Cause
force diagram on the two molecules of liquid.
This clip was under the water level has risen gently and smoothly. Surface tension prevents the trombone overwhelm and broke the blue glass.
Surface tension is caused by the attraction between molecules of the liquid by various intermolecular forces. In most of the liquid, each molecule is pulled equally in all directions by neighboring liquid molecules, resulting in a net force of zero. A liquid surface, the molecules are drawn inward by other molecules deeper inside the liquid and are not attracted as intensely by the molecules in the neighboring environment (either vacuum, the air or other liquid). Therefore, all molecules at the surface are subjected to an internal force of molecular attraction which is balanced by the liquid resistance to compression, which means that there is no net force inwards . However, it is a driving force to decrease the surface. Therefore, the liquid shrinks until it has the lowest surface area possible. This explains the shapes of spherical water droplets.
Another view is that the molecule in contact with a neighbor is in a lower energy state if it was not in contact with a neighbor. Molecules inside have all as neighbors as they can possibly have. But the boundary molecules have fewer neighbors than the molecules inside and are therefore in a higher state of energy. For the liquid to minimize its energy state, we must minimize the number of molecules limit and must reduce its surface.
Following the reduction of surface, surface takes the form Smooth it can (mathematical proof that “soft” forms to minimize the surface based on the use of the equation Euleragrange). Since any curve shape of the surface results in a larger area, 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.
Effects in everyday life
water Bead on a sheet
water dripping from a tap
The effects of surface tension can be seen with ordinary water:
Beads of rainwater on the surface a waxed car. The water adheres to the wax slightly and strongly to itself, the clusters of water then drops. The surface tension that makes them almost spherical form, because the sphere is the smallest possible area to volume ratio
formation of drops occurs when a mass of liquid is stretched. The animation shows the water tap while respecting the weight gain until it is extended to a point that bind the surface tension can no longer tap. It then separates and forms the lower surface tension in a sphere. If a stream were on tap, the flow can not be broken down during its fall. Severity from the watercourse, surface tension and then clamped in the spheres.
Floating objects denser than water occurs when the object is not wettable and its weight is small enough to be supported by forces arising from surface tension.
The separation of oil and water is caused by the surface tension between different liquids. This type of surface tension is called “surface tension”, but the physics are the same.
Tears of wine is the formation of drops and streams on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between different surface tensions of water and ethanol.
Surface tension is visible in other common phenomena, especially when certain substances, surfactants, are used to decrease:
soap bubbles are very large surface areas with very little bulk. Bubbles in pure water are unstable. The addition of surfactants, however, can have a stabilizing effect on the bubbles (see the Marangoni effect). Note that surfactants are effective in reducing the surface tension of water by a factor of three or plus.Emulsions />
Physics basic
Two definitions
The diagram shows, in cross section, a needle floating on the surface of the water. Its weight, FW, depresses the surface, and is balanced by surface tension forces on either side, FS, which are each parallel to the surface of the water to where it comes into contact with the needle. Note that the horizontal components of the FS two arrows point in opposite directions, they cancel each other, but the vertical point components in the same direction and therefore add to the balance Fw.
Surface tension, represented by the symbol 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 wire length, L. The wire is pulled into the film by a force equal to 2 liters (the factor of 2 because the soap film has two sides, so both surfaces). The surface tension is measured in force per unit length. Its SI unit is newton per meter, but the CGS unit dyne / cm is also used. A dyn / cm corresponds to 0. 001 N / m.
An equivalent definition, that which is useful in thermodynamics, is work done per unit area. As such, in order to increase the surface of a body fluid of an amount, A, a quantity of work, A, is necessary. This work is stored as potential energy. Therefore the surface tension can also be measured in SI units joules per square meter and in the CGS, as ergs per cm2. Mechanical systems try to find a state of minimal potential energy, a drop of free liquid naturally assumes a spherical shape, which has the minimum area for a given volume.
The equivalence of the measurement of energy per unit area force per unit length can be proven by dimensional analysis.
water spiders water spiders, a town that touches the neuston surface tension < , br /> water striders use surface tension to walk on the surface of a pondydrophobic setae on tarsi keep the insect afloat for a hydrophilic apical claw penetrates the surface, allowing it to “grip” of water. The surface of the water behaves like an elastic film: the insect’s feet leave marks on the surface of the water, increasing its surface. This represents an increase of potential energy by the surface tension of water equal to the loss of potential energy of the lowered center of mass insect.
