## Dgf

Figure 8.3 Variation of oxygen partial pressure and radius in a bubble held at a depth. a: Partial pressures inside the bubble are equal to partial pressures in solution that has been elevated by a pressure increment, PI, determined by both hydrostatic pressure and surface tension at the bubble. b: Oxygen partial pressures, pO2, in the bubble (subscript b) and in solution (subscript s) with respect to time, under a hypothetical regime of hydrostatic pressure only (thin line) or combined hydrostatic pressure and bubble surface tension (heavy line). c: Bubble radius under a hypothetical regime of hydrostatic pressure only (thin line) or combined hydrostatic pressure and bubble surface tension (heavy line).

time

pressures in it high. This additional force comes from surface tension.

You will remember surface tension from the last chapter. At any interface between air and water, a surface tension force pulls on the interface, in parallel to it (Fig. 8.2). When surface tension acts at the spherical air-water interface of a bubble, it compresses the bubble, just as the stretched wall of a rubber balloon compresses the air inside. What keeps the bubble from stabilizing is the way the surface tension force depends upon bubble size. This relation is expressed by the law of LaPlace, which states:

where Ap is the increased pressure, y is the water's surface tension (about 73 mN m-1), and r is the bubble's radius (m). A bubble 1 cm in diameter (r =.5 cm = .005 m), therefore, would have an internal pressure elevated by about 29 Pa from surface tension forces alone. The bubble collapses because these surface tension forces increase as the bubble shrinks. If the bubble shrinks to one-tenth its original diameter (r = .0005 m), for example, the pressure inside the bubble will increase tenfold. This increased pressure will keep the partial pressures of gases in the bubble perpetually higher than those in the water (Fig. 8.3). Consequently, the bubble never equilibrates and must collapse itself out of existence.

The Ege Effect and Bubble Aqualungs We're now ready to revisit the Ege effect. So far, we have been dealing with bubbles in which the only possible movement of gas is between the bubble and water. The physical forces operating in a bubble in this circumstance always drive both nitrogen and oxygen one way and one way only—out of the bubble and into solution. If an insect is breathing from the bubble, however, the picture changes dramatically (Fig. 8.4). We now have an additional avenue for the movement of gas—namely, the movement of oxygen from the bubble to the insect. As the insect consumes oxygen from the bubble, the bubble pO2 will drop, faster than it would if the bubble was simply losing oxygen to the water. If the beetle draws down the oxygen fast enough, the bubble pO2 eventually falls below the pO2 in the water. Now the partial pressure difference for oxygen is reversed, and oxygen will diffuse from the water into the bubble, where it can be consumed by the insect. In short, the bubble carried by an aquatic insect is not simply an oxygen store;it is also serving as a gill, removing oxygen from solution and conveying it through the bubble to the insect. Bubbles used in this way are known as bubble gills.

We now see why Ege got his seemingly bizarre result with oxygen-filled bubbles. When the bubble is filled with air, the insect need not remove too much oxygen before the ApO2 reverses and starts driving oxygen from the water into the bubble. With a bubble of pure oxygen, however, pO2 inside the bubble never falls below the pO2 in solution. Oxygen flux is always outward, the bubble shrinks quickly, and the animal will die if it is not able to come to the surface.