Probing medium viscoelasticity using signal transmission through coupled harmonic oscillators

Longitudinal waves can propagate quickly through incompressible Newtonian Fluids (like water). For closely spaced transmitter-receivers, a signal emitted by a transmitter can backpropagate through the medium to the receiver and cause motional resonance of the system. This paper explores a similar problem in Jeffery viscoelastic fluid constituted of multiple polymeric time-constants. We optically trap two particles in harmonic potentials, externally modulate one particle (transmitter) with different frequencies and waveforms and see its effects on the hydrodynamically coupled motion of the other particle (receiver). The resulting resonance characteristics of this coupled system is related to the polymeric time-constants; the quality factor falls off with increasing polymeric time constants. We demonstrate this experimentally by tracking the fluctuation-response of each particle through the Optical Tweezers setup and the correlation between their trajectories. Also, the transmission and attenuation of the signal through the polymeric mesh over the delta-correlated viscous noise gives a rich physical insight into the microrheological property of the viscoelastic fluid.