Surface curvature and pressure
surface tension forces acting on a tiny (differential) surface patch. x and y indicate the amount of focus on the dimensions of the patch. The balance of forces in tension with pressure leads to the equation Youngaplace
If no force acts normal to a surface tension, the surface must remain flat. But if the pressure of a different side of the surface pressure on the other hand, the difference in surface pressure times the surface results in a normal force. For the surface tension forces to cancel the force due to pressure, the surface must be curved. The diagram shows how the surface curvature of a small patch of surface leads to an element of net surface tension forces acting perpendicular to the center of the patch. When all forces are balanced equation that results is known as the equation Youngaplace:
following cases:
p is the pressure difference.
is the surface tension.
Rx and Ry are the radii of curvature in each of the axes that are parallel to the surface.
The quantity in parentheses on the right side is done (twice) the mean curvature of the surface (depending on normalization).
solutions to this equation to determine the shape of water drops, puddles, meniscus, bubbles, and all other manner determined by surface tension (eg in the form of impressions that a spider feet of water make the surface of a pond).
The table below shows how the pressure Internal increases with a drop of water with a radius decreases. For not very small drops, the effect is subtle, but the pressure difference becomes enormous when the drop sizes approach the molecular size. (Of course, within a single molecule of the concept loses its meaning.)
P for water drops of different radii at STP
droplet radius
1 mm
0. 1 mm 1 m
10 nm p (atm)
0. 0014
0. 0144
1.
436 143. 6
liquid surface as a computer
minimum surface to find the form of the minimal area bounded by a frame of arbitrary shape by using strictly mathematical means can be a daunting intimidating. However, in shaping the framework of wire and dip in soap solution, a minimum area of approximately appear in the soap film resulting in a few seconds. Without a single calculation, the soap film arrives at a solution to a complex equation minimization of its own.
The reason is that the pressure difference across a liquid interface is proportional to the mean curvature as shown in the equation of Young-Laplace. For a soap film opened, the pressure difference is zero, then the mean curvature is zero and the minimal surfaces have the property of zero mean curvature.
Contact angles as no liquid can exist in a perfect vacuum for very long, the surface of a liquid is an interface between the liquid and another medium. The top surface of a pond, for example, is an interface between water and air basin. The surface tension, then, is not a property of the liquid alone, but a property of the liquid interface with another medium. If a liquid is in a container, then the more air / liquid interface at its upper surface, there is an interface between the liquid and the container walls. The surface tension between liquid and air is usually different (over) its surface tension with the walls of a container. And where two surfaces meet, their geometry should be such that all the forces of imbalance.
Forces to the point of contact listed under the contact angle greater than 90 (left) and less than 90 ( right)
When the two surfaces meet, they form a contact angle, which is the angle of the tangent to the surface and the solid surface. The diagram at right shows two examples. tension forces are shown for the air-liquid interface, the interface liquid-solid and solid-air interface. The left example is where the difference is between the solid and liquid-solid surface tension of air, lower the surface tension of liquid air, but it is nevertheless positive, which is
In diagram, the vertical and horizontal forces must cancel exactly at the point of contact. The horizontal component is canceled by the force of adhesion.
The balance of forces more revealing, however, is in the vertical direction. The vertical component of the void must be exactly the force.
Liquid Solid
angle contactl’eau
glass soda lime glass leaded
fused quartz 0éthanol
diethyl ether tetrachloride carboneglycérol
acid acétiquel’eau
paraffin 107argent
90 methyl iodide
soda lime glass
29
glass leaded
30
fused quartz 33mercure
soda lime glass 140
Some liquid-solid contact angles
Since the forces are in direct proportion to their respective surface tension, we have also
Where Is the surface tension of liquid-solid
Is the surface tension of liquid-air
Is the surface tension of solid-air
The contact angle, where a concave meniscus contact angle is less than 90 and has a convex meniscus contact angle greater than 90.
This means that , although the difference is between the liquid-solid surface tension and solid-air, difficult to measure directly, it can be inferred from the contact angle can be easily measured if the surface tension of liquid air, 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 voltage difference liquid-solid/solid-air surface must be negative:
Contact angles Special
Note that in the particular case of a money-water interface, where the contact angle is equal to 90, the difference in surface tension is exactly zero liquid-solid/solid-air.
Another special case is where the contact angle is exactly 180. Water with specially prepared Teflon approaches that. Contact angle of 180 occurs when the surface tension of liquid-solid is exactly equal to the surface tension of liquid air.
Measurement methods
surface tension can be measured by using the pendant drop method on a goniometer.
