Surface tension
Overview
 
Surface tension is a property of the surface of a liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

 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 (e.g. water striders) to run on the water surface. This property is caused by cohesion
Cohesion (chemistry)
Cohesion or cohesive attraction or cohesive force is the action or property of like molecules sticking together, being mutually attractive...

 of similar molecules, and is responsible for many of the behaviors of liquids.

Surface tension has the dimension
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

 of force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

 per unit length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

, or of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 per unit area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

.
Encyclopedia
Surface tension is a property of the surface of a liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

 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 (e.g. water striders) to run on the water surface. This property is caused by cohesion
Cohesion (chemistry)
Cohesion or cohesive attraction or cohesive force is the action or property of like molecules sticking together, being mutually attractive...

 of similar molecules, and is responsible for many of the behaviors of liquids.

Surface tension has the dimension
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

 of force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

 per unit length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

, or of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 per unit area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy
Surface energy
Surface energy quantifies the disruption of intermolecular bonds that occur when a surface is created. In the physics of solids, surfaces must be intrinsically less energetically favorable than the bulk of a material, otherwise there would be a driving force for surfaces to be created, removing...

—which is a more general term in the sense that it applies also to solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

s and not just liquids.

In materials science
Materials science
Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This scientific field investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It incorporates...

, surface tension is used for either surface stress
Surface stress
Surface stress was first defined by Josiah Willard Gibbs as the amount of reversible work per unit area needed to elastically stretch a pre-existing surface. A similar term called “surface free energy”, which represents the excess free energy per unit area needed to create a new surface, is easily...

 or surface free energy
Surface energy
Surface energy quantifies the disruption of intermolecular bonds that occur when a surface is created. In the physics of solids, surfaces must be intrinsically less energetically favorable than the bulk of a material, otherwise there would be a driving force for surfaces to be created, removing...

.

Cause

The cohesive forces among the liquid molecules are responsible for this phenomenon of surface tension. In the bulk of the liquid, each molecule is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have other molecules on all sides of them and therefore are pulled inwards. This creates some internal pressure
Internal pressure
Internal pressure is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature. It has the same dimensions as pressure, the SI unit of which is 1 pascal.Internal pressure is usually given the symbol \pi_T...

 and forces liquid surfaces to contract to the minimal area.

Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the cohesive forces of the surface layer. In the absence of other forces, including gravity, drops of virtually all liquids would be perfectly spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law
Young–Laplace equation
In physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although usage on the...

.

Another way to view it is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone (not in contact with a neighbor). The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules) and therefore have a higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized quantity of boundary molecules results in a minimized surface area.

As a result of surface area minimization, a surface will assume the smoothest shape it can (mathematical proof that "smooth" shapes minimize surface area relies on use of the Euler–Lagrange equation). Since any curvature in the surface shape results in greater area, a higher energy will also result. Consequently the surface will push back against any curvature in much the same way as a ball pushed uphill will push back to minimize its gravitational potential energy.

Water

Several effects of surface tension can be seen with ordinary water:

A. Beading of rain water on the surface of a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape, because a sphere has the smallest possible surface area to volume ratio.

B. Formation of drops
Drop (liquid)
A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the lower end of a tube or other surface boundary, producing a hanging drop called a pendant drop...

 occurs when a mass of liquid is stretched. The animation shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer bind it to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water were running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.

C. Floatation of objects denser than water occurs when the object is nonwettable and its weight is small enough to be borne by the forces arising from surface tension. For example, water striders use surface tension to walk on the surface of a pond. The surface of the water behaves like an elastic film: the insect's feet cause indentations in the water's surface, increasing its surface area.
D. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called "interface tension", but its physics are the same.

E. Tears of wine
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...

 is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol
Ethanol
Ethanol, also called ethyl alcohol, pure alcohol, grain alcohol, or drinking alcohol, is a volatile, flammable, colorless liquid. It is a psychoactive drug and one of the oldest recreational drugs. Best known as the type of alcohol found in alcoholic beverages, it is also used in thermometers, as a...

; it is induced by a combination of surface tension modification of water by ethanol
Ethanol
Ethanol, also called ethyl alcohol, pure alcohol, grain alcohol, or drinking alcohol, is a volatile, flammable, colorless liquid. It is a psychoactive drug and one of the oldest recreational drugs. Best known as the type of alcohol found in alcoholic beverages, it is also used in thermometers, as a...

 together with ethanol evaporating faster than water.

