Surface tension

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Surface tension is the elastic tendency of the fluid surface which makes it obtain the most probable surface area. Surface tension allows insects (eg water spiders), usually denser than water, to float and step on the surface of the water.

At the air-liquid interface, surface tension results from greater attraction of molecules of liquid to each other (due to cohesion) compared to molecules in air (due to adhesion). The net effect is the inner force on its surface that causes the liquid to behave as if its surface is covered with a stretched elastic membrane. Thus, the surface becomes under pressure from unbalanced forces, which may be where the term "surface tension" originates. Because of the relatively high attractiveness of water molecules with each other through hydrogen bonds, water has a higher surface tension (72.8 millinewton per meter at 20 ° C) than most other liquids. Surface tension is an important factor in the phenomenon of capillarity.

The surface tension has a force dimension per unit length, or energy per unit area. Both are equivalent, but when referring to energy per unit area, it is common to use the term surface energy, which is a more general term in the sense that applies also to solids.

In materials science, surface tension is used either for surface tension or surface free energy.

Video Surface tension

Cause

Because of the cohesive force, a molecule is pulled evenly in all directions by adjacent molecules of liquid, resulting in a net force of zero. The molecules on the surface do not have the same molecules on all sides of them and are therefore drawn inward. This creates some internal pressure and forces the liquid surface to contract to a minimal area. The tensile forces that work between molecules of the same type are called cohesive forces while those working among molecules of different kinds are called adhesive forces. When the cohesive force is stronger than the strength of the adhesive, the liquid acquires the convex meniscus (like mercury in a glass container). On the other hand, when the strength of the adhesive is stronger, the liquid surface is bent upward (like water in a glass)

Surface tension is responsible for the liquid droplet form. Although easily deformed, water droplets tend to be drawn into a round shape by an imbalance in the cohesive force of the surface layer. In the absence of other forces, including gravity, drops of almost all the fluid will be roughly round. The spherical shape minimizes the "wall stress" required from the surface layer according to Laplace's law.

Another way to see the surface tension is in terms of energy. A molecule in contact with a neighbor is in a lower energy state than if it is alone (not in contact with a neighbor). The interior molecules have many neighbors they may have, but the neighboring boundary molecules are lost (compared to the interior molecules) and therefore have higher energy. For liquids to minimize their energy state, the number of higher energy limit molecules must be minimized. The number of boundary molecules reduced produces minimal surface area. As a result of surface minimization, the surface will assume the finest form it can perform (mathematical proof that the "fine" shape minimizes the surface area depending on the use of the Euler-Lagrange equation). Because the curvature of the surface shape produces a larger area, higher energy will also be generated. As a result, the surface will push back against any curvature in the same way as pushing the ball up will push back to minimize its gravitational potential energy.

Maps Surface tension

Surface tension effects

Water

Beberapa efek tegangan permukaan dapat dilihat dengan air biasa:

Surfaktan

Surface tension is seen in other common phenomena, especially when surfactants are used to lower them:

• Soap bubbles have a very large surface area with very little mass. The bubbles in pure water are unstable. The addition of surfactant, however, can have a stabilizing effect on the bubbles (see Marangoni effect). Note that the surfactant actually reduces the water surface tension by a factor of three or more.
• The emulsion is a colloidal type in which the surface tension plays a role. Small pieces of oil suspended in pure water will spontaneously assemble themselves into a much larger mass. But the presence of surfactants provides a reduction in surface tension, which allows the stability of minute droplets of oil in most of the water (or vice versa).

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Physics

Physical unit

Tegangan permukaan, diwakili oleh symbol ? (alternatif ? atau T ), diukur berlaku per satuan panjang. Satuan SI-nya adalah newton per meter tetapi satuan cgs dyne per sentimeter juga digunakan.

