Researchers at Rice University, led by Sibani Lisa Biswal, chair of the Department of Chemical and Biomolecular Engineering, have identified a physical mechanism that explains how a single filament can form a knot while moving through a fluid under strong gravitational forces. The work addresses a long-standing question in soft-matter physics and polymer science: how an isolated filament, without collisions or external manipulation, can knot itself.
Cunha, L. H. P., Tubiana, L., Biswal, S. L., & MacKintosh, F. C. (2025). Hierarchical Knot Formation of Semiflexible Filaments Driven by Hydrodynamics. Physical Review Letters, 135(24), 248201. https://doi.org/10.1103/z7jb-fvjl
Knots are common across natural and engineered systems, appearing in DNA, proteins, synthetic polymers, and everyday materials. While knot formation in long, flexible chains is well documented, it has been difficult to explain how shorter or relatively stiff filaments could develop stable knots without external forcing. Traditional models typically assume that knotting requires either multiple interacting filaments or active mechanical agitation.
Sibani Lisa Biswal from Rice University stated,
“Our study suggests an experimentally achievable way to obtain long-lived, tight, complex knots in very short polymers, opening the possibility to better connect knot theoretical and polymer theory predictions with experimental observations.”
The new study shows that gravity-driven motion through a viscous fluid can be sufficient on its own. Using Brownian dynamics simulations, the researchers demonstrated that as a semiflexible filament sediments under strong gravitational fields, long-range hydrodynamic interactions between the filament and the surrounding fluid induce bending and folding. These flows cause one part of the filament to compact into a dense leading region while the remainder stretches into a trailing tail.
This uneven distribution of tension and drag creates configurations where loops naturally form and cross. Once crossings occur, the filament can reorganize into knotted states that persist over time. Rather than appearing instantaneously, the knots evolve gradually, tightening and rearranging into more stable topologies as the system relaxes under hydrodynamic forces.
The simulations revealed that both filament flexibility and gravitational strength play central roles. More flexible filaments were able to form a wider range of knot types, while stronger gravitational fields increased the probability that knots would not only form but remain stable. At sufficiently high field strengths, tension within the filament and friction between nearby segments acted together to prevent the knot from unraveling.
According to the researchers, this process resembles a hierarchical evolution rather than a single event. Initial loose configurations reorganize through a sequence of intermediate states, gradually settling into tighter and more persistent knots. This behavior provides insight into how complex topologies can emerge from relatively simple physical conditions.
The findings have implications beyond fluid mechanics. In biological systems, knotting influences how macromolecules such as DNA and proteins behave under confinement or flow. Knots can affect how genetic material is packed inside viruses, how DNA moves through nanopores, and how polymers separate during electrophoresis. Understanding the physical origin of knot formation helps clarify when such structures are likely to appear and how long they may persist.
From an engineering perspective, the work also informs the design of soft materials and nanostructures. If knotting can be controlled through external fields and fluid conditions, it may become possible to tune mechanical properties through topology rather than chemistry alone. This could be relevant for applications where strength, elasticity, or energy dissipation are influenced by internal structure.
The study also suggests a practical route for creating stable knots in relatively short polymers, something that has been difficult to achieve experimentally. Existing methods often require very long chains or specialized manipulation. Gravity-driven knotting, by contrast, relies on conditions that can be achieved using centrifugation or controlled flow environments.
By showing that hydrodynamics and gravity alone can drive knot formation, the research challenges conventional assumptions about polymer behavior in fluids. It highlights how subtle interactions between flow, force, and flexibility can lead to complex structures, even in systems that appear simple at first glance.
As researchers continue to explore how topology influences material behavior, this work provides a clearer physical foundation for understanding when and how knots emerge. It also opens opportunities for leveraging fluid-driven self-organization in both biological studies and engineered systems, where controlling structure at small scales remains a central challenge.
Adrian graduated with a Masters Degree (1st Class Honours) in Chemical Engineering from Chester University along with Harris. His master’s research aimed to develop a standardadised clean water oxygenation transfer procedure to test bubble diffusers that are currently used in the wastewater industry commercial market. He has also undergone placments in both US and China primarely focused within the R&D department and is an associate member of the Institute of Chemical Engineers (IChemE).
