Response function of a sphere in a viscoelastic two-fluid medium

Area of Science:

• Soft Matter Physics
• Rheology
• Biophysics

Background:

• Microrheology probes material properties at small scales.
• The generalized Stokes-Einstein relation (GSER) is a common tool for microrheology analysis.
• Understanding bead dynamics in complex fluids is crucial for accurate measurements.

Purpose of the Study:

• To investigate the validity of the GSER for a sphere in a model viscoelastic medium.
• To determine the frequency range where the GSER accurately predicts bead dynamics.
• To compare theoretical predictions with experimental relevance and Newtonian fluid behavior.

Main Methods:

• Simulating the dynamics of a rigid sphere within a model viscoelastic medium (elastic network + viscous fluid).
• Calculating the complete frequency-dependent response function of the sphere to an external force.
• Comparing the simulated response function to the GSER and the exact solution for a Newtonian fluid.

Main Results:

• The sphere's response function is approximated by the GSER only within a specific frequency range.
• This frequency range is dependent on the material properties of the sphere and the viscoelastic medium.
• Deviations from the GSER were observed outside this determined frequency range.

Conclusions:

• The GSER is not universally applicable across all frequencies in viscoelastic media.
• Material parameters of both the probe (sphere) and the medium significantly influence the GSER's accuracy.
• This work provides critical insights for interpreting microrheology experiments in complex fluids.