Because surface tension is manifested in various effects, it offers a number of paths to measure. Which method is best depends on the nature of the liquid being measured, the conditions under which the power must be measured and the stability of its surface when it is deformed.
From Noy Ring method: The traditional method used to measure surface or interfacial tension. Wetting properties of the surface or interface have little influence on the measurement technique. Maximum traction on the ring’s surface is measured.
A smaller version of Du Noy method uses a metal needle of small diameter, instead of a ring, in combination with a high sensitivity microbalance record maximum traction. The advantage of this method is that the very small sample volumes (up to several tens of microliters) can be measured with very high accuracy without the need to correct for buoyancy (a needle, or rather, a stem with a correct geometry). In addition, the measurement can be done very quickly, at least in 20 seconds. tensiometers multichannel music [CMCeeker] have recently been built based on this principle.
Wilhelmy plate method: a universal method especially suited to check surface tension over time intervals. A vertical plate of known perimeter is attached a balance, and the force due to wetting is measured.
Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter of a drop into a heavy phase is measured while both are rotated.
Pendant drop method: surface and interfacial tension can be measured by this technique, even at high temperatures and pressures . Geometry of a drop is analyzed optically. For more details, see fall.
Bubble pressure method (method Jaeger): A measurement technique for determining the surface tension at the age of the surface short. The maximum pressure of each bubble is measured.
Drop volume method: A method for determining the interfacial tension according to the age interface. Fluid density is pumped into a second liquid of different density and the time between the drops produced is measured.
Capillary rise method: The end of a capillary is dipped into the solution. The height at which the solution comes in the capillary is related to the surface tension by the equation below.
Stalagmometric method: A method of weighting and reading a drop of liquid.
sessile drop method: A method for determining surface tension and density by placing a drop on a substrate and measuring the contact angle (sessile drop technique see).
method Ink Test: A method for measuring the surface tension of the substrate with ink test and interpret the reaction of the ink. watch the video video to show the extent of surface tension effects
liquid in a vertical tube
Main article: Capillary action
Outline a mercury barometer
A barometer old style mercury consists of a vertical glass tube about 1 cm in diameter, partly filled with mercury, and with a blank (empty called Torricelli) in volume Unfilled (see diagram at right). Note that the level of mercury in the tube center is higher than at the edges, which makes the top surface of the mercury-shaped dome. The center of mass of the entire column of mercury would be slightly lower if the top surface of mercury have been stable over the entire crossection of the tube. But the high dome gives the area slightly less than the entire mass of mercury. Again the two effects combine to minimize the total potential energy. This surface shape is known as a convex meniscus.
The reason we consider the surface of the entire mass of mercury, including the portion of the surface is in contact with glass is because mercury does not comply with all the glass. Thus, the surface tension of mercury acts on its entire surface, including when in contact with the glass. If, instead of glass, the tube made of copper, the situation is very different. Mercury actively adheres to copper. Thus, in a copper tube, the mercury level in 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 that part of the liquid surface in contact with the container having the negative surface tension. The fluid then works to maximize the contact area. So in this way increases the surface contact with the container decreases rather than increases the potential energy. This decrease is sufficient to offset the increased potential energy associated with the lifting of the fluid near the walls of the container.
Illustration of capillary rise and fall. Red = contact angle less than 90, blue = contact angle greater than 90
If a tube is narrow enough and buy liquid walls is sufficiently strong, the surface tension can draw the liquid into the tube in a phenomenon known as capillary action. The height of the column is closed at is given by:
Where Is the height of the liquid is raised,
Is the surface tension of liquid air,
is the density of the liquid,
Is the radius of the capillary,
Is the acceleration due to gravity,
Is the contact angle it above. Note that if more than 90, such as mercury in a glass container, the liquid will be depressed rather than raised.
Puddles on surface
profile curve along a puddle water where the contact angle is 180. The curve is given by the formula: where
small puddles of water on a clean smooth surface have perceptible thickness.
Casting mercury on a flat horizontal sheet of glass results in a puddle of water that has a thick felt. (Do not try this unless under a hood. Vapor of Mercury is a toxic hazard). The pool will be distributed only to the point where he is a little less than half a centimeter thick, and not thinner. Again this is due to the action of the solid surface tension of mercury. The liquid mass flattens, because that brings the highest mercury levels as low as possible. But the surface tension at the same time acts to reduce the total area. The result is the compromise of a puddle of thick or less fixed.
