step during the manufacture of integrated circuits. Liquid spots left on the wafer surface can cause oxidation that damages components on the wafer. To avoid spotting, an alcohol
vapor
(IPA) or other organic compound in gas, vapor, or aerosol form is blown through a nozzle
over the wet wafer surface (or at the meniscus formed between the cleaning liquid and wafer as the wafer is lifted from an immersion bath), and the subsequent Marangoni effect causes a surface-tension gradient in the liquid allowing gravity to more-easily pull the liquid completely off the wafer surface, effectively leaving a dry wafer surface. A similar phenomenon has been creatively utilized to self-assemble nanoparticles with ordered arrays. Instead, an alcohol containing nanoparticles is spread on the substrate, followed by blowing the substrate with a humid air flow. The alcohol is evaporated under the flow. Simultaneously, water condenses and forms microdroplets on the substrate. Meanwhile, the nanoparticles in alcohol are transferred into the microdroplets and finally form numerous coffee rings on the substrate after drying.
The Marangoni effect is also important to the fields of welding
, crystal growth
and electron beam melting of metals.
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,...
between two fluids due to surface tension
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
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....
. In the case of temperature dependence, this phenomenon may be called thermo-capillary convection (or Bénard–Marangoni convection).
History
This phenomenon was first identified in the so called "tears of wineTears of wine
The phenomenon called tears of wine is manifested as a ring of clear liquid, near the top of a glass of wine, from which droplets continuously form and drop back into the wine. It is most readily observed in a wine which has a high alcohol content...
" by physicist James Thomson
James Thomson (engineer)
right|300px|James Thomson was an engineer and physicist whose reputation is substantial though it is overshadowed by that of his younger brother William Thomson .-Biography:Born in Belfast, he grew up mostly in Glasgow...
(Lord Kelvin
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...
's brother) in 1855. The general effect is named after Italian
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
physicist Carlo Marangoni
Carlo Marangoni
Carlo Giuseppe Matteo Marangoni was an Italian physicist.Marangoni graduated in 1865 from the University of Pavia, under the supervision of Giovanni Cantoni, with a dissertation entitled ""....
, who studied it for his doctoral dissertation at the University of Pavia
University of Pavia
The University of Pavia is a university located in Pavia, Lombardy, Italy. It was founded in 1361 and is organized in 9 Faculties.-History:...
and published his results in 1865. The most complete early treatment of the subject is due to Willard Gibbs.
Mechanism
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
pulls more strongly on the surrounding liquid than one with a low surface tension, the presence of a 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....
in surface tension
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
will naturally cause the liquid to flow away from regions of low surface tension. The surface tension
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
gradient can be caused by concentration gradient or by a temperature gradient (surface tension is a function of temperature).
As an example, wine
Wine
Wine is an alcoholic beverage, made of fermented fruit juice, usually from grapes. The natural chemical balance of grapes lets them ferment without the addition of sugars, acids, enzymes, or other nutrients. Grape wine is produced by fermenting crushed grapes using various types of yeast. Yeast...
may exhibit a visible effect called "tears
Tears of wine
The phenomenon called tears of wine is manifested as a ring of clear liquid, near the top of a glass of wine, from which droplets continuously form and drop back into the wine. It is most readily observed in a wine which has a high alcohol content...
", as shown in the photograph. The effect is a consequence of the fact that alcohol has a lower surface tension
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
than water. If alcohol is mixed with water inhomogeneously, a region with a lower concentration of alcohol (greater surface tension) will pull on the surrounding fluid more strongly than a region with a higher alcohol concentration (lower surface tension). The result is that the liquid tends to flow away from regions with higher alcohol concentrationalong the tension gradient. This can also be easily demonstrated by spreading a thin film of water on a smooth surface and then allowing a drop of alcohol to fall on the center of the film. The liquid will rush out of the region where the drop of alcohol fell.
The Marangoni number
Marangoni number
The Marangoni number is a dimensionless number named after Italian scientist Carlo Marangoni.The Marangoni number may be regarded as proportional to surface tension forces divided by viscous forces...
