Surface tension

The surface tension is the one occurring as a result of molecular forces phenomenon in liquids to keep the surface small. The surface of a liquid behaves like a stretched elastic film. This effect is, for example, the reason that water forms droplets, and helps that some insects can walk on water or a razor blade on water "floats".

A surface tension (Formula symbol: σ, γ ) is also sometimes referred to the interfacial tension. It is measured in the SI units kg / s ², equivalent to N / m.

• 5.1 bracket method
• 5.2 Measurement with the capillary
• 5.3 Other Methods

Importance

The surface tension is a pulling force is localized at the surface of a liquid and its direction of action is parallel to the liquid surface. Thus, a liquid surface is always under tension. A liquid surface can be compared to a stretched film from all directions, although the surface tension of a much lower force than the force which is necessary to stretch a film.

The surface tension of a liquid surface imparts special properties. This allows objects to float on a water surface, where their weight is not sufficient to overcome the surface tension. Clearly this is when, for example, puts a paper clip on a water surface. The surface tension as a force parallel to the liquid surface spanning this and thus carries the paper clip. This effect is also exploited by living organisms such as the water strider to walk on the surface of water can.

The surface tension is the reason that liquids assume a spherical shape, unless other forces act on them. A good example of this are liquid droplets are suspended in space almost no forces. To explain let us suppose a fluid whose shape is not spherical. The surface tension reaches parallel to the liquid surface and compensates curvatures. If other forces acting on a drop of liquid, so its shape deviates from the spherical. An example of this are liquid drops on a solid surface, where additionally attractive forces between the solid and liquid act (adhesion). The shape of the drop differs even more from the spherical from and wets the solid surface, the higher the adhesion between the solid and liquid.

Another example of the effect of the surface tension is the hexagonal shape of the honeycomb cells of the honey bees. The cells are first built around beeswax. The material is but by the ruling in the hive temperatures after ( flows ), forming planar interfaces ( minimal surfaces ) between the individual cells.

Physical background

Mechanical definition

There are two definitions that are consistent with the surface tension. On the one hand by the mechanical definition of the surface tension is a force per unit length and the thermodynamic after the surface tension is an energy per unit area. The mechanical definition can be explained by a bracket with the width by a liquid film is clamped. When the surface of the fluid film is increased by a force parallel to the surface by the amount, the work must be done. The surface tension is then defined as a work which is necessary to create a unit area. Thus arises. Accordingly, it is in the surface tension by a force per unit length which is parallel to the liquid surface.

The correctness of the idea of the surface tension as a force parallel to the surface is manifested in many measurement methods and effects such as the bracket method, the capillarity or the contact angle.

Thermodynamic definition

Thermodynamic presentation of surface tension as the energy per area of the image is due to the symmetry of the Flüssigkeitsoberlfäche liquid molecules is disturbed. The absence of liquid molecules are vertically offset to the liquid surface and thus "missing" binding energy must by positive energy. To increase the surface area of a liquid is required to power, wherein the surface tension is defined as the energy which is required for the liquid surface to a unit area to increase. Thus which follows the analogy of the notion " lack of binding energy " is shown to the mechanical definition.

This vivid interpretation, however, is not yet sufficient for the surface tension to define thermodynamically. To do this, one starts from the change in the Gibbs free energy at a constant temperature and constant pressure, which is described by equation, wherein. The enthalpy, the temperature and the entropy of features.

One can rewrite this equation by substituting the definition of enthalpy and takes into account that applies.

For the change in the internal energy is used, is the work performed. For the amount of heat. It follows:

The expression for the work can be decomposed into a term for the volume of work and not expansive work.

At constant temperature and pressure corresponds to the change in the free energy of the non- expansive work. This expression can now be associated with the surface tension. If only labor is expended to increase the surface of a liquid as this corresponds to the expression. Since the surface tension needs to be defined as energy per unit area or the surface of the liquid will Also taken into account. Thus follows:

Surface tension is therefore thermodynamically defined as the partial derivative of the free enthalpy after the surface at a constant temperature and constant pressure.

Molecular theory of surface tension

The idea of the lack of liquid molecules at the surface intuitively led to the assumption that the surface tension is a force perpendicular to Flüssikeitsoberlfäche. However, this does not match the mechanical definition of the surface tension. One must consider that act both attractive and repulsive forces on a molecule within a liquid to bring the mechanical definition in this case in accordance with the thermodynamic. While in a solid locally either attractive or repulsive forces as the particles are located at fixed locations, the molecules are mobile in a liquid. The distances between the liquid molecules can change and thus repulsive and attractive forces can act on a fluid particle. This fact can be illustrated in a Lennard -Jones potential. This generally describes the potential between two uncharged particles as a function of their distance. Advised the particles at short distances in contact so they repel each other while they get dressed at greater distances. While fixed in a solid state, the distance between two particles can be of the change in a liquid due to the thermal movement which enables attractive and repulsive forces of a liquid molecule. In the picture on the right is a schematic representation of a Lennard- Jones potential is shown that explains the forces between liquid molecules. Do the liquid molecules contact so they repel (orange area ) while they dress for large distances (blue area ). In a liquid, the distances between the particles are constantly changing due to the thermal motion, which is represented by the black double-headed arrow in the figure. Thus, acting on a liquid molecule both attractive and repulsive forces.