${\ displaystyle \ gamma = 1 ~ \ mathrm {\ frac {dyn} {cm}} = 1 ~ \ mathrm {\ frac {erg} {cm ^ {2}}} = 1 ~ \ mathrm {\ frac {mN} {m}} = 0.001 ~ \ mathrm {\ frac {N} {m}} = 0.001 ~ \ mathrm {\ frac {J} {m ^ { 2}}}} Â Â$

Pertumbuhan luas permukaan

Surface tension can be defined in terms of force or energy.

In terms of style: surface tension ? of the fluid is the force per unit length. In the illustration on the right, a rectangular frame, consisting of three movable (black) sides that form the "U" shape, and the fourth moving side (blue) that can slide to the right. The surface tension will pull the blue bar to the left; the F force required to hold the immobile side proportional to the length of L from the movable side. So the ratio of F / L depends only on the intrinsic nature of the liquid (composition, temperature, etc.), not on its geometry. For example, if the frame has a more complex shape, the ratio of F / L , with the L moveable length and F the force needed to stop it from sliding, found the same for all shapes. Therefore we define the surface tension as

${\ displaystyle \ gamma = {\ frac {1} {2}} {\ frac {F} {L}}.}$

The reason for 1 / 2 is that this movie has two sides, each of which contributes equally to compel; so the power contributed by one side is ? L = F / 2 .

In terms of energy: surface tension ? of the fluid is the ratio of fluid energy changes, and changes in the surface area of ​​the liquid (which causes energy changes). This can be easily related to the previous definition in terms of power: if F is the force needed to stop the side from start to the slide, then this is also a force that will keep the inner side circumstances slid at a constant speed (by Newton's Second Law). But if the side moves to the right (in the direction of force applied), the stretched surface area of ​​the liquid increases while the force employed in the liquid. This means that increasing the surface area increases the film's energy. Work done by style F in moving side by distance ? x is W = F ? x ; at the same time the total movie area is increased by ? A = 2 L ? x (factor 2 here because the liquid has two sides, two surfaces). So, multiplying the numerator and denominator ? = 1 / 2 F / L by ? x , we get it

${\ displaystyle \ gamma = {\ frac {F} {2L}} = {\ frac {F \ Delta x} {2L \ Delta x}} = {\ frac {W} {\ Delta A}}}$ .

This work W is, by ordinary argument, interpreted as stored as potential energy. As a result, surface tension can also be measured in SI systems as joules per square meter and in cgs systems as ergs per cm ² . Since the mechanical system tries to find the minimum potential energy state, the free liquid droplets naturally assume a sphere shape, which has a minimum surface area for a given volume. Equivalent energy measurements per unit area of ​​force per unit length can be proven by dimensional analysis.

Curvature and surface pressure

If no force works normally on a tightened surface, the surface should remain flat. But if the pressure on one side of the surface is different from the pressure on the other side, the difference in pressure times the surface area produces a normal force. In order for surface tension to force force force due to pressure, the surface must be curved. This diagram shows how the surface curvature of a small patch of surface leads to a net surface force force component acting normally to the center of the patch. When all forces are balanced, the resulting equation is known as the Young-Laplace equation:

${\ displaystyle \ Delta p = \ gamma \ left {{frac {1} {R_ {x}}} {\ frac {1} {R_ { y}}} \ right)}$

Where:

• ? p is the pressure difference, known as Laplace pressure.
• ? is the surface tension.
• R _x and R _y are the radius of curvature in each axis parallel to the surface.

Quantity in parentheses on the right side is actually (twice) the average curvature of the surface (depending on normalization). The solution to this equation determines the shape of water droplets, waterlogging, menisci, soap bubbles, and all other forms determined by the surface tension (such as the shape of the impression created by the water strider on the surface of the pool). The table below shows how the internal pressure of water droplets increases with decreasing radius. Because it is not too small, the effect becomes subtle, but the pressure difference becomes very large when the drop size is close to the size of the molecule. (In the boundary of one molecule, the concept becomes meaningless.)