Surfactants

Surface tension is visible in other common phenomena, especially when surfactant
Surfactant
Surfactants are compounds that lower the surface tension of a liquid, the interfacial tension between two liquids, or that between a liquid and a solid...

s are used to decrease it:
  • Soap bubble
    Soap bubble
    A soap bubble is a thin film of soapy water enclosing air, that forms a hollow sphere with an iridescent surface. Soap bubbles usually last for only a few seconds before bursting, either on their own or on contact with another object. They are often used for children's enjoyment, but they are also...

    s have very large surface areas with very little mass. Bubbles in pure water are unstable. The addition of surfactants, however, can have a stabilizing effect on the bubbles (see Marangoni effect
    Marangoni effect
    The Marangoni effect is the mass transfer along an interface between two fluids due to surface tension gradient...

    ). Notice that surfactants actually reduce the surface tension of water by a factor of three or more.

  • Emulsion
    Emulsion
    An emulsion is a mixture of two or more liquids that are normally immiscible . Emulsions are part of a more general class of two-phase systems of matter called colloids. Although the terms colloid and emulsion are sometimes used interchangeably, emulsion is used when both the dispersed and the...

    s are a type of solution in which surface tension plays a role. Tiny fragments of oil suspended in pure water will spontaneously assemble themselves into much larger masses. But the presence of a surfactant provides a decrease in surface tension, which permits stability of minute droplets of oil in the bulk of water (or vice versa).

Two definitions

Surface tension, represented by the symbol γ
Gamma
Gamma is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. It was derived from the Phoenician letter Gimel . Letters that arose from Gamma include the Roman C and G and the Cyrillic letters Ge Г and Ghe Ґ.-Greek:In Ancient Greek, gamma represented a...

 is defined as the force along a line of unit length, where the force is parallel to the surface but perpendicular to the line. One way to picture this is to imagine a flat soap film bounded on one side by a taut thread of length, L. The thread will be pulled toward the interior of the film by a force equal to 2L (the factor of 2 is because the soap film has two sides, hence two surfaces). Surface tension is therefore measured in force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

s per unit length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

. Its SI
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

 unit is newton per meter but the cgs unit of dyne
Dyne
In physics, the dyne is a unit of force specified in the centimetre-gram-second system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µN...

 per cm is also used. One dyn/cm corresponds to 0.001 N/m.

An equivalent definition, one that is useful in 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...

, is work done per unit area. As such, in order to increase the surface area of a mass of liquid by an amount, δA, a quantity of work, δA, is needed. This work is stored as potential energy. Consequently surface tension can be also measured in SI system as joules per square meter and in the cgs
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...

 system as erg
Erg
An erg is the unit of energy and mechanical work in the centimetre-gram-second system of units, symbol "erg". Its name is derived from the Greek ergon, meaning "work"....

s per cm2. Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape, which has the minimum surface area for a given volume.

The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

.

Surface curvature and pressure

If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side, the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be curved. The diagram shows how surface curvature of a tiny patch of surface leads to a net component of surface tension forces acting normal to the center of the patch. When all the forces are balanced, the resulting equation is known as the Young–Laplace equation
Young–Laplace equation
In physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although usage on the...

:


where:
  • Δp is the pressure difference.
  • is surface tension.
  • Rx and Ry are radii of curvature in each of the axes that are parallel to the surface.


The quantity in parentheses on the right hand side is in fact (twice) the mean curvature
Mean curvature
In mathematics, the mean curvature H of a surface S is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space....

 of the surface (depending on normalisation).

Solutions to this equation determine the shape of water drops, puddles, menisci, soap bubbles, and all other shapes determined by surface tension (such as the shape of the impressions that a water strider's feet make on the surface of a pond).

The table below shows how the internal pressure of a water droplet increases with decreasing radius. For not very small drops the effect is subtle, but the pressure difference becomes enormous when the drop sizes approach the molecular size. (In the limit of a single molecule the concept becomes meaningless.)
Δp for water drops of different radii at STP
Standard conditions for temperature and pressure
Standard condition for temperature and pressure are standard sets of conditions for experimental measurements established to allow comparisons to be made between different sets of data...

