Particle Image micro-Rheology (PIR) using displacement probability density function

We present a novel approach to perform passive microrheology. A method to measure the rheological properties of fluids from the Brownian motion of suspended particles. Rheological properties are found from the particles' mean square displacements (MSDs) as a function of measurement time lag. Current state-of-the-art approaches find the MSD by tracking multiple particles' trajectories. However, particle tracking approaches face many limitations, including low accuracy and high computational cost, and they are only applicable to low particle seeding densities. Here, we present a novel method, termed particle image rheometry (PIR), for estimating the particle ensemble MSD from the temporal evolution of the probability density function of the displacement as a function of measurement time lag. First, the probability density function (PDF) of the particle displacements for each time lag is found using a generalized ensemble image cross-correlation approach that eliminates the need for particle tracking. Then, PDFs are used to calculate the MSD from which the complex viscosity of the solution is measured. We evaluate the performance of PIR using synthetic datasets and show that it can achieve an error of less than 1% in passive microrheology measurements, which corresponds to a twofold lower error than existing methods. Finally, we compare the measured complex viscosity from PIR with bulk rheometry for a polymeric solution and show agreement between the two measurements.