A small bubble bursting in a liquid seems more whimsical than traumatic. But millions of bursting vapor bubbles can cause significant damage to rigid structures like boat propellers or deck supports. Can you imagine the damage such bubbles could cause to soft human tissue like the brain? In head impacts and concussions, vapor bubbles form and collapse violently, damaging human tissue. Fluid mechanics researchers at Purdue University have taken a step closer to understanding these phenomena.
The behavior of bubbles bursting in a liquid is generally understood. But when these bubbles form in a soft porous material, like human brain tissue, the physics becomes more complex.
“When a bubble collapses inside a liquid, it generates pressure shock waves,” said Hector Gomez, professor of mechanical Engineering and principal investigator. “The process of a vapor cavity forming and collapsing is what we call cavitation.”
“Cavitation has been studied since the 1800s,” said Pavlos Vlachos, professor of health engineering at St. Vincent and director of the Regenstrief Center for Health Engineering. “It’s a very complex area of study because it involves non-equilibrium thermodynamics, continuum mechanics, and many other micrometer- and microsecond-scale factors. After hundreds of years of research, we are only just beginning to understand these phenomena.
Even less is known about bubbles collapsing in soft porous materials, such as the brain or other bodily tissues. This is important, because understanding how these bubbles behave could lead to a better understanding of concussions – or even be used to deliver targeted drugs inside the body.
In new research published in the Proceedings of the Nexus of National Academies (PNAS)Gomez, Vlachos and collaborators presented the development of a mathematical model to describe the dynamics of these cavitation bubbles in a deformable porous medium.
Cavitation happens throughout the human body – for example, the cracking sound of your joints is the sound of bubbles bursting in the synovial fluid of your joints. When fluids inside the body are subjected to pressure waves – such as when football players experience head impacts – bubbles can form in the fluid surrounding the brain. And just like bubbles that damage boat propellers, bubbles that burst near the brain could damage its soft tissue.
“The human brain is like a slimy sponge filled with water; it has the consistency of gelatin,” Vlachos said. “Its material is porous, heterogeneous and anisotropic, creating a much more complex scenario. Our current knowledge of cavitation does not directly apply when such phenomena occur in the body.
Gomez and his collaborators developed a theoretical and computational model showing that the deformability of a porous material slows the collapse and expansion of cavitation bubbles. This breaks down the classic scaling relationship between bubble size and time.
“Our model embeds bubbles in deformable porous materials,” said Yu Leng, the paper’s first author and postdoctoral research associate working with Gomez. “Then we can extend the study of cavitation bubbles in pure liquid to soft tissues such as the human brain.”
Although complex, this model can also be reduced to an ordinary differential equation. “A hundred years ago, Lord Rayleigh developed the equation that describes the dynamics of a bubble in a fluid,” Gomez said. “We were able to augment this equation to describe when the medium is poroelastic. It’s quite amazing that this complex physics always leads to a simple and elegant equation.
Gomez and Vlachos are currently planning experiments to physically validate their results, but they are also considering the big picture. “One potential application is targeted drug delivery,” Gomez said. “Let’s say you want to deliver a drug directly into a tumor. You don’t want this drug dispersing elsewhere. We’ve seen encapsulations that hold the drug in isolation until it hits its target. Encapsulation can be broken using bubbles. Our research provides insight into how these bubbles collapse in the body and can lead to more efficient drug delivery.
“Another example of future possibilities is traumatic brain injury,” Leng said. “We can extend this research to study the impact of uncontrolled cavitation collapse on brain tissue when military personnel and civilians are exposed to shock waves.”
Gomez and Vlachos say they are excited to establish new basic science for understanding bubble dynamics in soft porous materials. “It opens up all kinds of possibilities for future research,” Gomez said, “and we’re excited to see how we and others will use this knowledge in the future.”
This research was supported in part by the US Department of Defense under the DEPSCoR program (Award FA9550-20-1-0165), the National Science Foundation (Award 1805817), and the US Department of Energy (Grant DE-SC0018357 ).
Screenwriter: Jared Pike, [email protected]765-496-0374
Source: Hector Gomez, [email protected]
Pavlos Vlachos, [email protected]
Cavitation in a soft porous material
Yu Leng, Pavlos P. Vlachos, Ruben Juanes and Hector Gomez
We study the collapse and expansion of a cavitation bubble in a deformable porous medium. We develop a continuum-scale model that couples the compressible fluid flow in the pore network with the elastic response of a solid skeleton. Under the assumption of spherical symmetry, our model can be reduced to an ordinary differential equation which extends the Rayleigh-Plesset equation to bubbles in soft porous media. The extended Rayleigh-Plesset equation reveals that finite size effects lead to the breaking of the universal scaling relationship between bubble radius and time that holds in the infinite size limit. Our data indicate that the deformability of the porous medium slows the processes of collapse and expansion, a result with important consequences for large-scale phenomena, from drug delivery to spore dispersal.