Droplet radius 1 mm 0.1 mm 1 μm
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

10 nm
Δp (atm
Atmosphere (unit)
The standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of pressure. For practical purposes it has been replaced by the bar which is 105 Pa...

)
0.0014 0.0144 1.436 143.6


Liquid surface

To find the shape of the minimal surface
Minimal surface
In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....

 bounded by some arbitrary shaped frame using strictly mathematical means can be a daunting task. Yet by fashioning the frame out of wire and dipping it in soap-solution, a locally minimal surface will appear in the resulting soap-film within seconds.

The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature
Mean curvature
In mathematics, the mean curvature H of a surface S is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space....

, as seen in the Young-Laplace equation. For an open soap film, the pressure difference is zero, hence the mean curvature is zero, and minimal surfaces have the property of zero mean curvature.

Contact angles

The surface of any liquid is an interface between that liquid and some other medium.In a mercury barometer, the upper liquid surface is an interface between the liquid and a vacuum containing some molecules of evaporated liquid. The top surface of a pond, for example, is an interface between the pond water and the air. Surface tension, then, is not a property of the liquid alone, but a property of the liquid's interface with another medium. If a liquid is in a container, then besides the liquid/air interface at its top surface, there is also an interface between the liquid and the walls of the container. The surface tension between the liquid and air is usually different (greater than) its surface tension with the walls of a container. And where the two surfaces meet, their geometry must be such that all forces balance.


Where the two surfaces meet, they form a contact angle
Contact angle
The contact angle is the angle at which a liquid/vapor interface meets a solid surface. The contact angle is specific for any given system and is determined by the interactions across the three interfaces. Most often the concept is illustrated with a small liquid droplet resting on a flat...

, , which is the angle the tangent to the surface makes with the solid surface. The diagram to the right shows two examples. Tension forces are shown for the liquid-air interface, the liquid-solid interface, and the solid-air interface. The example on the left is where the difference between the liquid-solid and solid-air surface tension, , is less than the liquid-air surface tension, , but is nevertheless positive, that is


In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point. The horizontal component of is canceled by the adhesive force, .


The more telling balance of forces, though, is in the vertical direction. The vertical component of must exactly cancel the force, .

Liquid Solid Contact angle
water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

cellpadding="0" cellspacing="0" border="0">
soda-lime glass
lead glass
fused quartz
ethanol
Ethanol
Ethanol, also called ethyl alcohol, pure alcohol, grain alcohol, or drinking alcohol, is a volatile, flammable, colorless liquid. It is a psychoactive drug and one of the oldest recreational drugs. Best known as the type of alcohol found in alcoholic beverages, it is also used in thermometers, as a...

diethyl ether
Diethyl ether
Diethyl ether, also known as ethyl ether, simply ether, or ethoxyethane, is an organic compound in the ether class with the formula . It is a colorless, highly volatile flammable liquid with a characteristic odor...

carbon tetrachloride
Carbon tetrachloride
Carbon tetrachloride, also known by many other names is the organic compound with the formula CCl4. It was formerly widely used in fire extinguishers, as a precursor to refrigerants, and as a cleaning agent...

glycerol
Glycerol
Glycerol is a simple polyol compound. It is a colorless, odorless, viscous liquid that is widely used in pharmaceutical formulations. Glycerol has three hydroxyl groups that are responsible for its solubility in water and its hygroscopic nature. The glycerol backbone is central to all lipids...

acetic acid
Acetic acid
Acetic acid is an organic compound with the chemical formula CH3CO2H . It is a colourless liquid that when undiluted is also called glacial acetic acid. Acetic acid is the main component of vinegar , and has a distinctive sour taste and pungent smell...

water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

paraffin wax 107° silver 90° methyl iodide
Iodomethane
Methyl iodide, also called iodomethane, and commonly abbreviated "MeI", is the chemical compound with the formula CH3I. It is a dense, colorless, volatile liquid. In terms of chemical structure, it is related to methane by replacement of one hydrogen atom by an atom of iodine. It is naturally...

soda-lime glass 29° lead glass 30° fused quartz 33° mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

soda-lime glass 140° Some liquid-solid contact angles

Since the forces are in direct proportion to their respective surface tensions, we also have:


where
  • is the liquid-solid surface tension,
  • is the liquid-air surface tension,
  • is the solid-air surface tension,
  • is the contact angle, where a concave meniscus
    Meniscus
    The meniscus is the curve in the upper surface of a liquid close to the surface of the container or another object, caused by surface tension. It can be either convex or concave. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the material of the...

     has contact angle less than 90° and a convex meniscus has contact angle of greater than 90°.