Floating objects

When an object is placed in a liquid, its weight spills the surface, and if the surface tension and downward force become equal from the balanced by the force of the voltage the surfaces on both sides F _s , each of which is parallel to the water level at the points where it contacts the object. Note that small movements in the body can cause the object to sink. Since the contact angle reduces the surface tension reduces the horizontal component of two arrows F _s in the opposite direction, so they cancel each other, but the component vertical pointing in the same direction and hence adding up balancing _w . The surface of the object should not be moistened for this to occur, and the weight must be low enough for the surface tension to support it.

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{         F                                    w                                      =         2                 F                                     s                                       cos                 ?                  <=>                          ?                                    w                                                A                                    w                                       L          g         =         2         ?          L          cos                 ?               {\ displaystyle F _ {\ mathrm {w}} = 2F _ {\ mathrm {s}} \ cos \ theta \ quad \ Leftrightarrow \ quad \ rho _ {mathrm {w}} A _ {mathrm {w}} Lg = 2 \ gamma L \ cos \ theta}  Â}

Liquid surface

To find the minimal surface shape that is limited by some random-shaped frames using tight mathematical methods can be a daunting task. But by framing the frame of the wire and dipping it into the soap solution, a local minimal surface will appear in the resulting soap film in seconds.

The reason for this is that the pressure difference at the fluid interface is proportional to the average curvature, as seen in the Young-Laplace equation. For open soap film, the zero pressure difference, then the average curvature is zero, and the minimum surface has a mean curvature of zero.

Contact corner

The surface of any liquid is the interface between the liquid and several other mediums. The upper surface of the pond, for example, is the interface between pond water and air. Surface tension, then, is not a property of the liquid itself, but a property of a liquid interface with another medium. If a liquid is in a container, then next to a liquid/air interface on its upper surface, there is also an interface between the liquid and the container wall. Surface tension between liquid and air is usually different (greater than) the surface tension with the container wall. 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, ? , which is the angle tangent to the surface with solid surface. Note that the angle is measured through the liquid , as shown in the diagram above. The diagram on the right shows two examples. Voltage force is shown for air-fluid interface, liquid-solid interface, and air-solid interface. The example on the left is where the difference between solid-water and solid-air solids, ? _ls - ? _sa , less than the liquid surface tension, ? _la , but remain positive, it is

_{          ?                                     l             a                                      & gt;                  ?                                     l              s                                      -                  ?                                     s             a                                      & gt;         0               {\ displaystyle \ gamma _ {\ mathrm {la}} & gt; \ gamma _ {\ mathrm {ls}} - \ gamma _ {\ mathrm {sa}} & gt; 0}  Â}

Dalam diagram, gaya vertikal dan horizontal harus dibatalkan tepat pada titik kontak, yang dikenal sebagai ekuilibrium. Komponen horizontal f _la dibatalkan oleh kekuatan perekat, f _A .

${\ displaystyle f _ {\ mathrm {A}} = f _ {\ mathrm {la}} \ sin \ theta}  ÂÂ$

Namun, kekuatan keseimbangan yang lebih jitu adalah dalam arah vertikal. Vertical component f _the harus benar-benar membatalkan gaya, f _ls .

${\ displaystyle f _ {\ mathrm {ls}} -f _ {\ mathrm {sa}} = - f _ {\ mathrm {la}} \ cos \ theta} Â Â$

Karena kekuatannya sebanding dengan tegangan permukaannya masing-masing, kita juga memiliki:

