Two-bead microrheology: modeling protocols.

Microbead rheology maps the fluctuations of beads immersed in soft matter to viscoelastic properties of the surrounding medium. In this paper, we present modeling extensions of the seminal results of Mason and Weitz [Phys. Rev. Lett. 74, 1250 (1995)] for a single bead and of Crocker [Phys. Rev. Lett. 85, 888 (2000)] and Levine and Lubensky [Phys. Rev. Lett. 85, 1774 (2000)] for two beads. We formulate the linear response analysis for two beads so that the model equations retain the local diffusive properties of each bead (through the memory kernel of the shell or depletion zone surrounding each bead) and the nonlocal dynamic moduli of the medium separating the beads (through the memory kernel that transmits fluctuations of one bead to the other). We then derive a 3x3 invertible system of equations relating: an isolated bead's autocorrelations, the autocorrelations and cross-correlations of two coupled beads; and the shell radius surrounding each bead, the memory kernels of the shell, and of the medium between the two beads.