This means that although the difference between the liquid-solid and solid-air surface tension, , is difficult to measure directly, it can be inferred from the easily measured contact angle, , if the liquid-air surface tension, , is known.

This same relationship exists in the diagram on the right. But in this case we see that because the contact angle is less than 90°, the liquid-solid/solid-air surface tension difference must be negative:

Special contact angles

Observe that in the special case of a water-silver interface where the contact angle is equal to 90°, the liquid-solid/solid-air surface tension difference is exactly zero.

Another special case is where the contact angle is exactly 180°. Water with specially prepared Teflon
Polytetrafluoroethylene
Polytetrafluoroethylene is a synthetic fluoropolymer of tetrafluoroethylene that finds numerous applications. PTFE is most well known by the DuPont brand name Teflon....

 approaches this. Contact angle of 180° occurs when the liquid-solid surface tension is exactly equal to the liquid-air surface tension.


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.
  • Du Noüy Ring method
    Du Noüy ring method
    The du Noüy ring method is one technique by which the surface tension of a liquid can be measured. The method involves slowly lifting a ring, often made of platinum, from the surface of a liquid...

    : 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.

  • Du Noüy-Padday method
    Du Noüy-Padday method
    The Du Noüy Padday method is a minimized version of the Du Noüy rod replacing a large platinum ring with a thin rod that is used to measure equilibrium surface tension or dynamic surface tension at an air–liquid interface. In this method, the rod is oriented perpendicular to the interface, and the...

    : 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
    Buoyancy
    In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...

     (for a needle or rather, rod, with proper geometry). Further, the measurement can be performed very quickly, minimally in about 20 seconds. First commercial multichannel tensiometers [CMCeeker] were recently built based on this principle.

  • Wilhelmy plate method
    Wilhelmy plate
    A Wilhelmy plate is a thin plate that is used to measure equilibrium surface or interfacial tension at an air–liquid or liquid–liquid interface. In this method, the plate is oriented perpendicular to the interface, and the force exerted on it is measured...

    : 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
    Spinning Drop Method
    Spinning drop method is one of the methods that is used to measure interfacial tension. Basically, measurements are carried out in a rotating horizontal tube which contains a dense fluid. One drop of a less dense liquid is placed inside the fluid...

    : 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 details, see Drop
    Drop (liquid)
    A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the lower end of a tube or other surface boundary, producing a hanging drop called a pendant drop...

    .

  • Bubble pressure method
    Bubble Pressure Method
    In physics, the maximum bubble pressure method, or in short bubble measure method, is a technique to measure the surface tension of a liquid, with surfactants.- Background :...

     (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 below.

  • Stalagmometric method
    Stalagmometric method
    The stalagmometric method is one of the most common methods for measuring surface tension. The principle is to measure the weight of the drops of the fluid falling from the capillary glass tube, and then calculate the surface tension of the specific fluid which we are interested in. We know the...

    : A method of weighting and reading a drop of liquid.

  • Sessile drop method: A method for determining surface tension and density
    Density
    The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

     by placing a drop on a substrate and measuring the contact angle
    Contact angle
    The contact angle is the angle at which a liquid/vapor interface meets a solid surface. The contact angle is specific for any given system and is determined by the interactions across the three interfaces. Most often the concept is illustrated with a small liquid droplet resting on a flat...

     (see Sessile drop technique).

  • 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 T = 0 K.

Liquid in a vertical tube

An old style mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

 barometer
Barometer
A barometer is a scientific instrument used in meteorology to measure atmospheric pressure. Pressure tendency can forecast short term changes in the weather...

 consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum (called Torricelli
Evangelista Torricelli
Evangelista Torricelli was an Italian physicist and mathematician, best known for his invention of the barometer.-Biography:Evangelista Torricelli was born in Faenza, part of the Papal States...

's vacuum) in the unfilled volume (see diagram to the right). Notice that the mercury level at the center of the tube is higher than at the edges, making the upper surface of the mercury dome-shaped. The center of mass of the entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire crossection of the tube. But the dome-shaped top gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is known as a convex meniscus.