$Â\; ÂÂ\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â{?}_{Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Âl\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Âs\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â}Â\; Â\; Â\; Â\; Â\; Â\; Â-Â\; Â\; Â\; Â\; Â\; Â{?}_{Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Âs\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Âa\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â}Â\; Â\; Â\; Â\; Â\; Â\; Â=Â\; Â\; Â\; Â\; Â\; Â\; Â-Â\; Â\; Â\; Â\; Â\; Â{?}_{Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Âl\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Âa\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â}Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂcosÂ\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â?Â\; Â\; Â\; Â\; Â}Â\; Â\; Â\{\backslash \; displaystyle\; \backslash \; gamma\; \_\; \{\backslash \; mathrm\; \{ls\}\}\; -\; \backslash \; gamma\; \{\{mathrm\; \{sa\}\}\; =\; -\; \backslash \; gamma\; \_\; \{\backslash \; mathrm\; \{la\; \}\}\; \backslash \; cos\; \backslash \; theta\}\; Â\; Â$

Where

• ? _ls is a liquid-solid surface tension,
• ? _la is the liquid surface tension,
• ? _sa is the solid-water surface tension,
• ? is the contact angle, where the concave meniscus has a contact angle less than 90 ° and the convex meniscus has a contact angle greater than 90 °.

This means that despite the difference between the solid-surface and solid-air tension surfaces, ? _ls - ? _sa , it is difficult to measure directly, it can be inferred from the air-liquid surface tension, ? _la , and the equilibrium contact angle, ? , which is a function of contact angles that move forward and easily disappear (see main article contact angle).

Hubungan yang sama ini ada dalam diagram di sebelah kanan. Tetapi dalam hal ini kita melihat bahwa karena sudut kontak kurang dari 90 °, perbedaan tegangan permukaan cair-padat/padat-udara harus negatif:

${\ displaystyle \ gamma {{mathrm {la}} & gt; 0 & gt; \ gam \ {\ mathrm {ls}} - \ gamma {\ mathrm {sa}}} Â Â$

Sudut kontak khusus

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

Kasus khusus lainnya adalah di mana sudut kontak tepat 180 °. Air dengan Teflon yang disiapkan khusus mendekati ini. Sudut kontak 180 ° terjadi ketika tegangan permukaan cair-padat persis sama dengan tegangan permukaan cairan-udara.

${\ displaystyle \ gamma _ {\ mathrm {la}} = \ gamma _ {\ mathrm {ls}} - \ gamma _ {\ mathrm {sa}} & gt; 0 \ qquad \ theta = 180 ^ {\ circ}}  ÂÂ$

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Metode pengukuran

Since the surface tension manifests itself in various effects, it offers a number of pathways for measurement. Which method is optimal depends on the nature of the fluid being measured, the conditions under which the tension should be measured, and the stability of the surface when it is deformed.

• Du NoÃÆ'¼y ring method: The traditional method used to measure surface tension or interface. The wetting properties of surfaces or interfaces have little effect on these measurement techniques. The maximum attraction given on the ring by the surface is measured.
• Du NoÃÆ'¼y-Padday Method: The reduced version of Du NoÃÆ'¼y method uses small diameter metal needles instead of rings, combined with high sensitivity microbalance to record maximum pull. The advantage of this method is that very small sample volumes (up to a few tens of microliters) can be measured with very high precision, without the need for correcting buoyancy (for needles or more precisely, rods, with proper geometry). Furthermore, the measurement can be done very quickly, at least in about 20 seconds. The first commercial multichannel tensiometer [CMCeeker] was recently built on this principle.
• Wilhelmy plate method: A universal method that is particularly suitable for checking surface tension in long time intervals. The vertical plates of the perimeter are known to be attached to the equilibrium, and forces caused by wetting are measured.
• Spinning drop method: This technique is ideal for measuring low interface voltages. The diameter of the drop in the weight phase is measured when both are rotated.
• Lost pendant method: Surface tension and interface can be measured by this technique, even at high temperature and pressure. The drop geometry is optically analyzed. For the pendant the maximum diameter and ratio between this parameter and the diameter at the maximum diameter distance of the apex drop has been used to evaluate the size and shape of the parameters to determine the surface tension.
• Bubble pressure method (Jaeger method): A measurement technique for determining surface tension at short surface ages. The maximum pressure of each bubble is measured.
• Volume decrease method: Method for determining interface stress as a function of interface age. The liquid from one density is pumped into the second liquid of different densities and the time between the resulting droplets is measured.
• Capillary Increase Method: The end of the capillary is inserted into the solution. The height at which the solution reaches inside the capillaries is related to the surface tension with the equations discussed below.
• Stalagmometric Method: Method of weighting and reading a drop of fluid.
• Sessile degradation method: Method for determining surface tension and density by placing a drop on the substrate and measuring the contact angle (see Sessile drop technique).
• The vibrational frequency of the raised drop: The natural frequency of the folded magnetic droplet vibration oscillation has been used to measure the superfluid surface tension of ⁴ He. This value is estimated at 0.375Ã, dyn/cm at T = 0Ã, K.
• Resonance oscillation of spherical and spherical fluid drops: This technique is based on measurement of the resonance frequency of the ball pendant pendant and the hemisphere being driven in oscillation by a modulated electric field. Surface tension and viscosity can be evaluated from the obtained resonance curve.

