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In day-to-day life all of us observe that a stream of water emerging from a faucet will break up into droplets, no matter how smoothly the stream is emitted from the faucet. This is due to a phenomenon called the Plateau–Rayleigh instability, which is entirely a consequence of the effects of surface tension.The explanation of this instability begins with the existence of tiny perturbations in the stream. These are always present, no matter how smooth the stream is. If the perturbations are resolved into sinusoidal components, we find that some components grow with time while others decay with time. Among those that grow with time, some grow at faster rates than others. Whether a component decays or grows, and how fast it grows is entirely a function of its wave number (a measure of how many peaks and troughs per centimeter) and the radii of the original cylindrical stream.

Gallery

Image:UnstableLiquidSheet.jpg|Breakup of a moving sheet of water bouncing off of a spoon.Image:SurfaceTension.jpg|Photo of flowing water adhering to a hand. Surface tension creates the sheet of water between the flow and the hand.Image:Ggb in soap bubble 1.jpg|A soap bubble balances surface tension forces against internal pneumatic pressure.Image:2006-01-15 coin on water.jpg|Surface tension prevents a coin from sinking: the coin is indisputably denser than water, so it must be displacing a volume greater than its own for buoyancy to balance mass.Image:3_Moeda_(5).jpg|An aluminium coin floats on the surface of the water at 10 Â°C. Any extra weight would drop the coin to the bottom.Image:Dscn3156-daisy-water 1200x900.jpg|A daisy. The entirety of the flower lies below the level of the (undisturbed) free surface. The water rises smoothly around its edge. Surface tension prevents water from displacing the air between the petals and possibly submerging the flower.Image:Surface Tension 01.jpg|A metal paper clip floats on water. Several can usually be carefully added without overflow of water.Image:Paperclip floating on water (with 'contour lines').jpg|A metal paperclip floating on water. A grille in front of the light has created the 'contour lines' which show the deformation in the water surface caused by the metal paper clip.

