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In physics, surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic sheet. This effect allows insects (such as the water strider) to walk on water, allows small metal objects such as needles, razor blades, or foil fragments to float on the surface of water, and causes capillary action. Interface tension is the name of the same effect when it takes place between two liquids. The Cause of Surface Tension Surface tension is caused by the attraction between the molecules of the liquid by various intermolecular forces. In the bulk of the liquid each molecule is pulled equally in all directions by neighboring liquid molecules, resulting in a net force of zero. At the surface of the liquid, the molecules are pulled inwards by other molecules deeper inside the liquid but they are not attracted as intensely by the molecules in the neighbouring medium (be it vacuum, air or another liquid). Therefore all of the molecules at the surface are subject to an inward force of molecular attraction which can be balanced only by the resistance of the liquid to compression. Thus the liquid squeezes itself together until it has the locally lowest surface area possible. Another way to think about it is that a molecule in contact with a neighbor is in a lower state of energy than if it weren't in contact with a neighbor. The interior molecules all have as many neighbors as they can possibly have. But the boundary molecules have fewer neighbors than interior molecules and are therefore in a higher state of energy. For the liquid to minimize its energy state, it must minimize its number of boundary molecules and therefore minimize its surface area. Surface tension in everyday life Some examples of the effects of surface tension seen with ordinary water: Surface tension has a big influence on other common phenomena, especially when certain substances, surfactants, are used to decrease it: Physics Definition of Surface Tension Surface tension is represented by the symbol σ, γ or T and 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 γL. Surface tension is therefore measured in newtons per meter (N·m-1), although the cgs unit of dynes per cm is normally used. A better definition of surface tension, in order to treat its thermodynamics, is work done per unit area. As such, in order to increase the surface area of a mass of liquid an amount, δA, a quantity of work, γδA, is needed. Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape. This is because a sphere has the minimum surface area for a given volume. Therefore surface tension can be also measured in joules per square metre (J·m-2), or, in the cgs system, ergs per cm2. The equivalence of both units can be proved by dimensional analysis. A related quantity is the energy of cohesion, which is the energy released when two bodies of the same liquid become joined by a boundary of unit area. Since this process involves the removal of a unit area of surface from each of the two bodies of liquid, the energy of cohesion is equal to twice the surface energy. A similar concept, the energy of adhesion, applies to two bodies of different liquids. Energy of adhesion is linked to the surface tension of an interface between two liquids. See also Cassie's law. Water Strider Physics The photograph shows water striders standing on the surface of a pond. It is clearly visible that their feet cause indentations in the water's surface. And it is intuitively evident that the surface with indentations has more surface area than a flat surface. If surface tension tends to minimize surface area, how is it that the water striders are increasing the surface area? Recall that what nature really tries to minimize is potential energy. By increasing the surface area of the water, the water striders have increased the potential energy of that surface. But note also that the water striders' center of mass is lower than it would be if they were standing on a flat surface. So their potential energy is decreased. Indeed when you combine the two effects, the net potential energy is minimized. If the water striders depressed the surface any more, the increased surface energy would more than cancel the decreased energy of lowering the insects' center of mass. If they depressed the surface any less, their higher center of mass would more than cancel the reduction in surface energy. The photo of the water striders also illustrates the notion of surface tension being like having an elastic film over the surface of the liquid. In the surface depressions at their feet it is easy to see that the reaction of that imagined elastic film is exactly countering the weight of the insects. Liquid in a Vertical Tube An old style mercury barometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a 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 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 rather than higher 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 compensate for the increase potential energy associated with the lifting of the fluid near the walls of the container. The angle of contact of the surface of the liquid with the wall of the container can be used to determine the surface tension of the liquid-solid interface provided that the surface tension of the liquid-air interface is known. The relationship is given by: where
where
ho is the density of the liquid,
Pool of Liquid on a Nonadhesive Surface Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness (do not try this except under a fume hood. Mercury vapor is a toxic hazard). 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, 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 nonadhesive horizontal surface is given by where For mercury, and , which gives . For water at 25 °C, and , which gives . In reality, the thicknesses of the puddles will be slightly less than these calculated values. This is due to the fact that surface tension of the mercury-glass interface is slightly less than that of the mercury-air interface. Likewise, the surface tension of the water-wax interface is less than that of the water-air interface. The contact angle, as described in the previous subsection, determines by how much the puddle thickness is reduced from the theoretical. Liquid Surfaces as Minimization Solver To find 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, the minimal surface will appear in the resulting soap-film within seconds. Without a single calculation, the soap-film solves the complex minimization equation on its own. Measuring methods Thermodynamic Definition As stated above, the mechanical work needed to increase a surface is . For a reversible process, , therefore at constant temperature and pressure, surface tension equals Gibbs free energy per surface area: , where is Gibbs free energy and is the area. From the definition it is easy to understand that decreasing the surface area of a substance is always spontaneous (ΔG<0), on the contrary, in order to increase its surface a certain amount of energy is needed, as the process is, per se, non spontaneous (ΔG>0). A measure of how spontaneous (or non-spontaneous) is the change in the surface area is precisely the surface tension. The definition of Gibbs free energy can be arranged to so partial derivation yields and applying the equations of state we obtain , where means entropy per surface area. Rearranging the previous expression Kelvin Equation I is obtained. It states that surface enthalpy or surface energy (different from surface free energy) depends both on surface tension and its derivative with temperature at constant pressure Influence of temperature on surface tension Surface tension dependes on temperature, for that reason, when a value is given for the surface tension of an interface, temperature must be explicitely stated. The general trend is that surface tension decreases with temperature, reaching a value of 0 at the critical temperature. There are only empirical equations to relate surface tension and temperature: is the molar volume of that substance is the critical temperature is a constant for each substance. For example for water k = 1.03 erg/°C, V = 18 ml/mol and TC = 374°C. ight)^n is a constant for each liquid and n is an empirical factor, whose value is 11/9 for organic liquids Both take into account the fact that surface tension reaches 0 at the critical temperature. Influence of solute concentration on surface tension Solutes can have different effects on surface tension depending on their structure: Gibbs isotherm 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 and the temperature Certain assumptions are taken in its deduction, therefore Gibbs isotherm can only be applied to ideal (very dilute) solutions with two components. Pressure jump across a curved surface If viscous forces are absent, the pressure jump across a curved surface is given by the Young-Laplace Equation, which relates pressure inside a liquid with the pressure outside it, the surface tension and the geometry of the surface. . This equation can be applied to any surface: The table shows an example of how the pressure increases, showing that for not very small drops the effect is subtle but the pressure difference becomes great when the drop sizes approach the molecular size (a drop with a 1 nm radius contais approximately 100 water molecules), this can be attributed to the fact that at a very small scale the laws of continuum physics can not be applied anymore. Influence of particle size on vapour pressure Starting from Clausius-Clapeyron relation Kelvin Equation II can be obtained; it explains that because of surface tension, vapor pressure for small droplets of liquid in suspension is greater than standard vapor pressure of that same liquid when the interface is flat. That is to say that when a liquid is forming small droplets, the concentration of vapor of that liquid in the surroundings is greater, this is due to the fact that 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 is the Kelvin radius, the radius of the droplets. This equation is used in catalyst chemistry to assess mesoporosity for solids. The table shows some calculated values of this effect for water at different drop sizes: The effect becomes clear for very low drop sizes, as a drop on 1 nm radius has about 100 molecules inside, which is a quantity small enough to require a quantum mechanics analysis. Surface tension values See Surface tension values for a list of surface tension or interface tension for some interfaces. See also | |||||||
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