The reason we consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass, is because mercury does not adhere at all to glass. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass, the tube were made out of copper, the situation would be very different. Mercury aggressively adheres to copper. So in a copper tube, the level of mercury at the center of the tube will be lower than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls of its container, we consider the part of the fluid's surface area that is in contact with the container to have negative surface tension. The fluid then works to maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That decrease is enough to compensate for the increased potential energy associated with lifting the fluid near the walls of the container.

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon known as capillary action
Capillary action
Capillary action, or capilarity, is the ability of a liquid to flow against gravity where liquid spontanously rise in a narrow space such as between the hair of a paint-brush, in a thin tube, or in porous material such as paper or in some non-porous material such as liquified carbon fiber, or in a...

. The height the column is lifted to is given by:


where
  • is the height the liquid is lifted,
  • is the liquid-air surface tension,
  • is the density of the liquid,
  • is the radius of the capillary,
  • is the acceleration due to gravity,
  • is the angle of contact described above. If is greater than 90°, as with mercury in a glass container, the liquid will be depressed rather than lifted.


Puddles on a surface

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness. The puddle will spread out only to the point where it is a little under half a centimeter thick, and no thinner. Again this is due to the action of mercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as possible, but the surface tension, at the same time, is acting to reduce the total surface area. The result is the compromise of a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, lime water or even saline, but only on a surface made of a substance that the water does not adhere to. Wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface, say a waxed sheet of glass, will behave similarly to the mercury poured onto glass.

The thickness of a puddle of liquid on a surface whose contact angle is 180° is given by:


where
is the depth of the puddle in centimeters or meters.
is the surface tension of the liquid in dynes per centimeter or newtons per meter.
is the acceleration due to gravity and is equal to 980 cm/s2 or 9.8 m/s2
is the density of the liquid in grams per cubic centimeter or kilograms per cubic meter


In reality, the thicknesses of the puddles will be slightly less than what is predicted by the above formula because very few surfaces have a contact angle of 180° with any liquid. When the contact angle is less than 180°, the thickness is given by:


For mercury on glass, γHg = 487 dyn/cm, ρHg = 13.5 g/cm3 and θ = 140°, which gives hHg = 0.36 cm. For water on paraffin at 25 °C, γ = 72 dyn/cm, ρ = 1.0 g/cm3, and θ = 107° which gives hH2O = 0.44 cm.

The formula also predicts that when the contact angle is 0°, the liquid will spread out into a micro-thin layer over the surface. Such a surface is said to be fully wettable by the liquid.

The breakup of streams into drops

In day-to-day life we all 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
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...

 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.

Thermodynamics

As stated above, the mechanical work needed to increase a surface is . Hence at constant temperature and pressure, surface tension equals Gibbs free energy
Gibbs free energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...

 per surface area:


where is Gibbs free energy and is the area.

Thermodynamics requires that all spontaneous changes of state are accompanied by a decrease in Gibbs free energy.

From this it is easy to understand why decreasing the surface area of a mass of liquid is always spontaneous
Spontaneous process
A spontaneous process is the time-evolution of a system in which it releases free energy and moves to a lower, more thermodynamically stable energy state...

 (), 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 free energy is defined by the equation, , where is enthalpy
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...

 and is entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

. Based upon this and the fact that surface tension is Gibbs free energy per unit area, it is possible to obtain the following expression for entropy per unit area:


Kelvin's
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...

 Equation for surfaces arises by rearranging the previous equations. It states that surface enthalpy or surface energy
Surface energy
Surface energy quantifies the disruption of intermolecular bonds that occur when a surface is created. In the physics of solids, surfaces must be intrinsically less energetically favorable than the bulk of a material, otherwise there would be a driving force for surfaces to be created, removing...

 (different from surface free energy
Specific surface energy
specific surface energy, also known as surface free energy, is the amount of increase of free energy when the area of surface increases by every unit area. It can be calculated using Stefan's formula. Specific surface energy is the same as surface tension for isotropic materials, but different...

) depends both on surface tension and its derivative with temperature at constant pressure by the relationship.

Thermodynamics of soap bubble

The pressure inside an ideal (one surface) soap bubble can be derived from thermodynamic free energy considerations. At constant temperature and particle number, , the differential Helmholtz free energy is given by


where is the difference in pressure inside and outside of the bubble, and is the surface tension. In equilibrium, , and so,
.


