ABSTRACT
The goal of a microrheological experiment is to infer the viscoelastic
properties of thematerial (e.g., a complex fluid) fromameasurement
of the trajectories of an immersed micron-sized bead. The size of
the bead is large compared with the size of individual molecules
of the fluid (a few nanometres), but still small enough so that
the bead experiences the effect of thermal fluctuations of the
fluid. In the absence of any external driving the bead is then in
thermal equilibriumwith the surrounding fluid, which acts as a heat
reservoir. As a consequence, the motion of the bead is governed
by the laws of statistical mechanics prescribing, e.g., precise
probabilities for the bead’s position and velocity. In this chapter,
we discuss the statistical mechanical foundations of microrheology.
We develop in particular the mathematical formalism that allows to
describe the dynamics of the bead and derive relations between the
quantities of interest and the directly measurable observables.
