In their textbook "Ecological Economics" (2004), Herman Daly and Joshua Farley say that the limits to human population growth may lie not in resource depletion, but in the waste absorption capacity of the environment. This can be understood with the following analogy. Water purification filters usually contain a resin that turns color when it becomes saturated, i.e., it cannot absorb any more pollutants. The interface between the two colors of resin (the reaction front) will migrate through the column from the inlet towards the outlet. Water flowing from the outlet will be purified until the interface reaches the end of the column, at which point the column resin is saturated in pollutants and cannot absorb any more. From that time on the outlet water will be just as polluted as the input water. In this case, the waste absorption capacity of the filter has been exceeded. Our environment acts as a filter, purifying water that passes through it, but eventually the filter will become saturated.
Let’s examine this in a little more detail. What happens when the concentration of a pollutant in a sediment-water system (lake or stream) keeps increasing? Examine langmuir 10-007. Imagine that we pour uranium U into a beaker containing water and sediment. Some of the U will dissolve in the solution, but some will adsorb onto the surface of mineral grains in the sediment. At first the proportions of U in solution and adsorbed to sediment will be constant as the total U concentration increases (move along a straight line away from the origin). As concentrations get higher the number of available sites for U to sorb onto mineral surfaces begins to decrease, and a greater proportion of U enters the fluid, causing the adsorption isotherm to level off and approach a slope of zero when the adsorption sites become “saturated”. Eventually even the solution becomes saturated, i.e., it can’t dissolve any more U. What happens then? Any additional U added to the system will precipitate out as a U-rich mineral (in this case Schoepite) that is added to the sediment and therefore causes the sediment concentration of uranium to begin increasing again. Note that as long as the solutions remains saturated in Schoepite, any additional U we add will go into the sediment, increasing the U concentration in the sediment. Conversely, no matter how much additional U we add, the concentration of U in the solution is fixed at its highest possible concentration. In this case, we have saturated our filter.
Let’s look at some slightly more complicated models in which the sediment but not the solution becomes saturated. Polluted water enters a beaker with sediment, equilibrates with the sediment, and then is replaced with another batch of polluted water. At first, a large proportion of the pollutant will sorb onto the sediment, causing the concentration in the solution to decrease substantially. As more batches of polluted water equilibrate with the sediment, the concentration of pollutant in the sediment will increase, and therefore the concentration of pollutant in the water that exits the beaker will increase in direct proportion. As the sediment approaches “saturation”, it can sorb less pollutant, so most of the pollutant remains in solution, and our sediment filter become increasingly ineffective.
What if we stop polluting? Can the system recover? Start adding batches of fresh water. You would observe that the water that exits the beaker would at first have high concentrations of pollutant because our sediment filter was saturated in pollutants. But with time, the concentration of pollutant in the sediment and in the exiting fluid would decrease and eventually go to zero. Thus, we can “flush” pollutants out of a sediment-water system such as a stream or lake, but it may take a long time and a lot of fresh water to remove all of the pollutant, especially if the pollutant strongly sorbs to the sediment (which is why PCB’s are still in Hudson River sediments after many decades).
Now imagine a reservoir such as a swamp with one stream entering and one stream exiting. If the stream entering the swamp is polluted, sediments near its entrance point will strip pollutants out of solution. With time, a concentration gradient will develop across the swamp, with high pollutant levels near the input stream and low levels near the output stream. As polluted water flows across the swamp, it encounters sediments with decreasing pollutant concentrations, so the concentration of the pollutant in the solution will continuously decrease. The water becomes increasingly pure as it traverses the swamp. In nature, swamps do an excellent job of filtering pollutants from water. However, if pollutants continue to enter the swamp, the total pollutant concentration in the swamp will keep increasing. Eventually sediments near the input stream will become saturated, and that “saturation front” will slowly migrate across the swamp until it reaches the output stream. At that point the entire swamp system has become saturated, and the output water will be just as polluted as the input water. As in our beaker example, if we stop polluting and the water in the input stream becomes pure again, then over time the process will be reversed, and the pollutants will slowly be flushed out of the swamp.