Two-point particle tracking microrheology of nematic complex fluids

Many biological and technological complex fluids exhibit tight microstructural alignment that confers them nematic mechanical properties. Among these we count liquid crystals and biopolymer networks, which are often available in microscopic amounts. However, current microrheological methods cannot measure the directional viscoelastic coefficients that appear in the constitutive relation of nematic complex fluids. This article presents directional two-point particle-tracking microrheology (D2PTM) - a novel microrheology technique to determine these coefficients. We establish the theoretical foundation for D2PTM by analyzing the motion of a probing microscopic particle embedded in a nematic complex fluid, and the mutual hydrodynamic interactions between pairs of distant particles. From this analysis, we generalize the formulation of two-point particle tracking microrheology for nematic complex fluids, and demonstrate that the new formulation provides sufficient information to fully characterize the anisotropic viscoelastic coefficients of such materials. We test D2PTM by simulating the Brownian motion of particles in nematic viscoelastic fluids with prescribed directional frequency-dependent shear moduli, showing that D2PTM accurately recovers the prescribed shear moduli. Furthermore, we experimentally validate D2PTM by applying it to a lyotropic nematic liquid crystal, and demonstrate that this new microrheology method provides results in agreement with dynamic light scattering measurements. Lastly, we illustrate the experimental application of the new technique to characterize nematic F-actin solutions. These experiments constitute the first microrheological measurement of the directional viscoelastic coefficients of an anisotropic soft material.