Probing non-equilibrium patterns in active complex fluids

A complex fluid material made up of active particles is inherently out of equilibrium due to the activity, or movement, of the particles. Examples of active particles include colloidal nanomotors and swimming microorganisms. The interactions between active particles are often termed non-reciprocal, in apparent violation of Newton's third law of motion, which states that every action has an equal and opposite reaction.

Researchers at Carnegie Mellon and their collaborators created an experimental active droplet system to probe the patterns that develop in materials with non-reciprocal interactions. "With this chemical system, we can explore non-reciprocal interactions that can lead to structures that you couldn't see in equilibrium systems," says Aditya Khair.

A new study in Angewandte Chemie advances the understanding of how non-reciprocal systems self-organize into predictable patterns without external forces like magnetic or electrical fields. Harnessing these systems can be applied to develop new materials that are reconfigurable or stimuli-responsive, like those needed for pollutant removal or medical treatment.

Through experimental and computational approaches, researchers looked at a model non-reciprocal system of active droplets. Around a millimeter in size, active droplets are oil droplets that solubilize in an aqueous solution of micellar surfactants. Under certain conditions, as fluid mechanical stresses develop on the surface of the droplets, they will move relative to each other. "There's no external force making an active droplet move. In some sense, it's converting the chemical energy associated with solubilization into motion," says Khair, professor of chemical engineering at Carnegie Mellon. If a pair of droplets solubilizes at different rates, they experience non-reciprocal interactions that lead to the center of mass between the droplets changing in time. What is happening to one droplet is not equal and opposite to the other, a violation of Newton's third law.

Much of the literature on active droplet systems is about single droplets or pairs of droplets, even though materials processing applications would involve many droplets. To help meet this need, Khair joined researchers at The Pennsylvania State University and Eindhoven University of Technology to investigate the larger scale structures of active droplet systems that non-reciprocal interactions drive.

With this chemical system, we can explore non-reciprocal interactions that can lead to structures that you couldn't see in equilibrium systems.

Aditya Khair, Professor, Chemical Engineering

They first experimented with a binary system of two types of oils, which solubilize at different rates because they are chemically different. The different solubilization rates set off a non-reciprocal interaction. Experiments showed that the droplets self-organize into structures ranging from chains to flowers to clusters. Researchers then looked at ternary systems, with three types of oil droplets, and found a hierarchy of structures.

Khair and R. Kailasham, then a postdoctoral fellow in the Department of Chemical Engineering and now a faculty member at IIT Indore, defined quantitative metrics to analyze the experimental results. They also compared the experimental results against a simulation model. The model idealized the active droplets as active disks that can emit a dissolved substance at different rates, driving non-reciprocal interactions. "We saw a reasonable qualitative agreement between the simulation framework and the experiments," says Khair.

The research leverages insights from pairs of active droplets to understand much larger scale suspensions of droplets. Although Khair's work is centered in colloid science and complex fluids rheology, non-reciprocal interactions are considered to be an inherent feature of all out-of-equilibrium systems, including social systems. People, for example, respond to stimuli in different ways, leading to non-reciprocal effects.

For media inquiries, please contact Lauren Smith at lsmith2@andrew.cmu.edu.

Video source, top: Y. Liu, R. Kailasham, P. G. Moerman, A. S. Khair, L. D. Zarzar, Angew. Chem. Int. Ed. 2024, 63, e202409382. https://doi.org/10.1002/anie.202409382