Over the ocean, carbon dioxide rests at equilibrium between the water and gas phases. The CO2 will dissolve in water, but not infinitely, and if there is too much CO2 in the water it pops back out into the air. The amount of CO2 that stays in the water at any given time is set by the pH of the ocean - the lower the pH, the more CO2 the ocean can carry. At the ocean's current pH, seawater carries about 147 times more CO2 per unit volume than air. This makes it a very concentrated source of CO2, promising for anyone who aims to extract that carbon dioxide for long term storage.
How do you get the CO2 out of the water? One way might be take a filtered sample of ocean water and boil it off to collect the gases. This, as one can imagine, would use a lot of energy - the ocean is mostly water, after all. This kind of approach is not economic. An alternative approach would be to add chemicals to the water, either a base to crash out the CO2 as a carbonate, or an acid to change the pH so the CO2 partitions back to air. Both of these approaches require transporting lots of chemicals, and so have their limits as well (though moving base to the ocean has merit in some geographies).
The best solution would be to create acid and base in situ, in ocean water. This can actually be done thanks to the unique property of water that it can act simultaneously as a weak acid (a source of protons) and a weak base (a source of hydroxides). Using a process called electrodialysis, seawater is passed in between two membranes, one of which is permeable only to positive charges like protons, the other only to negative charges like hydroxides. When a voltage is dropped across this system, protons in the water migrate through the first membrane to form an acidic stream, while hydroxides in the water migrate through the second membrane to form a basic stream. For every molecule of acid, a molecule of base is created, but these streams are physically separated and can be handled independently.
The CO2 in the acid stream tends to want to go back to the gas phase, and pulling a small vacuum on it will encourage it to turn to vapor, where it can be captured. This is more or less the process being scaled by Captura, a VC-funded spin-off from Caltech. Once the CO2 is captured, the acid and base streams are recombined and returned to the ocean. Other approaches can be used as well - the startups Heimdal and Ebb Carbon are performing this process in brines formed at reverse osmosis plants, and are capturing and selling the HCl acids they produce as well. Seachange, a startup from UCSD, is using the acid stream to accelerate rock weathering, and reacts the CO2 with rock rather than pulling a vacuum to capture it. The rock is dumped in the ocean at the end of the process, increasing the available carbonate stocks in the sea as well.
All of these approaches are interesting science projects, but they don't become technologies unless the electrodialysis membranes are cheap and durable enough. Today, electrodialysis is used in some industrial processes in ways that are similar to how they'd be used in carbon capture. But industrial processes use controlled conditions, and oceans are a bit more free-form. The estimates for the cost of electrodialysis processes today are generally >$200/ton CO2 captured, though the brine process creates an additional revenue stream that will lower the effective cost further.
Good materials science can matter a lot here, but good materials science is hard, and often slow. I don't consider these electrodialysis processes candidates for scale up in the short term. But the space is worth watching.
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