Thermodynamics

Thermodynamic theories of surface tension

J.W. Gibbs developed the thermodynamic theory of capillarity basedon the idea of surfaces of discontinuity.{{Citation| last = Gibbs| first = J.W.| year = 2002| orig-year = 1876–1878| title = The Scientific Papers of J. Willard Gibbs| chapter = On the Equilibrium of Heterogeneous Substances| volume = 1| publisher = Ox Bow Press| place = Woodbridge, CT| pages = 55–354| editor-last = Bumstead| editor-first = H.A.| editor2-last = Van Nameeds| editor2-first = R.G.| isbn = 978-0918024770}} Gibbs considered the case of a sharp mathematical surface being placed somewhere within the microscopically fuzzy physical interface that exists between two homogeneous substances. Realizing that the exact choice of the surface's location was somewhat arbitrary, he left it flexible. Since the interface exists in thermal and chemical equilibrium with the substances around it (having temperature {{mvar|T}} and chemical potentials {{math|μi}}), Gibbs considered the case where the surface may have excess energy, excess entropy, and excess particles, finding the natural free energy function in this case to be U - TS - mu_1 N_1 - mu_2 N_2 cdots , a quantity later named as the grand potential and given the symbol Omega.(File:Gibbs Model.tif|thumb|Gibbs' placement of a precise mathematical surface in a fuzzy physical interface.)Considering a given subvolume V containing a surface of discontinuity, the volume is divided by the mathematical surface into two parts A and B, with volumes V_text{A} and V_text{B}, with V = V_text{A} + V_text{B} exactly. Now, if the two parts A and B were homogeneous fluids (with pressures p_text{A}, p_text{B}) and remained perfectly homogeneous right up to the mathematical boundary, without any surface effects, the total grand potential of this volume would be simply -p_text{A} V_text{A} - p_text{B} V_text{B}. The surface effects of interest are a modification to this, and they can be all collected into a surface free energy term Omega_text{S} so the total grand potential of the volume becomes:Omega = -p_text{A} V_text{A} - p_text{B} V_text{B} + Omega_text{S}.For sufficiently macroscopic and gently curved surfaces, the surface free energy must simply be proportional to the surface area:BOOK, Landau, Lifshitz, Course of Theoretical Physics Volume 5: Statistical Physics I, 1980, Pergamon, 517–537, 3, Omega_text{S} = gamma A,for surface tension gamma and surface area A.As stated above, this implies the mechanical work needed to increase a surface area A is {{math|dW {{=}} γ dA}}, assuming the volumes on each side do not change. Thermodynamics requires that for systems held at constant chemical potential and temperature, all spontaneous changes of state are accompanied by a decrease in this free energy Omega, that is, an increase in total entropy taking into account the possible movement of energy and particles from the surface into the surrounding fluids. From this it is easy to understand why decreasing the surface area of a mass of liquid is always spontaneous, provided it is not coupled to any other energy changes. It follows that in order to increase surface area, a certain amount of energy must be added.Gibbs and other scientists have wrestled with the arbitrariness in the exact microscopic placement of the surface.JOURNAL, Rusanov, A, Surface thermodynamics revisited, Surface Science Reports, 58, 5–8, 2005, 111–239, 0167-5729, 10.1016/j.surfrep.2005.08.002, 2005SurSR..58..111R, For microscopic surfaces with very tight curvatures, it is not correct to assume the surface tension is independent of size, and topics like the Tolman length come into play. For a macroscopic-sized surface (and planar surfaces), the surface placement does not have a significant effect on {{mvar|γ}}; however, it does have a very strong effect on the values of the surface entropy, surface excess mass densities, and surface internal energy,{{r|gibbseq|p=237}} which are the partial derivatives of the surface tension function gamma(T, mu_1, mu_2, cdots).Gibbs emphasized that for solids, the surface free energy may be completely different from surface stress (what he called surface tension):{{r|gibbseq|p=315}} the surface free energy is the work required to form the surface, while surface stress is the work required to stretch the surface. In the case of a two-fluid interface, there is no distinction between forming and stretching because the fluids and the surface completely replenish their nature when the surface is stretched. For a solid, stretching the surface, even elastically, results in a fundamentally changed surface. Further, the surface stress on a solid is a directional quantity (a stress tensor) while surface energy is scalar.Fifteen years after Gibbs, J.D. van der Waals developed the theory of capillarity effects based on the hypothesis of a continuous variation of density.{{Citation| last = van der Waals| first = J.D.| translator-last = Rowlinson| translator-first = J.S.| year = 1979| orig-year = 1893| title = The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density| journal = J. Stat. Phys.| volume = 20| issue = 2| pages = 197–200| bibcode =1979JSP....20..197R| doi = 10.1007/BF01011513| s2cid = 122954999}} He added to the energy density the term c (nabla rho)^2, where c is the capillarity coefficient and ρ is the density. For the multiphase equilibria, the results of the van der Waals approach practically coincide with the Gibbs formulae, but for modelling of the dynamics of phase transitions the van der Waals approach is much more convenient.{{Citation| last1 = Cahn| first1 = J.W.| last2 = Hilliard| first2 = J.E.| year = 1958| title = Free energy of a nonuniform system. I. Interfacial free energy| journal = J. Chem. Phys.| pages = 258–266| doi = 10.1063/1.1744102 | bibcode= 1958JChPh..28..258C| volume=28| issue = 2}}{{Citation| last1 = Langer| first1 = J.S.| last2 = Bar-On| first2 = M.| last3 = Miller| first3 = H.D.| year = 1975| title = New computational method in the theory of spinodal decomposition| journal = Phys. Rev. A | pages = 1417–1429| doi = 10.1103/PhysRevA.11.1417| bibcode= 1975PhRvA..11.1417L issue = 4}} The van der Waals capillarity energy is now widely used in the phase field models of multiphase flows. Such terms are also discovered in the dynamics of non-equilibrium gases.{{Citation| last1 = Gorban| first1 = A.N.| last2 = Karlin| first2 = I. V.| year = 2016| title = Beyond Navier–Stokes equations: capillarity of ideal gas| type = Review article| journal = Contemporary Physics| doi = 10.1080/00107514.2016.1256123 | url =weblink| arxiv= 1702.00831| bibcode= 2017ConPh..58...70G| volume=58| issue = 1| pages=70–90| s2cid = 55317543}}

