Key Takeaways
- A Harvard study shows that soft materials, like gels and biological tissue, support boat wake-like surface waves.
- Because wake shape encodes material properties, the surface patterns could offer medical diagnostic applications.
A new study by scientists in the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) shows that when a pressure disturbance moves across an ultrasoft elastic material, such as a gel or a biological tissue, it generates a V-shaped wake that’s strikingly similar to the waves that travel behind a boat.
Published in Physical Review Letters, the study offers a unified perspective, combining experiments and theory, on surface motion that spans fluids, solids, and the soft materials that lie between. It opens the door to new approaches to imaging and understanding the behavior of both natural and engineered soft materials.
The research was led by L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, Organismic and Evolutionary Biology, and Physics, in SEAS and FAS, and includes first author and former postdoctoral researcher Aditi Chakrabarti; postdoctoral researcher Divya Jaganathan, and SEAS research associate Robert Haussman.
Mahadevan said he was initially led by simple curiosity. “I suspected that there ought to be a natural way to smoothly interpolate between the behavior of surface waves on solids and fluids, partly inspired by watching boat wake along the Charles, where I walk almost every day,” he said.
The subject lay dormant until Chakrabarti was able to create an experimental setting to visualize these wakes. Working together with Jaganathan, the team was then able to provide a theoretical framework to explain their observations quantitatively.
For over a century, scientists have treated ship wakes and surface waves in solids as fundamentally different phenomena. The wakes behind a boat, first explained by Lord Kelvin, arise from waves on a liquid surface. By contrast, waves that travel along the surface of solids, such as from earthquakes, first explained by Lord Rayleigh, behave differently. The new Harvard study reveals that very soft materials, such as biological tissue, blur this distinction.
In these materials, waves ripple outward like water but also deform the material like an elastic solid. The result is a hybrid behavior — a wake that looks familiar but carries new information about the material itself.
At the heart of the discovery is a simple geometric idea: the angle of the wake depends on how fast the disturbance moves, compared to how quickly waves can travel through the material. When the disturbance moves faster, or when the material is softer, the wake narrows. This relationship turns the wake into a natural diagnostic signal. Rather than probing a material by pressing into it or cutting through it, one can infer its properties simply by observing how waves propagate along its surface.
The insight could have implications for soft-tissue diagnostics in medical contexts, in which clinicians measure the stiffness of tissue, for example, to detect tumors. In effect, soft tissues can be “read” through the wakes they produce.
Beyond applications, the study points to a broader principle: moving disturbances leave behind patterns that reflect the inner physics of the medium. What’s more, Mahadevan said: “Much of our work reflects a broader scientific instinct: to search for the sublime, and the arcane, hidden within the mundane,” and this is one more example of how the everyday ordinary world is full of wonders, if we only choose to see carefully.”
Press Contact
Anne J. Manning | amanning@seas.harvard.edu