For a spherical bubble, the volume and surface area are given simply by
,

and
.


Substituting these relations into the previous expression, we find
,


which is equivalent to the Young-Laplace equation when Rx = Ry. For real soap bubbles, the pressure is doubled due to the presence of two interfaces, one inside and one outside.

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
Eötvös rule
The Eötvös rule, named after the Hungarian physicist Loránd Eötvös enables the prediction of the surface tension of an arbitrary liquid pure substance at all temperatures. The density, molar mass and the critical temperature of the liquid have to be known. At the critical point the surface...

. There are only empirical equations to relate surface tension and temperature:
  • Eötvös:

Here V is the molar volume of a substance, TC is the critical temperature and k is a constant valid for almost all substances. A typical value is k = 2.1 x 10−7 [J K−1 mol−2/3]. For water one can further use V = 18 ml/mol and TC = 374°C.

A variant on Eötvös is described by Ramay and Shields:


where the temperature offset of 6 kelvins provides the formula with a better fit to reality at lower temperatures.
  • Guggenheim-Katayama:



is a constant for each liquid and n is an empirical factor, whose value is 11/9 for organic liquids. This equation was also proposed by van der Waals
Johannes Diderik van der Waals
Johannes Diderik van der Waals was a Dutch theoretical physicist and thermodynamicist famous for his work on an equation of state for gases and liquids....

, who further proposed that could be given by the expression, , where is a universal constant for all liquids, and is the critical pressure of the liquid (although later experiments found 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 their structure:
  • Little or no effect, for example sugar
    Sugar
    Sugar is a class of edible crystalline carbohydrates, mainly sucrose, lactose, and fructose, characterized by a sweet flavor.Sucrose in its refined form primarily comes from sugar cane and sugar beet...

  • Increase surface tension, inorganic salts
  • Decrease surface tension progressively, alcohols
  • Decrease surface tension and, once a minimum is reached, no more effect: surfactants


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
Gibbs isotherm
The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension...

 states that:     
  • 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

  • is the concentration of the substance in the bulk solution.

  • is the gas constant
    Gas constant
    The gas constant is a physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy The gas constant (also known as the molar, universal,...

     and the temperature
    Temperature
    Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...



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

The Clausius-Clapeyron relation
Clausius-Clapeyron relation
The Clausius–Clapeyron relation, named after Rudolf Clausius and Benoît Paul Émile Clapeyron, who defined it sometime after 1834, is a way of characterizing a discontinuous phase transition between two phases of matter. On a pressure–temperature diagram, the line separating the two phases is known...

 leads to another equation also attributed to Kelvin. It explains why, because of surface tension, the vapor pressure
Vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure of a vapor in thermodynamic equilibrium with its condensed phases in a closed system. All liquids have a tendency to evaporate, and some solids can sublimate into a gaseous form...

 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.


  • is the standard vapor pressure for that liquid at that temperature and pressure.
  • is the molar volume.
  • is the gas constant
    Gas constant
    The gas constant is a physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy The gas constant (also known as the molar, universal,...



is the Kelvin radius, the radius of the droplets.

The effect explains supersaturation
Supersaturation
The term supersaturation refers to a solution that contains more of the dissolved material than could be dissolved by the solvent under normal circumstances...

 of vapors. In the absence of nucleation
Nucleation
Nucleation is the extremely localized budding of a distinct thermodynamic phase. Some examples of phases that may form by way of nucleation in liquids are gaseous bubbles, crystals or glassy regions. Creation of liquid droplets in saturated vapor is also characterized by 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
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

 point.

This equation is also used in catalyst chemistry to assess mesoporosity
Mesoporous material
A mesoporous material is a material containing pores with diameters between 2 and 50 nm.Porous materials are classified into several kinds by their size...

 for solids.

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:
P/P0 for water drops of different radii at STP
Standard conditions for temperature and pressure
Standard condition for temperature and pressure are standard sets of conditions for experimental measurements established to allow comparisons to be made between different sets of data...

Droplet radius (nm) 1000 100 10 1
P/P0 1.001 1.011 1.114 2.95


The 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
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 analysis.

Data table

style="background:#C0C0F0; border: 1px solid #AAA" |Surface tension of various liquids in dyn
Dyne
In physics, the dyne is a unit of force specified in the centimetre-gram-second system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µN...