Thermodynamics of bubbles

The pressure inside an ideal spherical bubble can be derived from thermodynamic free energy considerations. The above free energy can be written as:Omega = -Delta P V_text{A} - p_text{B} V + gamma Awhere Delta P = p_text{A} - p_text{B} is the pressure difference between the inside (A) and outside (B) of the bubble, and V_text{A} is the bubble volume. In equilibrium, {{math|1=dΩ = 0}}, and so,Delta P,dV_text{A} = gamma, dA.For a spherical bubble, the volume and surface area are given simply byV_text{A} = tfrac43pi R^3 quadrightarrowquad dV_text{A} = 4pi R^2 ,dR,andA = 4pi R^2 quadrightarrowquad dA = 8pi R, dR.Substituting these relations into the previous expression, we findDelta P = frac{2}{R}gamma,which is equivalent to the Rx {{=}} Ry}}.

Influence of temperature

Surface tension is dependent on temperature. For that reason, when a value is given for the surface tension of an interface, temperature must be explicitly stated. The general trend is that surface tension decreases with the increase of temperature, reaching a value of 0 at the critical temperature. For further details see Eötvös rule. There are only empirical equations to relate surface tension and temperature:

• Eötvös:WEB,weblink Surface Tension by the Ring Method (Du Nouy Method), 2007-09-08, PHYWE, 2007-09-27,weblink" title="web.archive.org/web/20070927010256weblink">weblink live, BOOK, The Physics and Chemistry of Surfaces, 3rd ed, Adam, Neil Kensington, Oxford University Press, 1941, WEB,weblink Physical Properties Sources Index: Eötvös Constant, 2008-11-16, dead,weblink" title="web.archive.org/web/20110706231759weblink">weblink 2011-07-06, gamma V^{2/3} = k(T_mathrm{C}-T) . Here {{mvar|V}} is the molar volume of a substance, {{math|TC}} is the critical temperature and {{mvar|k}} is a constant valid for almost all substances. A typical value is {{mvar|k}} = {{val|2.1|e=-7|u=J K−1 mol−{{2/3}}}}. For water one can further use {{mvar|V}} = 18 ml/mol and {{math|TC}} = 647 K (374 Â°C).JOURNAL, 10.1063/1.555688,weblink International Tables of the Surface Tension of Water, Journal of Physical and Chemical Reference Data, 12, 3, 817, 1983, Vargaftik, N. B., Volkov, B. N., Voljak, L. D., 1983JPCRD..12..817V, 2017-07-13, 2016-12-21,weblink" title="web.archive.org/web/20161221094427weblink">weblink dead, A variant on Eötvös is described by Ramay and Shields:BOOK, Physical Chemistry, 3rd ed, Moore, Walter J., Prentice Hall, 1962, gamma V^{2/3} = k left(T_mathrm{C} - T - 6,mathrm{K}right) where the temperature offset of 6 K provides the formula with a better fit to reality at lower temperatures.
• Guggenheim–Katayama: gamma = gamma^circ left( 1-frac{T}{T_mathrm C} right)^n {{math|γ°}} is a constant for each liquid and {{mvar|n}} is an empirical factor, whose value is {{sfrac|11|9}} for organic liquids. This equation was also proposed by van der Waals, who further proposed that {{math|γ°}} could be given by the expression K_2 T^{1/3}_mathrm{C} P^{2/3}_mathrm{C}, where {{math|K2}} is a universal constant for all liquids, and {{math|PC}} is the critical pressure of the liquid (although later experiments found {{math|K2}} to vary to some degree from one liquid to another).

Both Guggenheim–Katayama and Eötvös take into account the fact that surface tension reaches 0 at the critical temperature, whereas Ramay and Shields fails to match reality at this endpoint.