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Effects

Liquid in vertical tube

The old-style mercury barometer consists of a vertical glass tube of about 1 cm diameter partially filled with mercury, and with a vacuum (called Torricelli vacuum) in unallocated volume (see diagram on the right). Note that the mercury level in the center of the tube is higher than the edge, making the top surface of the mercury-shaped dome. The center of mass of the entire mercury column will be slightly lower if the top surface of mercury is flat across the tubular cross section. But the dome-shaped top provides little surface area to the entire mass of mercury. Again two effects combine to minimize the total potential energy. This kind of surface is known as the convex meniscus.

We consider the entire surface area of ​​the mass of mercury, including the surfaces that come into contact with glass, since mercury is not attached to the glass at all. So the surface tension of mercury works across the entire surface area, including where it comes in contact with glass. If it was not glass, the tube was made of copper, the situation would be very different. Mercury aggressively obeys copper. So in a copper tube, the mercury level at the center of the tube will be lower than at the tip (ie, the concave meniscus). In situations where liquid holds the wall of the container, we assume that part of the surface area of ​​the fluid in contact with the container has a negative surface tension . The liquid then works to maximize the contact surface area. So in this case increasing the area in contact with the container is reduced rather than increasing the potential energy. The decrease was sufficient to offset the increase in potential energy associated with lifting the fluid near the container wall.

Jika tabung cukup sempit dan adhesi cair ke dindingnya cukup kuat, tegangan permukaan dapat menarik cairan ke atas tabung dalam fenomena yang dikenal sebagai kapiler. Ketinggian yang dicabut kolom diberikan oleh hukum Jurin:

${\ displaystyle h = {\ frac {2 \ gamma {{mathrm {la}} \ cos \ theta} {\ rho gr}}} Â Â$

Where

• h is the height of the removed fluid,
• ? _la is the liquid surface tension,
• ? is the density of the liquid,
• r is the capillary radius,
• g is acceleration due to gravity,
• ? is the contact angle described above. If ? greater than 90Ã, Â °, just as mercury is in a glass container, the liquid will be more depressed than lifted.

Inundation on the surface

Pouring mercury into a sheet of horizontal sheet glass produces puddles that have a clear thickness. The puddle will spread only to the point where it is slightly under half a centimeter thick, and no thinner. Again this is caused by the action of the strong surface tension of mercury. The liquid mass is flat because it brings as much mercury to the highest possible level, but the surface tension, at the same time, acts to reduce the total surface area. The result of the compromise is a puddle with almost fixed thickness.

The same surface tension demonstration can be performed with water, lime or even salt water, but only on surfaces made of a substance not watched by water. Candles are such substances. Water poured onto a smooth, flat, horizontal wax surface, say a waxed glass sheet, will behave similarly to mercury poured into a glass.

