In the Classroom edited by
Overhead Projector Demonstrations
Doris K. Kolb
Demonstration of Surface Tension
Bradley University Peoria, IL 61625
Andrew J. Rosenthal School of Biological and Molecular Sciences, Oxford Brookes University, Oxford OX3 0BP, UK;
[email protected] Background Surface tension is a fundamental obstacle in the spontaneous formation of bubbles, droplets, and crystal nuclei in liquids. It acts as a driving force to destabilize colloidal systems containing bubbles, droplets, and crystals. Such mechanisms as Ostwald ripening in emulsions, disproportionation in foams, and ice crystal growth in frozen foods during storage are the result of this phenomenon. In these contexts it has substantial implications for many industrial situations, such as leavening of doughs and batters, ice formation during freezing, and emulsion and foam stability. A number of techniques have been Gas used to determine surface tension. The maximum bubble pressure technique (Fig. 1) is simple in its operation and, compared with techniques such as capillary rise, contact angle, or the torsion balance with either a du Nouy ring or a Wilhemy plate, it has the advantage that a fresh surface is formed each time, avoiding problems of surface contamination. Figure 1. MaxThe maximum bubble pressure techimum bubble pres- nique employs a capillary tube, which is sure technique. immersed into the liquid being tested. The pressure required to force a bubble out of the tip of the capillary is measured. As the bubble forms, the maximum pressure difference between the capillary and atmospheric pressure (∆P) occurs when the bubble is the same diameter as the capillary tube:
∆P = ρg h + 2σ r The first term on the right-hand side of the equation explains the hydrostatic pressure exerted by the height of the liquid above the tip of the capillary. The components of this term are the density of the liquid (ρ), the acceleration due to gravity (g), and the depth of immersion of the capillary below the surface of the liquid (h). The second term on the righthand side accounts for the surface tension of the liquid and is referred to as the Laplace excess pressure, being the difference in pressure between the inside of the bubble and the liquid at the same hydrostatic pressure. The force is created by the liquid’s surface tension (σ) pulling on the radius of curvature of the bubble (r). Thus if one compares the pressure inside two adjacent bubbles (one smaller than the other) at the same depth in a liquid, it is clear that the small bubble will have a higher internal pressure than the large bubble, whose internal pressure will be closer to the hydrostatic pressure of the liquid (Fig. 2). As a consequence, the concentration of dissolved gas immediately next to the small bubble is higher than that
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adjacent to the large bubble. This concentration gradient results in gas diffusion from the vicinity of the small bubble to the large one. As dissolved gas diffuses, its concentration around the small bubble falls, and to maintain equilibrium more gas dissolves from the small bubble. Consequently the bubble shrinks, reducing its radius and raising the internal pressure, which in turn causes more gas to dissolve. Obviously this kind of chain reaction causes the bubble’s internal pressure to rise rapidly until the Figure 2. Illustration of conbubble disappears altogether! centration gradient of disThis is the phenomenon of dis- solved gas adjacent to small proportionation, which is one and large bubbles. mechanism of foam instability. An analogous phenomenon happens in emulsions, where diffusion from small drops to large ones occurs, resulting in Ostwald ripening. The Laplace excess pressure (2σ/r) is also responsible for preventing the spontaneous formation of ice crystals during freezing and the formation of bubbles in carbonated drinks. Have you ever noticed that the bubbles that rise to the surface of the glass in a fizzy drink, such as coke, beer, or champagne, tend to come off at one or two points on the surface of the glass? Usually at these points you will find a scratch or a bit of muck where the glass was not perfectly clean or intact. These inhomogeneities provide a nucleus on which the bubble grows. Why do bubbles not form elsewhere? We can appreciate the reason if we consider a hypothetical tiny bubble with a radius close to zero. Presumably its internal pressure would be approaching infinity, and under such conditions the gas would redissolve. Consequently bubbles normally form either by growing on existing particles (e.g., antibumping granules, scratches or dirt on the side of a glass) or by mechanical break-up of larger ones (e.g., when egg white is whisked or dough folded in the baking of bread). The Laplace equation explains how surface tension acts as a resistance to the formation of ice crystals during freezing of water or aqueous systems, such as biological materials. It is difficult to spontaneously create ice crystals with an infinitely small radius because the stress caused by the surface tension on the tiny particle is large enough to cause it to melt. Ice crystal formation is consequently considered to be a two-step process: nucleation and crystal growth. Once nuclei are present, additional water molecules can become deposited on
