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49-401: At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion ) than to the molecules in the air (due to adhesion ). There are two primary mechanisms in play. One is an inward force on the surface molecules causing the liquid to contract. Second is a tangential force parallel to the surface of the liquid. This tangential force

98-430: A = γ l s − γ s a > 0 θ = 180 ∘ {\displaystyle \gamma _{\mathrm {la} }=\gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }>0\qquad \theta =180^{\circ }} An old style mercury barometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with

147-446: A glass flask is a good example of the effects of the ratio between cohesive and adhesive forces. Because of its high cohesion and low adhesion to the glass, mercury does not spread out to cover the bottom of the flask, and if enough is placed in the flask to cover the bottom, it exhibits a strongly convex meniscus, whereas the meniscus of water is concave . Mercury will not wet the glass, unlike water and many other liquids , and if

196-477: A "solid-like" state upon which light-weight or low-density materials can be placed. Water , for example, is strongly cohesive as each molecule may make four hydrogen bonds to other water molecules in a tetrahedral configuration. This results in a relatively strong Coulomb force between molecules. In simple terms, the polarity (a state in which a molecule is oppositely charged on its poles) of water molecules allows them to be attracted to each other. The polarity

245-401: 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 centimetre 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

294-441: A liquid is the force per unit length. In the illustration on the right, the rectangular frame, composed of three unmovable sides (black) that form a "U" shape, and a fourth movable side (blue) that can slide to the right. Surface tension will pull the blue bar to the left; the force F required to hold the movable side is proportional to the length L of the immobile side. Thus the ratio ⁠ F / L ⁠ depends only on

343-511: A spherical shape by the imbalance in cohesive forces of the surface layer. In the absence of other forces, drops of virtually all liquids would be approximately spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law . Another way to view surface tension is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone. The interior molecules have as many neighbors as they can possibly have, but

392-450: A vacuum (called Torricelli '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 cross-section of the tube. But the dome-shaped top gives slightly less surface area to

441-407: 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.) When an object is placed on a liquid, its weight F w depresses the surface, and if surface tension and downward force become equal then it

490-406: Is balanced by the surface tension forces on either side F s , which are each parallel to the water's surface at the points where it contacts the object. Notice that small movement in the body may cause the object to sink. As the angle of contact decreases, surface tension decreases. The horizontal components of the two F s arrows point in opposite directions, so they cancel each other, but

539-412: Is common to use the term surface energy , which is a more general term in the sense that it applies also to solids . In materials science , surface tension is used for either surface stress or surface energy . Due to the cohesive forces , a molecule located away from the surface is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at

SECTION 10

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588-791: Is doing work on the liquid. This means that increasing the surface area increases the energy of the film. The work done by the force F in moving the side by distance Δ x is W = F Δ x ; at the same time the total area of the film increases by Δ A = 2 L Δ x (the factor of 2 is here because the liquid has two sides, two surfaces). Thus, multiplying both the numerator and the denominator of γ = ⁠ 1 / 2 ⁠ ⁠ F / L ⁠ by Δ x , we get γ = F 2 L = F Δ x 2 L Δ x = W Δ A . {\displaystyle \gamma ={\frac {F}{2L}}={\frac {F\Delta x}{2L\Delta x}}={\frac {W}{\Delta A}}.} This work W is, by

637-408: Is due to the electronegativity of the atom of oxygen: oxygen is more electronegative than the atoms of hydrogen, so the electrons they share through the covalent bonds are more often close to oxygen rather than hydrogen. These are called polar covalent bonds, covalent bonds between atoms that thus become oppositely charged. In the case of a water molecule, the hydrogen atoms carry positive charges while

686-399: Is generally referred to as the surface tension. The net effect is the liquid behaves as if its surface were covered with a stretched elastic membrane. But this analogy must not be taken too far as the tension in an elastic membrane is dependent on the amount of deformation of the membrane while surface tension is an inherent property of the liquid – air or liquid – vapour interface. Because of

735-400: Is in contact with the glass. If instead of glass, the tube was 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

784-427: Is in the vertical direction. The vertical component of f la must exactly cancel the difference of the forces along the solid surface, f ls − f sa . f l s − f s a = − f l a cos ⁡ θ {\displaystyle f_{\mathrm {ls} }-f_{\mathrm {sa} }=-f_{\mathrm {la} }\cos \theta } Since