Influence of solute concentration

Solutes can have different effects on surface tension depending on the nature of the surface and the solute:

• Little or no effect, for example sugar at water|air, most organic compounds at oil/air
• Increase surface tension, most inorganic salts at water|air
• Non-monotonic change, most inorganic acids at water|air
• Decrease surface tension progressively, as with most amphiphiles, e.g., alcohols at water|air
• Decrease surface tension until certain critical concentration, and no effect afterwards: surfactants that form micelles

What complicates the effect is that a solute can exist in a different concentration at the surface of a solvent than in its bulk. This difference varies from one solute–solvent combination to another.Gibbs isotherm states that:Gamma = - frac{1}{RT} left( frac{partial gamma}{partial ln C} right)_{T,P}

• {{mvar|Γ}} is known as surface concentration, it represents excess of solute per unit area of the surface over what would be present if the bulk concentration prevailed all the way to the surface. It has units of mol/m2
• {{mvar|C}} is the concentration of the substance in the bulk solution.
• {{mvar|R}} is the gas constant and {{mvar|T}} the temperature

Certain assumptions are taken in its deduction, therefore Gibbs isotherm can only be applied to ideal (very dilute) solutions with two components.

Influence of particle size on vapor pressure

{{See also|Gibbs–Thomson effect}}The Clausius–Clapeyron relation leads to another equation also attributed to Kelvin, as the Kelvin equation. It explains why, because of surface tension, the vapor pressure for small droplets of liquid in suspension is greater than standard vapor pressure of that same liquid when the interface is flat. That is to say that when a liquid is forming small droplets, the equilibrium concentration of its vapor in its surroundings is greater. This arises because the pressure inside the droplet is greater than outside.P_mathrm{v}^mathrm{fog}=P_mathrm{v}^circ e^{V 2gamma/(RT r_mathrm{k})}

• {{math|Pv°}} is the standard vapor pressure for that liquid at that temperature and pressure.
• {{mvar|V}} is the molar volume.
• {{mvar|R}} is the gas constant
• {{math|rk}} is the Kelvin radius, the radius of the droplets.

The effect explains supersaturation of vapors. In the absence of nucleation sites, tiny droplets must form before they can evolve into larger droplets. This requires a vapor pressure many times the vapor pressure at the phase transition point.This equation is also used in catalyst chemistry to assess mesoporosity for solids.Ertl, G.; Knözinger, H. and Weitkamp, J. (1997). Handbook of heterogeneous catalysis, Vol. 2, p. 430. Wiley-VCH, Weinheim. {{ISBN|3-527-31241-2}}The effect can be viewed in terms of the average number of molecular neighbors of surface molecules (see diagram).The table shows some calculated values of this effect for water at different drop sizes:{| class="toccolours" border="1" style="float: center; margin: 0 0 1em 1em; border-collapse: collapse;"! style="text-align:center; background:#c0c0f0;" colspan="5"|{{math|{{sfrac|P|P0}}}} for water drops of different radii at STP style="text-align:center;" Droplet radius (nm)1000100101 style="text-align:center;" {{mathPP0}}}}> 1.001 style="text-align:center;"1.114 style="text-align:center;"| 2.95The effect becomes clear for very small drop sizes, as a drop of 1 nm radius has about 100 molecules inside, which is a quantity small enough to require a quantum mechanics analysis.

Methods of measurement

Because surface tension manifests itself in various effects, it offers a number of paths to its measurement. Which method is optimal depends upon the nature of the liquid being measured, the conditions under which its tension is to be measured, and the stability of its surface when it is deformed. An instrument that measures surface tension is called tensiometer.