, a dimensionless value, can be used to characterize the relative effects of surface tension and viscous forces.
A very detailed mathematical treatment of this from the point of view of the Navier–Stokes equations and the equations of thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
can be found in the first third of Subrahmanyan Chandrasekhar's
Subrahmanyan Chandrasekhar
Subrahmanyan Chandrasekhar, FRS ) was an Indian origin American astrophysicist who, with William A. Fowler, won the 1983 Nobel Prize for Physics for key discoveries that led to the currently accepted theory on the later evolutionary stages of massive stars...
Hydrodynamic and Hydromagnetic Stability, originally published in 1961 by Oxford, and republished by Dover in 1981.
Significance to transport phenomena
Under earth conditions, the effect of gravity causing density-driven convectionConvection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....
in a system with a temperature gradient along a fluid/fluid interface is usually much stronger than the Marangoni effect. Many experiments (ESA MASER 1-3) have been conducted under microgravity conditions aboard sounding rockets to observe the Marangoni effect without the influence of gravity.
The effect of the Marangoni effect on heat transfer in the presence of gas bubbles on the heating surface (e.g., in subcooled nucleate boiling) has long been ignored, but it is currently a topic of ongoing research interest because of its potential fundamental importance to the understanding of heat transfer in boiling.
Examples and application
A familiar example is in soap filmSoap film
Soap films are thin layers of liquid surrounded by air. For example, if two soap bubbles enters in contact, they merged and a thin film is created in between. Thus, foams are composed of a network of films connected by Plateau borders...
s: the Marangoni effect stabilizes soap films. Another instance of the Marangoni effect appears in the behavior of convection cells, the so-called Bénard cells.
One important application of the Marangoni effect is the use for drying silicon
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...
wafers
Wafer (electronics)
A wafer is a thin slice of semiconductor material, such as a silicon crystal, used in the fabrication of integrated circuits and other microdevices...
after a wet processing step during the manufacture of integrated circuits. Liquid spots left on the wafer surface can cause oxidation that damages components on the wafer. To avoid spotting, an alcohol
Alcohol
In chemistry, an alcohol is an organic compound in which the hydroxy functional group is bound to a carbon atom. In particular, this carbon center should be saturated, having single bonds to three other atoms....
vapor
Vapor
A vapor or vapour is a substance in the gas phase at a temperature lower than its critical point....
(IPA) or other organic compound in gas, vapor, or aerosol form is blown through a nozzle
Nozzle
A nozzle is a device designed to control the direction or characteristics of a fluid flow as it exits an enclosed chamber or pipe via an orifice....
over the wet wafer surface (or at the meniscus formed between the cleaning liquid and wafer as the wafer is lifted from an immersion bath), and the subsequent Marangoni effect causes a surface-tension gradient in the liquid allowing gravity to more-easily pull the liquid completely off the wafer surface, effectively leaving a dry wafer surface. A similar phenomenon has been creatively utilized to self-assemble nanoparticles with ordered arrays. Instead, an alcohol containing nanoparticles is spread on the substrate, followed by blowing the substrate with a humid air flow. The alcohol is evaporated under the flow. Simultaneously, water condenses and forms microdroplets on the substrate. Meanwhile, the nanoparticles in alcohol are transferred into the microdroplets and finally form numerous coffee rings on the substrate after drying.
The Marangoni effect is also important to the fields of welding
Welding
Welding is a fabrication or sculptural process that joins materials, usually metals or thermoplastics, by causing coalescence. This is often done by melting the workpieces and adding a filler material to form a pool of molten material that cools to become a strong joint, with pressure sometimes...
, crystal growth
Crystal growth
A crystal is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. Crystal growth is a major stage of a crystallization process, and consists in the addition of new atoms, ions, or polymer strings into...
and electron beam melting of metals.
External links
- Motoring Oil Drops Physical Review Focus February 22, 2005
- Marangoni wafer drying