Can be interpreted, the repulsive forces as the contact forces. Due to this, their effect can be so considered isotropic in space as independent of direction. The attractive forces within a liquid act for longer distances, are due to the structure of the molecules and can be considered depending on the direction in space, are thus considered anisotropic.

The density of the liquid changes at the phase boundary between liquid and gas phase by leaps and bounds in the range of a few molecular lengths until it remains constant at the value of the liquid inside. This causes the repulsive forces in the liquid until they reach the constant value of the liquid inside quickly increases at the surface and that the increase in all directions is the same size due to the isotropic nature of the repulsive forces. To further explain the picture is right in which the forces are illustrated on a liquid molecule on the surface and in the interior. At the Flüssigkeitsoberlfläche the symmetry is disturbed, ie the molecules there are in the vertical direction no neighboring molecules. Thus acting in the vertical direction only from the bottom repulsive forces ( gray arrow ) on the molecules. The repulsive forces in the vertical direction by attractive forces (orange arrow) In order to preserve the balance of power balanced. In the horizontal direction, that is parallel to the surface, this is not necessary, as the symmetry is undisturbed. This means that act in the horizontal direction on all sides repulsive forces on the liquid molecules at the surface. In addition to the repulsive forces and attractive forces acting in the horizontal direction. However, these are not necessary in order to preserve the balance of power and therefore can and due to their anisotropic nature in its amount greater than the repulsive forces be. This means that at the liquid surface in the horizontal direction, the attracting forces act on the liquid molecules are greater than the repelling forces. In the liquid inside the attractive and repulsive forces on a molecule the same size.

In order to understand the surface tension as a force parallel to the surface further, it is illustrative to divide the liquid into two halves, as it is shown in the right picture. There you'll see a dotted and a non- dotted half, these only serve to mark the two parts. Considering the forces exerted by the non- dotted part of the dotted portion of the liquid. a ) First you put the dividing line between the liquid halves parallel to Flüssigkeitsoberlfläche. In the direction of the liquid inside the density increases, hence the repulsive forces (gray) are larger on the dotted part. These are offset by attractive forces (orange). b. ) If you put the dividing line between the halves in a vertical direction so you can turn the repulsive forces acting on the draw dotted part. These are due to their isotropic nature in its amount equal to the vertical direction. However, the attractive forces on the dotted part are not isotropic in nature and can be larger in magnitude than the repulsive forces. It is also evident that this difference decreases the further one progresses into the liquid inside. After only a few molecular lengths attractive and repulsive forces balance out in the horizontal direction, since the density increases in the direction of the liquid inside. c. ) The non- dotted part of the liquid exerts an attractive force on the dotted part of the decreases in the direction of the liquid inside.

In summary it can be said that in the range of a few molecular lengths, the density of the liquid surface (red curve on the right) will change until it reaches the constant value of the liquid inside. This has the result that a pulling force acts on the liquid surface in the horizontal direction. The blue curve in the image on the right describes the difference between attractive and repulsive force exerted by the non- dotted part of the liquid on the dotted portion in the horizontal direction. Match the surface tension, and is in range of a few molecular diameters located on the surface.

Dependencies

• Applies water from the value at 20 ° C and the desired temperature T, the following approximate equation:

• In a drop of liquid, there is, due to the surface tension of an increased pressure, as well as in the interior of a soap bubble. The pressure increase in the drop of liquid is described by the Young-Laplace equation
• Upon formation of liquid particles of condensation nuclei of the curvature effect occurs. It can be shown that on the curved surfaces of the resulting liquid drops of a higher saturated vapor pressure occurs as compared to a flat surface.
• Surface active agents such as surfactants put down the surface tension. Their effect can be described by a π the surface tension opposite lateral pressure. π is no pressure, but also has the same unit as the surface tension.
• The adjacent air layer is saturated by the vapor of the liquid. The penetration of other vapors from the outside can significantly change the surface tension.
• The surface tension is temperature dependent and increases with increasing temperature in general. At the critical point, it is zero. The temperature dependence is described by the Eötvössche rule; already indicated above equation is applicable for water special case of this rule.

Values

In mN / m = 10 -3N / m

Water, a relatively high surface tension (see also pressure water tables ), only the mercury is much higher.

Measurement

One can measure the surface tension, for example, with the help of the ring ( Lecomte De Nouy ), plate ( Wilhelmy ) or Frame method ( Lenard ), with a tensiometer or by the capillary.