• Du Noüy ring method: The traditional method used to measure surface or interfacial tension. Wetting properties of the surface or interface have little influence on this measuring technique. Maximum pull exerted on the ring by the surface is measured.
• Wilhelmy plate method: A universal method especially suited to check surface tension over long time intervals. A vertical plate of known perimeter is attached to a balance, and the force due to wetting is measured.
• Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter of a drop within a heavy phase is measured while both are rotated.
• Pendant drop method: Surface and interfacial tension can be measured by this technique, even at elevated temperatures and pressures. Geometry of a drop is analyzed optically. For pendant drops the maximum diameter and the ratio between this parameter and the diameter at the distance of the maximum diameter from the drop apex has been used to evaluate the size and shape parameters in order to determine surface tension.
• Bubble pressure method (Jaeger's method): A measurement technique for determining surface tension at short surface ages. Maximum pressure of each bubble is measured.
• Drop volume method: A method for determining interfacial tension as a function of interface age. Liquid of one density is pumped into a second liquid of a different density and time between drops produced is measured.
• Capillary rise method: The end of a capillary is immersed into the solution. The height at which the solution reaches inside the capillary is related to the surface tension by the equation discussed above.WEB,weblink Surface Tension (physics lecture notes), Calvert, James B, 2007-09-08, University of Denver, 2007-09-15,weblink" title="web.archive.org/web/20070915112348weblink">weblink live,
• Stalagmometric method: A method of weighting and reading a drop of liquid.
• Sessile drop method: A method for determining surface tension and density by placing a drop on a substrate and measuring the contact angle (see Sessile drop technique).WEB,weblink Sessile Drop Method, 2007-09-08, Dataphysics,weblink" title="web.archive.org/web/20070808082309weblink">weblink August 8, 2007,
• Du Noüy–Padday method: A minimized version of Du Noüy method uses a small diameter metal needle instead of a ring, in combination with a high sensitivity microbalance to record maximum pull. The advantage of this method is that very small sample volumes (down to few tens of microliters) can be measured with very high precision, without the need to correct for buoyancy (for a needle or rather, rod, with proper geometry). Further, the measurement can be performed very quickly, minimally in about 20 seconds.
• Vibrational frequency of levitated drops: The natural frequency of vibrational oscillations of magnetically levitated drops has been used to measure the surface tension of superfluid 4He. This value is estimated to be 0.375 dyn/cm at {{mvar|T}} = 0 K.JOURNAL, 10.1103/PhysRevB.66.214504, Surface tension of liquid 4He as measured using the vibration modes of a levitated drop, 2002, Vicente, C., Yao, W., Maris, H., Seidel, G., Physical Review B, 66, 21, 214504, 2002PhRvB..66u4504V,
• Resonant oscillations of spherical and hemispherical liquid drop: The technique is based on measuring the resonant frequency of spherical and hemispherical pendant droplets driven in oscillations by a modulated electric field. The surface tension and viscosity can be evaluated from the obtained resonant curves.JOURNAL, 10.1016/j.colsurfa.2013.12.013, 460, Droplet oscillations driven by an electric field, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 351–354, 2014, Zografov, Nikolay, JOURNAL, 10.1524/zpch.2013.0420, 227, 12, Electrically Driven Resonant Oscillations of Pendant Hemispherical Liquid Droplet and Possibility to Evaluate the Surface Tension in Real Time, Zeitschrift für Physikalische Chemie, 2013, Tankovsky, N., 1759–1766, 101722165, JOURNAL, 10.1524/zpch.2011.0074, 225, 4, Oscillations of a Hanging Liquid Drop, Driven by Interfacial Dielectric Force, Zeitschrift für Physikalische Chemie, 405–411, 2011, Tankovsky, Nikolay, 101625925,
• Drop-bounce method: This method is based on aerodynamic levitation with a split-able nozzle design. After dropping a stably levitated droplet onto a platform, the sample deforms and bounces back, oscillating in mid-air as it tries to minimize its surface area. Through this oscillation behavior, the liquid's surface tension and viscosity can be measured.JOURNAL, Sun, Yifan, Muta, Hiroaki, Ohishi, Yuji, Novel Method for Surface Tension Measurement: the Drop-Bounce Method, Microgravity Science and Technology, June 2021, 33, 3, 32, 10.1007/s12217-021-09883-7, 2021MicST..33...32S, free,

Values

Surface tension of various liquids in dyn/cm against airLange's Handbook of Chemistry (1967) 10th ed. pp 1661–1665 {{ISBN|0-07-016190-9}} (11th ed.)Mixture compositions denoted "%" are by mass dyn/cm is equivalent to the SI units of mN/m (millinewton per meter)">

Data table{| class"wikitable sortable" style"margin:0; text-align: right;"Surface tension of various liquids in dyn/cm against airLange's Handbook of Chemistry (1967) 10th ed. pp 1661–1665 {{ISBN|0-07-016190-9}} (11th ed.)Mixture compositions denoted "%" are by mass dyn/cm is equivalent to the SI units of mN/m (millinewton per meter)