833-454: Is the action or property of like molecules sticking together, being mutually attractive. It is an intrinsic property of a substance that is caused by the shape and structure of its molecules, which makes the distribution of surrounding electrons irregular when molecules get close to one another, creating electrical attraction that can maintain a macroscopic structure such as a water drop . Cohesion allows for surface tension , creating

882-407: Is visible in other common phenomena, especially when surfactants are used to decrease it: 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,

931-465: Is where the difference between the liquid–solid and solid–air surface tension, γ ls − γ sa , is less than the liquid–air surface tension, γ la , but is nevertheless positive, that is γ l a > γ l s − γ s a > 0 {\displaystyle \gamma _{\mathrm {la} }>\gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }>0} In

980-416: The ⁠ 1 / 2 ⁠ is that the film has two sides (two surfaces), each of which contributes equally to the force; so the force contributed by a single side is γL = ⁠ F / 2 ⁠ . Surface tension γ of a liquid is the ratio of the change in the energy of the liquid to the change in the surface area of the liquid (that led to the change in energy). This can be easily related to

1029-460: 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. The surface of any liquid is an interface between that liquid and some other medium. 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

SECTION 20

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1078-654: The usual arguments , interpreted as being stored as potential energy. Consequently, surface tension can be also measured in SI system as joules per square meter and in the cgs system as ergs per cm. 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 . Several effects of surface tension can be seen with ordinary water: Surface tension

1127-477: The Advancement of Science . The dyne is defined as "the force required to accelerate a mass of one gram at a rate of one centimetre per second squared". An equivalent definition of the dyne is "that force which, acting for one second, will produce a change of velocity of one centimetre per second in a mass of one gram". One dyne is equal to 10 micronewtons, 10 N or to 10 nsn (nano sthenes ) in

1176-414: The boundary molecules are missing neighbors (compared to interior molecules) and therefore have higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized number of boundary molecules results in a minimal surface area. As a result of surface area minimization, a surface will assume a smooth shape. Surface tension, represented by

1225-519: 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 . The height to which the column is lifted is given by Jurin's law : h = 2 γ l a cos ⁡ θ ρ g r {\displaystyle h={\frac {2\gamma _{\mathrm {la} }\cos \theta }{\rho gr}}} where Pouring mercury onto

1274-426: The diagram, both the vertical and horizontal forces must cancel exactly at the contact point, known as equilibrium . The horizontal component of f la is canceled by the adhesive force, f A . f A = f l a sin ⁡ θ {\displaystyle f_{\mathrm {A} }=f_{\mathrm {la} }\sin \theta } The more telling balance of forces, though,

1323-407: The difference between the liquid–solid and solid–air surface tension, γ ls − γ sa , is difficult to measure directly, it can be inferred from the liquid–air surface tension, γ la , and the equilibrium contact angle, θ , which is a function of the easily measurable advancing and receding contact angles (see main article contact angle ). This same relationship exists in the diagram on

1372-421: 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. We consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass, because mercury does not adhere to glass at all. So the surface tension of the mercury acts over its entire surface area, including where it

1421-402: 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

1470-417: The forces are in direct proportion to their respective surface tensions, we also have: γ l s − γ s a = − γ l a cos ⁡ θ {\displaystyle \gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }=-\gamma _{\mathrm {la} }\cos \theta } where This means that although

1519-489: The glass is tipped, it will 'roll' around inside. Dyne The dyne (symbol: dyn ; from Ancient Greek δύναμις ( dúnamis )  'power, force') is a derived unit of force specified in the centimetre–gram–second (CGS) system of units, a predecessor of the modern SI . The name dyne was first proposed as a CGS unit of force in 1873 by a Committee of the British Association for

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1568-500: The intrinsic properties of the liquid (composition, temperature, etc.), not on its geometry. For example, if the frame had a more complicated shape, the ratio ⁠ F / L ⁠ , with L the length of the movable side and F the force required to stop it from sliding, is found to be the same for all shapes. We therefore define the surface tension as γ = F 2 L . {\displaystyle \gamma ={\frac {F}{2L}}.} The reason for

1617-474: 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

1666-464: The mercury poured onto glass. The thickness of a puddle of liquid on a surface whose contact angle is 180° is given by: h = 2 γ g ρ {\displaystyle h=2{\sqrt {\frac {\gamma }{g\rho }}}} where Cohesion (chemistry) In chemistry and physics , cohesion (from Latin cohaesiō  'cohesion, unity'), also called cohesive attraction or cohesive force ,