Also can be measured through an optical evaluation of the lying or hanging drops, and so determine the surface tension of the liquid.

Ironing method

Wherein the bracket method (also known as pull-off ), a strap with a soldered- in extremely fine wire (usually platinum ) suspended in the liquid so that it just immersed in the liquid and is wetted by it. With a precision spring balance the tension is then gradually increased to the bracket. The wire is then withdrawn from the liquid, and pulling a liquid film. At a certain point, this film breaks off.

Pulling the strap work is done against the surface tension. From the maximum pulling force on the strap, before the liquid film is torn off, the dimensions of the bow and the density of the liquid, the surface tension can then be calculated.

Liquids such as ethanol and the wire lengths of 2 - 3 cm at a radius of 0.1 mm, the expected value for the composition in the two to three digit milligram range. So there are very precise scales necessary. At a measurement uncertainty of the scale of 5 mg and a measurement of the wire to 1 micron exactly the maximum error of the final result is an 8 to 12 %.

Measurement with the capillary

In this measurement method one takes advantage of the capillary, so that liquids rise in thin tubes upwards. You need a container (such as a cell) and a very thin capillary. This is then simply placed into the liquid and the height of rise is measured.

Since the liquid theoretically infinitely long will it take to reach their Full Time, considering the first liquid in the capillary (about using a syringe ) up and then letting it drop again. The surface tension can then be read directly from the riser height when the density of the liquid and the capillary radius are known. Since the measurement is quite difficult, you take disposable micropipettes and measures their length. Since the volume is known, the inner radius can thus be calculated.

Water reaches in capillaries having a radius of 0.2 mm, heights of rise of up to 7 cm. For the exact measurement as possible the height of rise, for example, is a cathetometer. If the density of the liquid exactly known and can read the riser height to the nearest 0.1 mm, the fault is in the low single-digit percentage range.

Other methods

• Du- Nouy ring method: classical method for measuring the interfacial tension and surface tension. Not critical, even in difficult wet conditions. Measures the force a raised ring from the liquid lamella.
• Wilhelmy plate method: universal method especially suited for surface tension measurements over a longer time range. Measures the force that results from the wetting of a vertically suspended plate.
• Contact angle measurement: Is also shed light on the wettability of a substance. About the Young's equation can be calculated from the cosine of the contact angle of the surface tension.
• Spinning drop method: For the determination of interfacial tensions. Particularly suitable for low to extremely low measuring ranges. The diameter is measured of a rotating drop in the heavy phase.
• Pendant drop method: suitable for surface and interfacial tension measurements. Measurement capability even under extreme pressures and temperatures. Optical measuring the drop shape. Size of the drops dripping from a capillary tube is proportional to the surface tension.
• Sessile drop method: determination of surface and interfacial tension from the profile of a sessile droplet on a substrate. In the past, popular method for testing of liquid metals and alloys, since the measurement is relatively easy to achieve at high temperatures and / or extreme pressure using this method.
• Bubble Pressure Method suitable for the metrological detection of the dynamic surface tension (measured as a function of the surface age ). Standard measurement methods are the maximum pressure method and differential pressure method.
• Drop volume method: the superior method for the dynamic measurement of interfacial tensions. The rate of the number of drops in the shares a given volume of liquid.
• Test inks method: one in the industry (eg in the bonding of self-adhesive films ) on plastics used test. On the surface to be tested a colored liquid ( "ink" ) is applied with a defined surface tension with a brush. If the surface is wetted by the ink ( ie the brush stroke remains for > 3 seconds exist without contract ), the surface tension of the surface under test is equal to or greater than that of the test ink. On the other hand pulls the brush stroke within three seconds together, the surface tension of the tested surface is smaller than that of the test ink.
• Expanding / Oscillating Drop Method (EDM / ODM): Method for detecting the oberflächenrheologischen properties of liquids. Describes the dependence of surface tension on the degree and the speed of the surface area of a drop, which is either rapidly expanded and then is stopped (EDM ), or a sinusoidally oscillating oscillation subject (ODM). Using this measurement technique, the foam stability and emulsion stability can be described.
• Method with a mixture of Ethylenglycolmonoethyleter and formamide. Both liquids are mixed in a certain ratio to each other. This gives a defined dyne level to the surface tension determination. The components of this mixture by means of a tensiometer.
• Stalagmometer method is based on the drop shape.

Historical

The concept of surface tension was first used in 1629 by Niccolo Cabeo and clarified in 1751 by Johann Andreas Segner of. On the theory in 1805 by Thomas Young, in 1806 by Pierre -Simon Laplace, Siméon Denis Poisson in 1830 by (see also Young-Laplace equation, Young's equation) and from 1842 to 1868 by Joseph Plateau of value was contributed.