## O

bubble ^ water bubble ^ water

Figure 8.4 Conversion of a bubble to a gill. a: Fluxes of oxygen and nitrogen in a bubble attached to an insect that is consuming oxygen. b: For oxygen in a bubble attached to an insect, the characteristic curve of pO2(b) is not as described in Figure 8.3. At first pO2(b) pO2(s) and oxygen diffuses into the water. But for a short while pO2(b) < pO2(s), as indicated by the shaded area (where oxygen diffuses from the water into the bubble). Eventually, pO2(b) rises again, oxygen diffuses out into the water, and the bubble collapses.

bubble ^ water bubble ^ water

Occam's Razor and the Replenishing of Bubble Gills A bubble gill, useful as it is, suffers from a serious limitation: it is temporary. The insect might be able to extract more oxygen from the bubble than was originally contained in it, but invariably the bubble will shrink, and the animal will have to return to the surface to replenish it. But air is a mixture of oxygen and nitrogen. When a beetle replenishes its bubble, what, exactly, is being replenished? The simplest answer to this question is that, obviously, it is the oxygen that is being replenished—it is oxygen that is consumed, and so it is the oxygen that must be replaced. The simplest answer is, in this case, not quite the correct answer—illustrating, again, the dangers of relying too closely on Occam's razor.

A bubble's effectiveness as a gill is enhanced by slowing the bubble's shrinkage rate. The longer the bubble endures, the longer the beetle will be able to extract oxygen from the water, and the more oxygen it will extract. In fact, it is fairly easy to predict how effective a bubble gill will be from a number known as the gill factor, G. The gill factor simply compares the quantity of oxygen extracted from the water with the quantity of oxygen initially contained within the bubble. A gill factor of five, for example, means that a bubble gill initially containing one milliliter of oxygen will extract five milliliters of oxygen from the water.

The gill factor is determined by the relative ease with which nitrogen and oxygen cross the boundary between the bubble and water. This is quantified by the invasion coefficient, i, which is the product of two properties: the diffusion coefficient of the particular gas in water, D, and the gas's Bunsen solubility coefficient, a. The invasion coefficients for oxygen, nitrogen, and carbon dioxide are as follows:

icO2 = ®Co2Dco2 = 1.56 X 10-7 cm2 s-1 kPa-1 [8.3c]

Note that carbon dioxide has the largest invasion coefficient, nearly two orders of magnitude larger than the coefficients for oxygen or nitrogen. Carbon dioxide, therefore, crosses the boundary between bubble and water most rapidly of the three. Paradoxically, this means that CO2 will have little role to play in the behavior of a bubble gill: it leaves the bubble so rapidly once it is released from the insect's body that it contributes only slightly to the bubble's total pressure. However, the invasion coefficients of oxygen and nitrogen are closer in value, with nitrogen's being about half that for oxygen. This similarity has important implications for the performance of bubble gills. Oxygen's larger invasion coefficient means it will cross the boundary between the bubble and water more rapidly than nitrogen. Consequently, in a bubble standing alone, the air contained in it will become richer in nitrogen as the bubble shrinks. A bubble gill turns this disparity to advantage. As long as the animal keeps the oxygen's partial pressure lower in the bubble than in the water, oxygen's larger invasion coefficient will ensure that oxygen flows into the bubble more rapidly than nitrogen flows out. Thus, bubble volume is maintained mostly by the nitrogen: oxygen is mainly flowing through the bubble rather than into it. It is the presence of the nitrogen, therefore, that retards the shrinkage rate of the bubble and permits it to exist as a gill for a longer time. How long is made explicit by calculating the gill factor for a bubble gill. Gill factor is:

where fO2 and fN 2 are the fractional concentrations of oxygen and nitrogen, roughly 0.21 (21 percent) and 0.79 (79 percent), respectively. Plugging in the numbers reveals the gill factor for a bubble gill made from air to be about 8.3. A bubble gill therefore delivers to the beetle 830 percent of the oxygen initially contained in the bubble. But look what happens if the quantity of nitrogen in the bubble (expressed as fNi) is allowed to drop, say, to 60 percent (fNi = 0.6) and oxygen is elevated to 40 percent (fOi = 0.4): the gill factor drops to 3.28, and the bubble extracts less oxygen.

Clearly, what is being replenished by the insect dur ing its trips to the surface is not the oxygen in the bubble but the nitrogen. The oxygen initially contained in the bubble is quickly used up: the insect will benefit only if this oxygen can be replaced with oxygen from the water. These benefits accrue only as long as the bubble endures, and this is ensured by the continuing presence of nitrogen: it is the maintenance of nitrogen volume in the bubble rather than the extraction of oxygen that is the secret of the bubble gill.

Clearly, the simplest explanation for bubbles as diving bells is wrong on two counts. First, the bubble is not a buoyancy device, it is a respiratory structure even if it is used in different ways by different types of diving beetles. Second, it functions as a respiratory structure not because of the oxygen contained within it but because of the nitrogen. Thus, diving bell spiders and some beetles are solving the problem of being aquatic air breathers in a manner similar to how physiologically aquatic earthworms inhabit soil. Rather than retooling their bodies to form gills, aquatic beetles and spiders have solved their gas exchange problems by co-opting their locomotory muscles to power a bulk flow of nitrogen from air into a submerged structure that does the work of a gill for them.