Demonstration same surface tension that can be done with water, but only on a surface consisting a substance that water does not comply. The wax is such a substance. Water poured on a wax surface smooth, flat, horizontal, for example a sheet of waxed glass, behave similarly to mercury spilled on the glass.
The thickness of a pool of liquid on a surface with contact angles of 180 is given by:
Where Is the depth of the puddle in centimeters or meters.
Is the surface tension 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
Illustration of how the lower contact angle leads to a reduction in the depth puddle of
In fact, the thickness of standing water will be slightly lower than that predicted by the above formula, as very few surfaces have a contact angle of 180 with a liquid . When the contact angle is less than 180, the thickness is given by:
For mercury on glass, and giving. For water with oil at 25 ° C, and giving.
The formula also provides that when the contact angle is 0, the liquid will spread out in a micro-thin layer on surface. Such a surface is said to be fully wettable by the liquid.
The dismantling of streams into droplets
intermediate step of a jet breaking into drops. Bending radii in the axial direction are presented. The equation for the radius of the river is, where is the radius of the disturbed air flow, the amplitude of the disturbance is the distance along the axis of the river, and the wavenumber
; Category: instability Plateauayleigh
In everyday life we all see a trickle of water from a tap will break up into droplets, regardless of the fluid flow is delivered by the tap. This is due to a phenomenon called Plateauayleigh instability, which is entirely a consequence of surface tension effects.
The explanation for this instability began with the existence of small perturbations in the stream. They are always present, whatever the flow is smooth. If the disturbance is resolved into component sine, we find that some components increase with time, while others decay over time. Among those that develop over time, some grow at a faster rate than others. Whether a component or decay develops, and how fast it grows is entirely based on its wave number (a measure of the number of peaks and troughs / cm) and radius of the original river cylindrical.
Thermodynamics As mentioned above, the mechanical work necessary to increase the surface is. Therefore, at constant temperature and pressure, surface tension is equal to the Gibbs energy per unit area:
Where is Gibbs and is the area.
Thermodynamics requires all the spontaneous changes of state are accompanied by a decrease in Gibbs free energy.
From this it is easy to see why reducing the surface of a body of liquid is always spontaneous () , provided it is not coupled to energy changes. It follows that, in order to increase the area, a certain amount of energy must be added.
Gibbs free energy is defined by the equation, where is the enthalpy and entropy is . Based on this and the fact that the surface tension is the free energy per unit area, it is possible to obtain the following expression for the entropy per unit area: Kelvin equation
surfaces arises rearranging the previous equations. It states that surface enthalpy or surface energy (different surface free energy) depends both on the surface tension and its derivative with temperature at constant pressure by the relationship.
Thermodynamics of bubble
The pressure inside a soap bubble (surface) ideal can be deduced from considerations of thermodynamic free energy. At constant temperature and the number of particles, dN = dT = 0, the Helmholtz differential free energy is given by
Where P is the pressure difference inside and outside the bubble, and surface tension. At equilbrium, dF = 0, and thus,
.
For a spherical bubble, the volume and surface area are given just
,
< , br />.
Substituting these relations in the previous expression, we find
This is equivalent to the Young-Laplace equation where Rx = Ry. For real soap bubbles, pressure is doubled due to the presence of two interfaces, one inside and one outside.
Influence of temperature
Temperature dependence of the voltage surface of pure water
temperature dependence of surface tension of benzene
Surface tension depends on temperature. For this reason, when a value is given for the surface tension of the interface, the temperature must be explicitly stated. The general trend is that the surface tension decreases with increasing temperature, reaching a value of 0 to the critical temperature. For more details see section ETV. Only empirical equations to relate the surface tension and temperature: ETV
Here V is the molar volume of the substance, TC is the critical temperature and k is a constant valid for almost all substances. A typical value is k = 2. 1 x 107 [J mol K1-2 / 3]. For water you can still use the V = 18 ml / mol and TC = 374 C
A variant is described by ETV Ramay and Shields:
Where the difference in temperature 6 Kelvin formula provides a better fit with reality at lower temperatures.
Guggenheim-Katayama
Is a constant for each liquid and n is an empirical factor, whose value is 11 / 9 for body fluids. This equation has been proposed by van der Waals, who also proposed that could be given by the expression, which is a universal constant for all liquids, and the critical pressure of the liquid (although later experiments found to vary some degree of liquid to another).
Both Guggenheim-Katayama and ETV reflect the fact that the surface tension reaches 0 at the critical temperature, while Ramay and Shields does not the 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
Increase the surface tension of inorganic salts
Decrease surface tension progressively, alcohols
Reduce surface tension and
