Microrheology relies on tracking the thermal or driven motion of microscopic particles in a soft material. It is well suited to the study of materials that have no three-dimensional realization, which makes them difficult to study using a macroscopic rheometer. For this reason, microrheology is becoming an important rheological probe of Langmuir monolayers and membranes. Interfacial microrheology, however, has been difficult to reconcile quantitatively with more traditional macroscopic approaches. We suggest that uncertainties in accounting for the mechanical coupling of the tracer particle to the interface or membrane are responsible for these discrepancies. To resolve them, we propose a new non-contact approach to interfacial microrheology that uses particles submerged in the subphase a known distance below the interface. In this first of two papers, we present calculations of the response function (and thus the equilibrium fluctuation spectrum) of a spherical particle submerged below a viscoelastic surface that has a finite surface tension and/or bending modulus. In the second paper, we compare these results to submerged particle microrheology in a few example systems, showing quantitative agreement.
R. Shlomovitz, A. A. Evans, T. Boatwright, M. Dennin, and A. J. Levine, Phys. Fluids, 26 071903 (2014) pdf
T. Boatwright, M. Dennin, R. Shlomovitz, A. A. Evans, and A. J. Levine, Phys. Fluids, 26 071904 (2014) pdf