/cm against air
Mixture %'s are by mass
dyn/cm is equivalent to the SI units of mN/m (milli-Newton per meter)
Liquid Temperature °C Surface tension, γ
Acetic acid
Acetic acid (data page)
- Material Safety Data Sheet : The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet for this chemical from a reliable source and follow its directions.***...

 
20 27.6
Acetic acid (40.1%) + Water 30 40.68
Acetic acid (10.0%) + Water 30 54.56
Acetone
Acetone (data page)
- Material Safety Data Sheet : The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet for this chemical from a reliable source and follow its directions.***...

 
20 23.7
Diethyl ether
Diethyl ether (data page)
- Material Safety Data Sheet : The handling of this chemical may incur notable safety precautions. It is highly recommended that you seek the Material Safety Datasheet for this chemical from a reliable source such as , and follow its directions...

 
20 17.0
Ethanol
Ethanol (data page)
- Material Safety Data Sheet : The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet for this chemical from a reliable source and follow its directions....

 
20 22.27
Ethanol (40%) + Water 25 29.63
Ethanol (11.1%) + Water 25 46.03
Glycerol
Glycerol (data page)
- Material Safety Data Sheet : The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet for this chemical from a reliable source and follow its directions.**...

 
20 63
n-Hexane
Hexane (data page)
- Material Safety Data Sheet : The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet for this chemical from a reliable source and follow its directions.***....

 
20 18.4
Hydrochloric acid
Hydrochloric acid
Hydrochloric acid is a solution of hydrogen chloride in water, that is a highly corrosive, strong mineral acid with many industrial uses. It is found naturally in gastric acid....

 17.7M aqueous solution
20 65.95
Isopropanol  20 21.7
Mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

 
15 487
Methanol
Methanol (data page)
- Material Safety Data Sheet : The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet for this chemical from a reliable source such as , and follow its directions...

 
20 22.6
n-Octane
Octane
Octane is a hydrocarbon and an alkane with the chemical formula C8H18, and the condensed structural formula CH36CH3. Octane has many structural isomers that differ by the amount and location of branching in the carbon chain...

 
20 21.8
Sodium chloride
Sodium chloride
Sodium chloride, also known as salt, common salt, table salt or halite, is an inorganic compound with the formula NaCl. Sodium chloride is the salt most responsible for the salinity of the ocean and of the extracellular fluid of many multicellular organisms...

 6.0M aqueous solution
20 82.55
Sucrose
Sucrose
Sucrose is the organic compound commonly known as table sugar and sometimes called saccharose. A white, odorless, crystalline powder with a sweet taste, it is best known for its role in human nutrition. The molecule is a disaccharide composed of glucose and fructose with the molecular formula...

 (55%) + water
20 76.45
Water
Water (data page)
This page provides supplementary data of the properties of water.Further comprehensive authoritative data can be found at the page on thermophysical properties of fluids.-Structure and properties:-Thermodynamic properties:-Liquid physical properties:...

 
0 75.64
Water 25 71.97
Water 50 67.91
Water 100 58.85

See also

  • Anti-fog
    Anti-fog
    Anti-fog agents, also known as anti-fogging agents and treatments, are chemicals which prevent the condensation of water in the form of small droplets on a surface which resemble fog...

  • Capillary wave
    Capillary wave
    A capillary wave is a wave traveling along the phase boundary of a fluid, whose dynamics are dominated by the effects of surface tension.Capillary waves are common in nature and the home, and are often referred to as ripples...

    —short waves on a water surface, governed by surface tension and inertia
  • Cheerio effect
    Cheerio effect
    In fluid mechanics, the Cheerios effect is the tendency for small wettable floating objects to attract one another. An example of the Cheerios effect is the phenomenon whereby breakfast cereal tends to clump together or cling to the sides of a bowl of milk. It is named for the breakfast cereal...

    —the tendency for small wettable floating objects to attract one another.
  • Cohesion
    Cohesion (chemistry)
    Cohesion or cohesive attraction or cohesive force is the action or property of like molecules sticking together, being mutually attractive...

  • Dimensionless numbers
    • Bond number
    • Capillary number
      Capillary number
      In fluid dynamics, the capillary number represents the relative effect of viscous forces versus surface tension acting across an interface between a liquid and a gas, or between two immiscible liquids...

