Extracting Active Fluctuating forces from Fluctuating motions of an active particle in a viscoelastic medium.

The study of active Brownian particles in viscoelastic media reveals the complex interplay between active and passive forces, resulting in combined active fluctuating motions that could simulate the scenario of active matter in biological systems. However, active forces, originating from their generation mechanisms, are difficult to separate from the Brownian motion due to the convoluted effects of both forces. By confining active Brownian particles in aqueous under a quadratic potential, the histogram of the pure active fluctuation can be extracted from known histograms of the total and the Brownian fluctuations by deconvolution. This approach holds promise for analyzing particle behavior in viscoelastic media, a more representative simulation of biological environments. Viscoelastic properties of a Carbopol 980NF-based hydrogel over an extended frequency range are measured using active microrheology. Motions of individual passive and active particles, i.e., electroosmosis-driven metallic Janus particles, embedded in the heterogeneous gel are measured by particle tracking. Particle trajectories are analyzed using methods including mean square displacement, particle position histograms, and power spectrum density to compare the limitations of each analytical method. The analysis advances our understanding of the interaction between active and passive forces of active motion in complex media and also lays a foundation for the study of the motion of active matter in biological systems.