Journal of Chemical Education • Vol. 78 No. 3 March 2001 • JChemEd.chem.wisc.edu
In the Classroom
their surface, producing larger crystals (crystal growth). But the creation of nuclei requires either (i) the presence of inhomogeneities, as occurs in so-called heterogeneous nucleation, where animal or plant cell components can act as nuclei for ice crystal growth, or (ii) when inhomogeneities are absent, so-called homogeneous nucleation, which occurs by the addition of free energy to overcome the resisting force of the surface tension. For homogeneous nucleation to occur, the liquid must be super-cooled (∆T ) below its equilibrium freezing temperature (Tf), and then energy must be introduced to overcome the interfacial tension (σ). The nuclei formed have a critical radius (r *) given by
r* =
2Tf σ L∆T
During freezing of foods or living tissues (cryogenics) it is normally desirable to produce small ice crystals, which cause relatively little disruption to the cellular tissues. Since the latent heat (L) and equilibrium freezing temperature (Tf) are fairly constant, the technologist can produce small ice crystals either by adding surfactants to lower the interfacial tension (which is often impractical) or by increasing the rate of cooling, which will result in a greater degree of supercooling. The idea that a force as small as surface tension can influence, and even prevent, so many industrial processes might seem preposterous to many students. I have found this simple overhead projector demonstration convinces my students of the power of this relatively small force. The Demonstration The demonstration (Fig. 3) requires •
two graduated 5-mL pipets,
•
one T connector with rubber tube on two of its limbs,
•
a crystallizing dish, and
•
some colored water (you can use a food color)
Graduated 5-mL pipets (not the bulb type) have relatively wide-bore tops. By selecting two identical pipets one can persuade the students that the restriction to air flow caused by the tip will regulate gas flow to the same extent whether the pipet is connected to the T connector with its wide end or with its tip. Thus if you blow into the T connector with the free ends of the apparatus open to the air, the gas expired air will flow at a similar rate through both pipets. The crystallizing dish is placed on the overhead projector and filled to a depth of about 5 cm with the colored water. The two pipets are immersed in the dish so that their ends are
both at the same depth—at the bottom. This assures that the same hydrostatic pressure is exerted on both tube openings. Ensuring that the Flexible tubing ends of the pipets are both visible on the overhead projector and taking care not to obscure the image with your head(!), very gently blow 5-mL pipet into the T connector. A stream of bubbles is produced, but only from the wide orifice. This demonstrates that, despite a similar resistance when the pipets are open to the air, when immersed in water, the Figure 3. Apparatus for smaller tube exerts greater resistance demonstrating Laplace excess pressure. to bubble formation. A more earnest application for this apparatus is in quantifying a liquid’s surface tension. The maximum bubble pressure technique described above is greatly influenced by the hydrostatic pressure exerted by the liquid. Working with two tubes of different diameter, von Cuny and Wolf showed that the surface tension could be determined from the difference in pressure between the two capillary tubes (1). A great advantage of this two-tube, differential technique is that the hydrostatic pressure no longer has an influence on the result because it varies in a similar manner for each capillary. Cuny and Wolf showed that if the vertical distance between the two tubes is set at two-thirds the difference in their radii, the surface tension becomes a direct function of the pressure difference between the two tubes. Such an innovation allows in-line measurement of surface tension, so that surfactants may be added as needed to processes such as the flight-type mechanical dishwashing machines found in large catering establishments. Traditionally such machines have had a continuous feed of fresh water and an overflow down the drain. The detergent (a mix of inorganic salts and surfactants) was added as the conductivity of the wash water fell. If we monitor the surface tension of the water, we can see it fall with the addition of surfactants. If food soil is added, then the surfactants combine with the soil, and the surface tension starts to rise. One is actually able to “titrate” the dirt off dishes, using the surface tension as an indicator (2). This allows the potential for process control based on surface tension as the measured variable. Literature Cited 1. von Cuny, K. H.; Wolf, K. L. Ann. Phys. 1956, 6 (17) 59–77. 2. Rosenthal, A.; Thorne, S. J. Am. Oil Chem. Soc. 1986, 63, 931–934.
JChemEd.chem.wisc.edu • Vol. 78 No. 3 March 2001 • Journal of Chemical Education
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