    • 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...

    • Weber number
      Weber number
      The Weber number is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It can be thought of as a measure of the relative importance of the...

  • Dortmund Data Bank
    Dortmund Data Bank
    The Dortmund Data Bank is a factual data bank for thermodynamic and thermophysical data. Its main usage is the data supply for process simulation where experimental data are the basis for the design, analysis, synthesis, and optimization of chemical processes...

    —contains experimental temperature-dependent surface tensions.
  • Electrodipping force
    Electrodipping force
    The electrodipping force is a force proposed to explain the observed attraction that arises among small colloidal particles attached to an interface between immiscible liquids. The particles are held there by surface tension. Normally the surface tension does not in itself give rise to an...

  • Electrowetting
    Electrowetting
    Electrowetting is the modification of the wetting properties of a surface with an applied electric field.-History:...

  • Eötvös rule
    Eötvös rule
    The Eötvös rule, named after the Hungarian physicist Loránd Eötvös enables the prediction of the surface tension of an arbitrary liquid pure substance at all temperatures. The density, molar mass and the critical temperature of the liquid have to be known. At the critical point the surface...

    —a rule for predicting surface tension dependent on temperature.
  • Fluid pipe
  • Hydrostatic equilibrium
    Hydrostatic equilibrium
    Hydrostatic equilibrium or hydrostatic balance is the condition in fluid mechanics where a volume of a fluid is at rest or at constant velocity. This occurs when compression due to gravity is balanced by a pressure gradient force...

    —the effect of gravity pulling matter into a round shape.
  • Meniscus
    Meniscus
    The meniscus is the curve in the upper surface of a liquid close to the surface of the container or another object, caused by surface tension. It can be either convex or concave. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the material of the...

    —surface curvature formed by a liquid in a container.
  • Mercury beating heart
    Mercury beating heart
    The mercury beating heart is an electrochemical redox reaction between the elements mercury, iron and chromium. The reaction causes a blob of mercury in water to oscillate....

    —a consequence of inhomogeneous surface tension.
  • Microfluidics
    Microfluidics
    Microfluidics deals with the behavior, precise control and manipulation of fluids that are geometrically constrained to a small, typically sub-millimeter, scale.Typically, micro means one of the following features:* small volumes...

  • Sessile drop technique
  • Specific surface energy
    Specific surface energy
    specific surface energy, also known as surface free energy, is the amount of increase of free energy when the area of surface increases by every unit area. It can be calculated using Stefan's formula. Specific surface energy is the same as surface tension for isotropic materials, but different...

    —same as surface tension in isotropic materials.
  • Spinning drop method
    Spinning Drop Method
    Spinning drop method is one of the methods that is used to measure interfacial tension. Basically, measurements are carried out in a rotating horizontal tube which contains a dense fluid. One drop of a less dense liquid is placed inside the fluid...

  • Stalagmometric method
    Stalagmometric method
    The stalagmometric method is one of the most common methods for measuring surface tension. The principle is to measure the weight of the drops of the fluid falling from the capillary glass tube, and then calculate the surface tension of the specific fluid which we are interested in. We know the...

  • Surface tension values
    Surface tension values
    Surface tension values for some interfaces at the indicated temperatures. Note that the SI units millinewtons per meter are equivalent to the cgs units, dynes per centimetre ....

  • Surfactant
    Surfactant
    Surfactants are compounds that lower the surface tension of a liquid, the interfacial tension between two liquids, or that between a liquid and a solid...

    s—substances which reduce surface tension.
  • Tears of wine
    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...

    —the surface tension induced phenomenon seen on the sides of glasses containing alcoholic beverages.
  • Tolman length
    Tolman length
    The Tolman length \delta measures the extent by which the surface tension of a small liquid drop deviates from its planar value...

    —leading term in correcting the surface tension for curved surfaces.
  • Wetting
    Wetting
    Wetting is the ability of a liquid to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. The degree of wetting is determined by a force balance between adhesive and cohesive forces.Wetting is important in the bonding or adherence of...

     and dewetting
    Dewetting
    In fluid mechanics, dewetting is one of the processes that can occur at a solid–liquid or liquid–liquid interface. Generally, dewetting describes the rupture of a thin liquid film on the substrate and the formation of droplets. The opposite process—spreading of a liquid on a substrate—is called...



External links

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