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medical physics surface tension and capillarity Surface Tension and Capillarity medical physics surface tension and capillarity Surface tension The property of liquids which is felt at the interface between the liquid and another fluid (typically a gas)...

medical physics surface tension and capillarity Surface Tension and Capillarity medical physics surface tension and capillarity Surface tension The property of liquids which is felt at the interface between the liquid and another fluid (typically a gas) is called Surface Tension. Surface tension has dimensions of force per unit length, and always acts parallel to the interface. Surface molecules are subject to an attractive force from nearby surface molecules so that the surface is in a state of tension (Figure 1). A soap bubble is a good example to illustrate the effects of surface tension. How does a soap bubble remain spherical in shape? The answer is that there is a higher pressure inside the bubble than outside, much like a balloon. In fact, surface tension in the soap film acts much the same as the tension in the skin of a balloon. Fig.1: Surface tension in molecule on the surface. medical physics surface tension and capillarity Consider a soap bubble of radius R with internal pressure p in and external (atmospheric) pressure pout. The excess pressure bubble Δp = pin − pout can be found by considering the free-body diagram of half a bubble (Figure 2). Note that surface tension acts along the circumference (resulting from cutting across the two interfaces) and the pressure acts on the area of the half-bubble. By statics, the net force due to the pressure is equal to the pressure times the projected area. Hence, balancing the forces due to surface tension and pressure difference: 2(2πR) σs = (πR2) Δp bubble Δp bubble = 4 σs / R Where σs: Surface tension of the fluid in air. Fig2. Soap bubble of radius R. Example: if the surface tension at soap bubble interface is 0.025N/m, what is the pressure difference between inside and outside of that bubble of radius 10mm? ơ 𝑝= ×. 𝑝= = 10 N/m2 × medical physics surface tension and capillarity Capillary Action We have seen that surface tension arises because of the intermolecular forces of attraction that molecules in a liquid exert on one another. These forces, which are between like molecules, are called cohesive forces. A liquid, however, is often in contact with a solid surface, such as glass. Then additional forces of attraction come into play. They occur between molecules of the liquid and molecules of the solid surface and, being between unlike molecules, are called adhesive forces. Consider a tube with a very small diameter, which is called a capillary. When a capillary, open at both ends, is inserted into a liquid, the result of the competition between cohesive and adhesive forces can be observed. For instance, (Figure 3) shows a glass capillary inserted into water. In this case, the adhesive forces are stronger than the cohesive forces, so that the water molecules are attracted to the glass more strongly than to each other. The result is that the water surface curves upward against the glass. It is said that the water “wets” the glass. The surface tension leads to a force F acting on the circular boundary between the water and the glass. This force is oriented at an angle ф, which is determined by the competition between the cohesive and adhesive forces. The vertical component of F pulls the water up into the tube to a height h. At this height the vertical component of F balances the weight of the column of water of length h. medical physics surface tension and capillarity (Figure 4) shows glass capillary inserted into mercury, a situation in which the adhesive forces are weaker than the cohesive forces. The mercury atoms are attracted to each other more strongly than they are to the glass. As a result, the mercury surface curve downward against the glass and the mercury does not “wet” the glass. Now, in contrast to the situation illustrated in (Figure 3), the surface tension leads to a force (F), the vertical component of which pulls the mercury down a distance (h) in the tube. The behavior of the liquids in both (Figures 3) and (Figure 4) is called capillary action. medical physics surface tension and capillarity Biomedical Applications of Capillary Action Many medical tests require drawing a small amount of blood, for example to determine the amount of glucose in someone with diabetes or the hematocrit level in an athlete. This procedure can be easily done because of capillary action, the ability of a liquid to flow up a small tube against gravity, as shown in the figure below. When your finger is pricked, a drop of blood forms and holds together due to surface tension the unbalanced intermolecular attractions at the surface of the drop. Then, when the open end of a narrow-diameter glass tube touches the drop of blood, the adhesive forces between the molecules in the blood and those at the glass surface draw the blood up the tube. How far the blood goes up the tube depends on the diameter of the tube (and the type of fluid). A small tube has a relatively large surface area for a given volume of blood, which results in larger (relative) attractive forces, allowing the blood to be drawn farther up the tube. The liquid itself is held together by its own cohesive forces. When the weight of the liquid in the tube generates a downward force equal to the upward force associated with capillary action, the liquid stops rising.