Marangoni effect
The Marangoni effect (also called the Gibbs–Marangoni effect) is the
History
This phenomenon was first identified in the so-called "
Mechanism
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).
In simple cases, the speed of the flow , where is the difference in surface tension and is the viscosity of the liquid. Water has a surface tension of around 0.07 N/m, and a viscosity of approximately 10−3 Pa s, at room temperature. So even variations of a few percent in the surface tension of water can generate Marangoni flows of almost 1 m/s. Thus Marangoni flows are common and easily observed.
For the case of a small drop of surfactant dropped onto the surface of water, Roché and coworkers[6] performed quantitative experiments and developed a simple model that was in approximate agreement with the experiments. This described the expansion in the radius of a patch of the surface covered in surfactant, due to an outward Marangoni flow at a speed . They found that speed of expansion of the surfactant-covered patch of the water surface occurred at speed of approximately
for the surface tension of water, , the (lower) surface tension of the surfactant-covered water surface, the viscosity of water, and the mass density of water. For N/m, i.e., of order tens of per cent reduction in surface tension of water, and as for water N m−6s3, we obtain the second equality above. This gives speeds that decrease as surfactant-covered region grows, but are of order cms/s to mm/s.
The equation is obtained by making a couple of simple approximations, the first is by equating the stress at the surface due to the concentration gradient of surfactant (which drives the Marangoni flow) with the viscous stresses (that oppose flow). The Marangoni stress , i.e., gradient in the surface tension due gradient in the surfactant concentration (from high in the centre of the expanding patch, to zero far from the patch). The viscous shear stress is simply the viscosity times the gradient in shear velocity , for the depth into the water of the flow due to the spreading patch. Roché and coworkers[6] assume that the momentum (which is directed radially) diffuses down into the liquid, during spreading, and so when the patch has reached a radius , , for the kinematic viscosity, which is the diffusion constant for momentum in a fluid. Equating the two stresses
where we approximated the gradient . Taking the 2/3 power of both sides gives the expression above.
The Marangoni number, a dimensionless value, can be used to characterize the relative effects of surface tension and viscous forces.
Tears of wine
As an example, wine may exhibit a visible effect called "tears of wine". The effect is a consequence of the fact that alcohol has a lower surface tension and higher volatility than water. The water/alcohol solution rises up the surface of the glass lowering the surface energy of the glass. Alcohol evaporates from the film leaving behind liquid with a higher surface tension (more water, less alcohol). This region with a lower concentration of alcohol (greater surface tension) pulls on the surrounding fluid more strongly than the regions with a higher alcohol concentration (lower in the glass). The result is the liquid is pulled up until its own weight exceeds the force of the effect, and the liquid drips back down the vessel's walls. 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.
Significance to transport phenomena
Under earth conditions, the effect of gravity causing
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.[8]
Examples and application
A familiar example is in
One important application of the Marangoni effect is the use for drying
A similar phenomenon has been creatively utilized to self-assemble nanoparticles into ordered arrays[9] and to grow ordered nanotubes.[10] An alcohol containing nanoparticles is spread on the substrate, followed by blowing humid air over the substrate. 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.
Another application is the manipulation of particles[11] taking advantage of the relevance of the surface tension effects at small scales. A controlled thermo-capillary convection is created by locally heating the air–water interface using an infrared laser. Then, this flow is used to control floating objects in both position and orientation and can prompt the self-assembly of floating objects, profiting from the Cheerios effect.
The Marangoni effect is also important to the fields of
See also
- Plateau–Rayleigh instability — an instability in a stream of liquid
- Diffusioosmosis - the Marangoni effect is flow at a fluid/fluid interface due to a gradient in the interfacial free energy, the analog at a fluid/solid interface is diffusioosmosis
References
- ^ a b "Marangoni Convection". COMSOL. Archived from the original on 2012-03-08. Retrieved 2014-08-06.
- ISBN 981-02-2657-8.
- ^ Thomson, James (1855). "On certain curious motions observable at the surfaces of wine and other alcoholic liquors". The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science. XLII: 330–333.
- ^ Marangoni, Carlo (1869). Sull'espansione delle goccie d'un liquido galleggianti sulla superficie di altro liquido [On the expansion of a droplet of a liquid floating on the surface of another liquid]. Pavia, Italy: Fratelli Fusi. p. 66.
- ^ Josiah Willard Gibbs (1878) "On the equilibrium of heterogeneous substances. Part II," Transactions of the Connecticut Academy of Arts and Sciences, 3 : 343-524. The equation for the energy that's required to create a surface between two phases appears on page 483. Reprinted in: Josiah Willard Gibbs with Henry Andrews Bumstead and Ralph Gibbs van Name, ed.s, The Scientific Papers of J. Willard Gibbs, ..., vol. 1, (New York, New York: Longmans, Green and Co., 1906), page 315.
- ^ S2CID 4837945.
- PMID 25910141.
- .
- PMID 18426208.
- S2CID 96266945.
- S2CID 232432662.
External links
- Motoring Oil Drops Physical Review Focus February 22, 2005
- Thin Film Physics, ISS astronaut Don Pettitdemonstrate. YouTube-movie.