Nonlinear Dynamics of Multi-Gas Bubbles: Time Evolution of Carbon Dioxide and Air in Aqueous Systems

The way gas bubbles behave and interact in liquids has fascinated scientists for years because they play a huge role in all sorts of natural events and everyday processes from the dramatic release of gases during a volcanic eruption to the fizz that makes soda bubbly. Even in cutting-edge medical therapies, understanding how bubbles form, grow, and collapse is key to tackling real-world problems across a variety of fields. Traditionally, researchers have kept things simple when studying bubbles, often assuming that they are made of just one type of gas, like carbon dioxide (CO₂) or air. However, bubbles in nature or industry are usually made of a mix of gases with different properties and these mixed-gas scenarios lead to bubble behaviors that just do not fit into the neat predictions of classic theories. The main challenge lies in how differently gases dissolve in water. For instance, CO₂ dissolves really well, while air is far less soluble. This mismatch creates unusual and surprising effects. Bubbles made of both CO₂ and air might grow in fits and starts, hold steady at certain sizes, or suddenly collapse when you least expect it. Classic bubble theory, which assumes bubbles either shrink to nothing or grow forever once they pass a critical size, simply cannot explain these quirks. Multi-gas interactions at the surface of a bubble are much more complex than that. A recent study, published in the journal Colloids and Surfaces A by Dr. Tomohiro Onda, tackles these challenges. Dr. Onda, a former research fellow at Kao Corporation in Japan, investigated how bubbles containing both CO₂ and air change over time. He used a mix of precise mathematical equations and computer simulations and developed equations to track bubble size and the pressures of the gases inside them.

At the center of his research were complex equations describing how a bubble’s size and the gas pressures inside it change over time. These equations took into account key factors like gas movement across the bubble’s surface, surface tension, and the give-and-take between CO₂ and air as they flowed in or out of the bubble. Dr. Onda solved these equations in two ways: analytically, to simplify things for easy cases, and numerically, for more complicated, real-world situations. The goal? To figure out how a single bubble’s size changes depending on its starting conditions, like how much CO₂ and air it contains or how big it is.

What he discovered was truly exciting. Bubbles with just CO₂ tend to behave predictably—they either grow steadily or shrink and disappear. But when both CO₂ and air are involved, things get much more chaotic. Some bubbles grew, shrank, then vanished altogether. Others hit weird plateaus, staying the same size for a while before eventually collapsing or growing uncontrollably. These unusual patterns came down to how CO₂, being highly soluble, diffuses in or out of the bubble much faster than air, which has low solubility. This imbalance creates strange dynamics. In some cases, bubbles even showed a “shrink-then-grow” behavior. As CO₂ rapidly escaped and its pressure dropped to an equilibrium point, air slowly diffusing into the bubble started to dominate its behavior, triggering a rebound in size. Dr. Onda also found that bubbles temporarily “paused” near their critical size, forming plateaus, and became incredibly sensitive—tiny changes in gas pressures could mean the difference between growing endlessly or vanishing completely. According to the author, he found that bubbles changed sluggishly when the rates of CO₂ leaving and air entering the bubble or those of CO₂ entering and air leaving the bubble nearly balanced each other. But these states didn’t last long—small changes eventually tipped the balance, and the bubbles either expanded or collapsed rapidly. Moreover, Dr. Onda’s simulations showed just how much a bubble’s initial makeup matters. Start with more air, and the bubble might grow before shrinking and collapsing. Start with mostly CO₂, and it could shrink first, then rebound as CO₂ and air diffuse in.

In conclusion, Dr. Tomohiro Onda’s research brings a fresh perspective to something surprisingly complex—bubbles. But these are not just any bubbles. They are tiny, dynamic systems made up of multiple gases, like CO₂ and air, that behave in unexpected and fascinating ways. Unlike single-gas bubbles, which tend to grow or shrink predictably, these mixed-gas bubbles can do all kinds of strange things: grow unevenly, temporarily stabilize at a certain size, or even collapse without warning. This work challenges older theories and fills a critical gap in our understanding of how bubbles actually behave in real-world scenarios. The practical impact of this research stretches across a wide range of industries. In everyday products like carbonated drinks, for instance, these findings could help companies fine-tune their formulas to control fizz, ensuring every sip feels just right. In skincare, where CO₂ bubbles are used in some products to deliver hydration or therapeutic benefits, understanding how bubbles stabilize could lead to better, longer-lasting results. Even in medical gas delivery systems, this knowledge could improve how gases are handled and delivered safely and effectively.

There is also a strong connection to the medical world. Decompression sickness, often called “the bends,” happens when bubbles form in a diver’s bloodstream due to rapid pressure changes. Dr. Onda’s work offers a way to better understand how these bubbles form, shrink, and dissolve, potentially improving both prevention and treatment strategies for divers and others exposed to sudden pressure shifts. Volcanologists, too, can take away valuable insights. Magma is full of bubbles made of mixed gases, and these play a big role in how eruptions unfold. By better understanding how these bubbles behave—especially how they grow, collapse, or stabilize—scientists can refine their models of volcanic activity and make better predictions, potentially saving lives in areas prone to eruptions. Engineers working in fields like wastewater treatment, chemical manufacturing, and gas delivery systems could also use these insights to design more efficient processes. Bubble behavior often determines how well gases are transferred in these systems, and accounting for the unique dynamics of mixed-gas bubbles could lead to big improvements in efficiency and energy use. Ultimately, this research is just the beginning.