New research explains how particles move in complex fluids under intermittent dynamics
June 4, 2025 | Kalyani Murali
Schematic representation of a diffusive colloidal particle undergoing stochastic resetting in a viscoelastic bath (featured as cover image in the Special Issue).
IMSc researchers and collaborators have developed a new theoretical framework to track particles in a complex fluid while they randomly start from scratch.
When we suspend pollen grains in water, they move randomly in the medium (the water) in a process known as Brownian motion. In this random journey, they collide with other particles, some of pollen and others of water. Now, consider some pollen stirred not into water but honey – a typical example of a viscoelastic medium, with liquid-like properties that deforms under stress but regains shape when the applied force is removed. In such a medium, the pollen grains face a lot more collisions. A group of researchers have recently described how solute particles (pollen in this example) move in a viscoelastic medium while randomly returning to their starting position.
In a recent study, researchers from The Institute of Mathematical Sciences (IMSc), Chennai along with collaborators from Delft University of Technology and Macedonian Academy of Sciences and Arts have made progress in resolving the complex dynamics of solute particles in a viscoelastic medium. In this work, they derived a general expression for the spread around the mean position of particles in a viscoelastic medium over time.
Viscoelastic media can deform and also retain their shape. For example, when squeezing a ketchup bottle, the ketchup deforms due to the applied stress while making its way out – a characteristic feature of elasticity. On the contrary, it retains its shape well when poured onto a flat surface – a feature of a viscous fluid. A viscoelastic medium also has a property of memory, where previous collisions of solute particles affect their subsequent behaviour.
In their paper, the researchers extended the existing theory of how solute particles behave in such fluids with memory, known as the Generalized Langevin Equation (GLE), while incorporating stochastic resetting dynamics. Stochastic resetting is a phenomenon where particles, while moving through the medium, intermittently reset to their starting points following a random waiting time.
The authors show that at very high resetting rates, the suspended particles move randomly without experiencing the usual resistance seen in a viscoelastic medium. In other words, they behave like Brownian particles. The researchers also validate their theoretical results using numerical simulations. This work establishes a theoretical framework for understanding resetting dynamics in a viscoelastic medium, opening future avenues of research in transport dynamics within complex fluids.
“We are currently investigating the ‘first-passage’ aspect of a viscoelastic particle under resetting. We are trying to see whether resetting can facilitate a search process conducted by particles in a viscoelastic medium”, says Arup Biswas, the lead author of the study. “The GLE is well established in capturing subdiffusive dynamics, particularly in describing equilibrium fluctuations of protein conformations. However, a key open challenge lies in understanding the timescale at which such a protein reaches its native state when it intermittently unbinds and resets to its initial conformation. Our forthcoming aim is to address this gap by developing a first-passage framework for systems with memory under stochastic resetting.” adds Arnab Pal, the lead Principal Investigator of this project.
Another immediate step is to study this phenomenon when resetting is not instantaneous and takes time. “This is particularly relevant to resetting experiments with colloids in viscoelastic medium and optical traps. The experiments are currently being conducted elsewhere, which we believe, will also shed light on the non-equilibrium responses due to resetting,’’ concludes Arnab.
Reference: Biswas, A., Dubbeldam, J. L. A., Sandev, T., & Pal, A. (2025). A resetting particle embedded in a viscoelastic bath. Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(3), 031102. https://doi.org/10.1063/5.0253019