! Liquid !! Temperature (°C)!! Surface tension, {{mvar|γ}}Acetic acid (data page)>Acetic acid 20 27.60| 40.68| 54.56Acetone (data page)>Acetone 20 23.70Blood >| 55.89 Diethyl ether (data page)>Diethyl ether 20 17.00Ethanol (data page)>Ethanol 20 22.27| 29.63| 46.03Glycerol (data page)>Glycerol 20 63.00Hexane (data page)>n-Hexane 20 18.40Hydrochloric acid 17.7 Molar solution>M aqueous solution 20 65.95Isopropanol (data page)>Isopropanol 20 21.70Superfluid helium-4>Liquid helium II −273 0.3710.1103/PHYSREV.163.200>TITLE=ON THE SURFACE TENSION OF LIQUID HELIUM IIVOLUME=163PAGES=200–205LAST1=BROUWERLAST2=PATHRIABIBCODE=1967PHRV..163..200B, Nitrogen>Liquid nitrogen −196 8.85Oxygen>Liquid oxygen −182 13.2Mercury (element)>Mercury 15 487.00Methanol (data page)>Methanol 20 22.60Silver chloride >JOURNAL=JOURNAL OF THE ELECTROCHEMICAL SOCIETYISSUE=3YEAR=1982FIRST1=ZFIRST2=WFIRST3=K, Sodium chloride/Calcium chloride (47/53 mole %) >VOLUME=56YEAR=1960FIRST1=CFIRST2=J, 10.1039/tf9605600840, Octane>n-Octane 20 21.80Sodium chloride 6.0 Molar solution>M aqueous solution 20 82.55Sucrose (55%) + water >| 76.45Water (data page)>Water 0 75.64| 71.97| 67.91| 58.85Toluene >| 27.73

Surface tension of water

The surface tension of pure liquid water in contact with its vapor has been given by IAPWSWEB,weblink Revised Release on Surface Tension of Ordinary Water Substance, International Association for the Properties of Water and Steam, June 2014, 2016-02-20, 2016-04-04,weblink" title="web.archive.org/web/20160404045530weblink">weblink live, asgamma_text{w} = 235.8left(1 - frac{T}{T_text{C}}right)^{1.256} left[1 - 0.625left(1 - frac{T}{T_text{C}}right)right]~text{mN/m},where both {{mvar|T}} and the critical temperature {{math|TC}} = 647.096 K are expressed in kelvins. The region of validity the entire vapor–liquid saturation curve, from the triple point (0.01 Â°C) to the critical point. It also provides reasonable results when extrapolated to metastable (supercooled) conditions, down to at least −25 Â°C. This formulation was originally adopted by IAPWS in 1976 and was adjusted in 1994 to conform to the International Temperature Scale of 1990.The uncertainty of this formulation is given over the full range of temperature by IAPWS. For temperatures below 100 Â°C, the uncertainty is ±0.5%.

Surface tension of seawater

Nayar et al.JOURNAL, 10.1063/1.4899037, J. Phys. Chem. Ref. Data, Surface tension of seawater, November 2014, 43, 4, 43103, 2014JPCRD..43d3103N, Nayar, K. G, Panchanathan, D, McKinley, G. H, Lienhard, J. H,weblink 1721.1/96884, free, 2018-04-20, 2022-09-22,weblink" title="web.archive.org/web/20220922033641weblink">weblink live, published reference data for the surface tension of seawater over the salinity range of {{nowrap|20 ≤ {{mvar|S}} ≤ 131 g/kg}} and a temperature range of {{nowrap|1 ≤ {{mvar|t}} ≤ 92 °C}} at atmospheric pressure. The range of temperature and salinity encompasses both the oceanographic range and the range of conditions encountered in thermal desalination technologies. The uncertainty of the measurements varied from 0.18 to 0.37 mN/m with the average uncertainty being 0.22 mN/m.Nayar et al. correlated the data with the following equation where {{math|γsw}} is the surface tension of seawater in mN/m, {{math|γw}} is the surface tension of water in mN/m, {{mvar|S}} is the reference salinityJOURNAL, Deep-Sea Research Part I, 55, 1, January 2008, 50, The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale, 2008DSRI...55...50M, 10.1016/j.dsr.2007.10.001, Millero, Frank J, Feistel, Rainer, Wright, Daniel G, McDougall, Trevor J, in g/kg, and {{mvar|t}} is temperature in degrees Celsius. The average absolute percentage deviation between measurements and the correlation was 0.19% while the maximum deviation is 0.60%.The International Association for the Properties of Water and Steam (IAPWS) has adopted this correlation as an international standard guideline.TECH REPORT,weblink Guideline on the Surface Tension of Seawater, IAPWS G14-19, International Association for the Properties of Water and Steam, October 2019, 2020-03-26, 2020-03-26,weblink" title="web.archive.org/web/20200326232003weblink">weblink live,