### The Plastron Gill

We still don't have a good explanation for bubble-carrying beetles that don't need to surface. However, our more complex, but more correct, understanding of bubble gills now lets us use Goldberg's lever to pry out the answer.

Bubbles normally collapse because the forces acting on them—hydrostatic pressure, surface tension, gas partial pressures—never balance. Bubble gills work because the insects using them intervene and manipulate two of these forces—partial pressures of oxygen and nitrogen—to delay the bubble's inevitable demise. What would happen, though, if an insect could somehow stop the bubble's march to self-destruction? Let us explore this question with a thought experiment.

We begin, as we did before, with a bubble formed from air and submerged to a certain depth. As the bubble is submerged, the increased hydrostatic pressure compresses the bubble, raising the partial pressures of all the gases in it. Oxygen and nitrogen therefore begin to diffuse out. So far, I am describing the behavior of a conventional bubble. As part of our thought experiment, though, let us do something novel. A real bubble is flexible, and its size can change depending upon the balance of forces acting on it: increase the hydrostatic pressure squeezing the bubble and it shrinks, for example. Let us now suppose that our imaginary bubble is stiff, so that it no longer can change size (Fig. 8.5). The gases in the stiff bubble can now come into equilibrium with the gases in the water in a way that they could not in the flexible bubble. Specifically, nitrogen and oxygen will diffuse out of the bubble, driven by their temporarily elevated partial pressures, until these partial pressures equilibrate with the pressures of the gases in solution.

Let's now complicate our thought experiment a bit: allow a beetle to breathe from the stiffened bubble and see what happens to the gas concentrations in it (Fig. 8.5). For two of the gases, nitrogen and carbon dioxide, the beetle will have little or no effect. The beetle neither consumes nor produces nitrogen, and because the bubble nitrogen is already in equilibrium with the water (ApN2 = 0), the bubble pN2 will be unchanged. As the beetle releases carbon dioxide into the bubble, its very high invasion coefficient will ensure that it dissolves rapidly in the water, keeping the bubble pCO2 near zero. But with oxygen, the picture is different. As the beetle consumes oxygen, the pO2 in the bubble obviously must fall, which drives a flux of oxygen in. The magnitude of this flux, as we well know by now, will be proportional to the ApO2, and this will increase until it is sufficiently large to deliver oxygen from the water as fast as the beetle consumes it. There it will come to equilibrium, allowing the beetle to sit and extract oxygen from the water indefinitely. The only reason a beetle with a stiff bubble ever need come to the surface

time shrinking bubble %

Figure 8.5 The development of a plastron gill. a: A hypothetical "rigid bubble" is attached to an insect consuming oxygen. b: Comparisons of the course of pO2(b) in a "rigid" bubble and a bubblethat is able to shrink. The pO2(b) in a rigid bubble doesn't increase, so oxygen continues to enter the bubble from the water. c: Comparisons of the course of pN2(b) in a "rigid" bubble and a bubble that is able to shrink. Eventually, pN2(b) reaches equilibrium with pN2(s).

time

Figure 8.5 The development of a plastron gill. a: A hypothetical "rigid bubble" is attached to an insect consuming oxygen. b: Comparisons of the course of pO2(b) in a "rigid" bubble and a bubblethat is able to shrink. The pO2(b) in a rigid bubble doesn't increase, so oxygen continues to enter the bubble from the water. c: Comparisons of the course of pN2(b) in a "rigid" bubble and a bubble that is able to shrink. Eventually, pN2(b) reaches equilibrium with pN2(s).

would be depletion of the oxygen in the water (which sometimes happens if the beetle is sharing its home with lots of other things that consume oxygen) or for needs unrelated to respiration (like having to lay eggs out of the water).

We now see how a bubble-carrying beetle could live underwater indefinitely. If a bubble gill's shrinkage could be opposed somehow, it could extract oxygen from the water indefinitely, and the beetle carrying it would never have to replenish it. The kind of gill I have just described in fact is widely employed by diving beetles, and it is called a plastron gill.5 Our little thought experiment has shown us how plastron gills work—if anything, they are simpler than conventional bubble gills. Most importantly, though, the thought experiment has given us a design principle for plastron gills: "stiffen" the bubble. In looking for novel types of plastron gills, one should look for mechanisms that make bubbles stiff, that is, resistant to collapse.

Let us apply this principle to a conventional plastron gill, formed from a permanent bubble carried on the surface of an insect's body. The internal pressures of a stiff bubble will come to a steady state when its internal pressure is ApO2 below the hydrostatic pressure acting on the bubble. In a formula:

where Pb and Ph are, respectively, the total pressure in the bubble and the hydrostatic pressure on the bubble (Fig. 8.6). The bubble is, therefore, operating under an imbalance of forces: water is squeezing down on it more powerfully than the gas in the bubble is pushing out. A real bubble, in contrast to our imaginary stiff bubble, would collapse under this imbalance. The fact that the bubble of a plastron gill does not can only mean that there is some force, not accounted for in

5. Plastron is from the Greek for "breastplate," so called because the bubble is usually carried on the beetle's ventral surface (onits "chest," as it were).

chitin hair (XS)

hydrostatic pressure