Treating inertia in passive microbead rheology

Area of Science:

• Physics
• Rheology
• Soft Matter

Background:

• Passive microbead rheology uses the generalized Stokes-Einstein relation (GSER) to link bead motion to material properties.
• The GSER neglects bead and fluid inertia, limiting its accuracy at high frequencies.
• Existing methods face issues like inertial oscillations and anomalous gaps in mean-square displacement (MSD).

Purpose of the Study:

• To develop a method for accurately analyzing passive microbead rheology at high frequencies by including inertia.
• To resolve paradoxes and discrepancies arising from inertia in viscoelastic measurements.
• To provide a correct procedure for taking the zero-mass limit in bead inertia calculations.

Main Methods:

• Developed a theoretical framework to incorporate bead and fluid inertia into passive microrheology.
• Analyzed a Maxwell fluid as a model viscoelastic medium.
• Investigated the role of a purely viscous element and fluid inertia (Basset force) in suppressing oscillations.

Main Results:

• Including bead inertia corrects the initial condition of the MSD but can cause oscillations.
• A small purely viscous element safely eliminates bead inertia effects and oscillations.
• Fluid inertia, particularly the Basset force, suppresses MSD oscillations when bead and fluid densities are comparable.

Conclusions:

• Accurate high-frequency passive microbead rheology requires proper treatment of inertia.
• The proposed methods resolve issues with the GSER, enabling more reliable viscoelastic measurements.
• The findings offer a pathway to overcome limitations in current microrheological analysis.