See also

{{Div col|colwidth=22em}}

• Anti-fog
• Capillary wave—short waves on a water surface, governed by surface tension and inertia
• Cheerio effect—the tendency for small wettable floating objects to attract one another.
• Cohesion
• Dimensionless numbers
  • Bond number or Eötvös number
  • Capillary number
  • Marangoni number
  • Weber number
• Dortmund Data Bank—contains experimental temperature-dependent surface tensions
• Electrodipping force
• Electrowetting
• Electrocapillarity
• Eötvös rule—a rule for predicting surface tension dependent on temperature
• Fluid pipe
• Hydrostatic equilibrium—the effect of gravity pulling matter into a round shape
• Interface (chemistry)
• Meniscus—surface curvature formed by a liquid in a container
• Mercury beating heart—a consequence of inhomogeneous surface tension
• Microfluidics
• Sessile drop technique
• Sow-Hsin Chen
• Specific surface energy—same as surface tension in isotropic materials.
• Spinning drop method
• Stalagmometric method
• Surface pressure
• Surface science
• Surface tension biomimetics
• Surface tension values
• Surfactants—substances which reduce surface tension.
• Szyszkowski equation—calculating surface tension of aqueous solutions
• Tears of wine—the surface tension induced phenomenon seen on the sides of glasses containing alcoholic beverages.
• Tolman length—leading term in correcting the surface tension for curved surfaces.
• Wetting and dewetting

{{Div col end}}

Explanatory notes

References

{{Reflist|colwidth=30em}}

External links

{{Commons}}

• "Why is surface tension parallel to the interface?". Physics Stack Exchange. Retrieved 2021-03-19.
• Berry, M V (1971-03-01). "The molecular mechanism of surface tension". Physics Education. 6 (2): 79–84. doi:10.1088/0031-9120/6/2/001. ISSN 0031-9120.
• Marchand, Antonin; Weijs, Joost H.; Snoeijer, Jacco H.; Andreotti, Bruno (2011-09-26). "Why is surface tension a force parallel to the interface?". American Journal of Physics. 79 (10): 999–1008. doi:10.1119/1.3619866. ISSN 0002-9505. arXiv:weblink
• On surface tension and interesting real-world cases
• Surface Tensions of Various Liquids
• Calculation of temperature-dependent surface tensions for some common components
• Surface tension calculator for aqueous solutions containing the ions H+, {{chem|NH|4|+}}, Na+, K+, Mg2+, Ca2+, {{chem|SO|4|2−}}, {{chem|NO|3|−}}, Cl−, {{chem|CO|3|2−}}, Br− and OH−.
• T. Proctor Hall (1893) New methods of measuring surface tension in liquids, Philosophical Magazine (series 5, 36: 385–415), link from Biodiversity Heritage Library.
• The Bubble Wall{{Dead link|date=March 2022 |bot=InternetArchiveBot |fix-attempted=yes }} (Audio slideshow from the National High Magnetic Field Laboratory explaining cohesion, surface tension and hydrogen bonds)
• C. Pfister: Interface Free Energy. Scholarpedia 2010 (from first principles of statistical mechanics)
• Surface and Interfacial Tension
• JOURNAL, Molten salts mixture surface tension, The Journal of Chemical Thermodynamics, 3, 2, 259–265, 10.1016/S0021-9614(71)80111-8, March 1971,

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