Ketebalan kubangan cairan pada permukaan yang sudut kontaknya 180 Â ° diberikan oleh:

${\ displaystyle h = 2 {\ sqrt {\ frac {\ gamma} {g \ rho}}}} Â Â$

Where

• h is the depth of the puddle in centimeters or meters.
• ? is the liquid surface tension in dynamics per centimeter or newton per meter.
• g is acceleration due to gravity and equals 980 cm/s ² or 9.8 m/s ²
• ? is the fluid density in grams per cubic centimeter or kilogram per cubic meter

Kenyataannya, ketebalan genangan sedikit lebih rendah dari yang diprediksi oleh rumus di atas karena sangat sedikit permukaan yang memiliki sudut kontak 180 Â ° dengan cairan apa pun. Ketika sudut kontak kurang dari 180 Â °, ketebalannya diberikan oleh:

${\ displaystyle h = {\ sqrt {\ frac {2 \ gamma {{mathrm {la}} \ kiri (1- \ cos \ theta \ right )} {g \ rho}}}.} Â Â$

For mercury on glass, ? _Hg = 487 dyn/cm, ? _Hg = 13.5 g/cm ³ and ? = 140Ã, Â °, giving h _Hg = 0.36 cm. For water on paraffin at 25 ° C, ? = 72 dyn/cm, ? = 1.0 g/cm ³ , and ? = 107Ã, Â ° giving h _{H 2 O} = 0.44 cm.

The formula also predicts that when the contact angle is 0 Â °, the liquid will spread to the micro-thin layer above the surface. Such surfaces are said to be fully moistened by liquids.

Breakup of streams into droplets

In everyday life we ​​all observe that the flow of water emerging from the faucet will break into droplets, no matter how smooth the flow flows from the faucet. This is due to a phenomenon called Plateau-Rayleigh instability, which is entirely a consequence of the effects of surface tension.

This explanation of instability begins with a small perturbation in the river. It's always there, no matter how smooth the flow is. If the disorder is resolved into a sinusoidal component, we find that some components grow over time while others decay over time. Among those that grew over time, some grew at a faster rate than others. Whether the component decays or grows, and how quickly it grows fully is a function of the wave number (the size of how many peaks and troughs per centimeter) and the radius of the original cylinder flow.

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Thermodynamics

Thermodynamic theory of surface tension

J.W. Gibbs developed the thermodynamic theory of capillarity based on the idea of ​​surface discontinuity. He introduces and studies the thermodynamics of two-dimensional objects - the surface. This surface has area, mass, entropy, energy, and free energy. As stated above, the mechanical work required to increase the surface area of ​​ A is dW = ? dA . Therefore at constant temperature and pressure, the surface tension is equal to Gibbs free energy per surface area:

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â?Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â=Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ÂÂÂÂ ( Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ...
                ?                  G        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,
                ?                 A        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,                       Â )                            Â¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯         Â mo moan,      Â¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯         Â mo moan,      Â ·                             < {\ displaystyle \ gamma = left ({\ frac {\ partial G} {\ partial A}} \ right) _ {T, P, n} }  Â}

where G is Gibbs free energy and A is the area.

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

From here it is easy to understand why the decrease in the surface area of ​​the liquid mass is always spontaneous (span> G & lt; 0 ), provided it is not combined with other energies. change. Therefore to increase the surface area, a certain amount of energy must be added.

Energi bebas Gibbs didefinisikan oleh persamaan G = H - TS , di mana H adalah entalpi dan S adalah entropi. Berdasarkan ini dan fakta bahwa tegangan permukaan adalah energi bebas Gibbs per satuan luas, adalah mungkin untuk mendapatkan ekspresi berikut untuk entropi per satuan luas:

${\ displaystyle \ left ({\ frac {\ parsial \ gamma} {\ parsial T}} \ kanan) _ {A, P} = - S ^ {A}}  ÂÂ$

The Kelvin equation for the surface appears by rearranging the previous equation. It states that the surface enthalpy or surface energy (different from surface free energy) depe

Source of the article : Wikipedia