1715-546: The oxygen atom has a negative charge. This charge polarization within the molecule allows it to align with adjacent molecules through strong intermolecular hydrogen bonding, rendering the bulk liquid cohesive. Van der Waals gases such as methane , however, have weak cohesion due only to van der Waals forces that operate by induced polarity in non-polar molecules. Cohesion, along with adhesion (attraction between unlike molecules), helps explain phenomena such as meniscus , surface tension and capillary action . Mercury in

1764-403: The previous definition in terms of force: if F is the force required to stop the side from starting to slide, then this is also the force that would keep the side in the state of sliding at a constant speed (by Newton's Second Law). But if the side is moving to the right (in the direction the force is applied), then the surface area of the stretched liquid is increasing while the applied force

1813-458: The relatively high attraction of water molecules to each other through a web of hydrogen bonds , water has a higher surface tension (72.8 millinewtons (mN) per meter at 20 °C) than most other liquids. Surface tension is an important factor in the phenomenon of capillarity . Surface tension has the dimension of force per unit length , or of energy per unit area . The two are equivalent, but when referring to energy per unit of area, it

1862-401: The right hand side is in fact (twice) the mean curvature 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

1911-433: 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: γ l a > 0 > γ l s − γ s a {\displaystyle \gamma _{\mathrm {la} }>0>\gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }} Observe that in

1960-430: The same time, is acting to reduce the total surface area. The result of the compromise is 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 to which water does not adhere. Wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface, say a waxed sheet of glass, will behave similarly to

2009-401: The same type are called cohesive forces, while those acting between molecules of different types are called adhesive forces. The balance between the cohesion of the liquid and its adhesion to the material of the container determines the degree of wetting , the contact angle , and the shape of meniscus . When cohesion dominates (specifically, adhesion energy is less than half of cohesion energy)

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2058-416: The shape of the minimal surface 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 , as seen in

2107-432: 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 approaches this. Contact angle of 180° occurs when the liquid–solid surface tension is exactly equal to the liquid–air surface tension. γ l

2156-413: The surface do not have the same molecules on all sides of them and therefore are pulled inward. This creates some internal pressure and forces liquid surfaces to contract to the minimum area. There is also a tension parallel to the surface at the liquid-air interface which will resist an external force, due to the cohesive nature of water molecules. The forces of attraction acting between molecules of

2205-552: 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 : Δ p = γ ( 1 R x + 1 R y ) {\displaystyle \Delta p=\gamma \left({\frac {1}{R_{x}}}+{\frac {1}{R_{y}}}\right)} where: The quantity in parentheses on

2254-907: The symbol γ (alternatively σ or T ), is measured in force per unit length . Its SI unit is newton per meter but the cgs unit of dyne per centimeter is also used. For example, γ = 1   d y n c m = 1   e r g c m 2 = 1   10 − 7 m ⋅ N 10 − 4 m 2 = 0.001   N m = 0.001   J m 2 . {\displaystyle \gamma =1~\mathrm {\frac {dyn}{cm}} =1~\mathrm {\frac {erg}{cm^{2}}} =1~\mathrm {\frac {10^{-7}\,m\cdot N}{10^{-4}\,m^{2}}} =0.001~\mathrm {\frac {N}{m}} =0.001~\mathrm {\frac {J}{m^{2}}} .} Surface tension can be defined in terms of force or energy. Surface tension γ of

2303-399: The two surfaces meet, they form a contact angle , θ , which is the angle the tangent to the surface makes with the solid surface. Note that the angle is measured through the liquid , as shown in the diagrams above. 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

2352-642: The vertical components point in the same direction and therefore add up to balance F w . The object's surface must not be wettable for this to happen, and its weight must be low enough for the surface tension to support it. If m denotes the mass of the needle and g acceleration due to gravity, we have F w = 2 F s sin ⁡ θ ⇔ m g = 2 γ L sin ⁡ θ {\displaystyle F_{\mathrm {w} }=2F_{\mathrm {s} }\sin \theta \quad \Leftrightarrow \quad mg=2\gamma L\sin \theta } To find

2401-422: The wetting is low and the meniscus is convex at a vertical wall (as for mercury in a glass container). On the other hand, when adhesion dominates (when adhesion energy is more than half of cohesion energy) the wetting is high and the similar meniscus is concave (as in water in a glass). Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into

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