Bayesian inference in active microrheology with wall and particle-particle interactions

Abstract: Active microrheology infers rheological properties from the motion of a force-driven probe. In small samples, however, the probe is often close to walls or other probes, and the resulting hydrodynamic interactions bias the inferred parameters. We present a Bayesian framework in which these interactions are built into simplified analytical models for Newtonian and linear viscoelastic fluids and test it on noisy synthetic data from finite-element simulations of Newtonian and Oldroyd-B fluids. Accounting for the interactions substantially improves the accuracy of the inferred parameters. Near a wall, oblique forcing allows the material parameters and the wall distance to be identified jointly from a single experiment. In the nonlinear viscoelastic regime, posterior predictive checks over multiple force levels reveal the inadequacy of the linear model. Finally, when the probe size is comparable to the heterogeneity length scale, the framework distinguishes spatial variations in the modulus from measurement noise.