Viscous dynamics of elastic filaments: from buckling instabilities to rheology

Elastic filaments and semiflexible polymers are ubiquitous in both biology and engineering, where they play a key role in cell mechanics and locomotion and are the constituents of many non-Newtonian fluids. In this talk, I will discuss the dynamics of elastic filaments in microscale flows, with focus on buckling instabilities that arise when viscous stresses overcome bending rigidity in the presence of thermal fluctuations. In simple shear flow, a series of morphological transitions is found to occur with increasing elastoviscous number, a dimensionless measure of flow strength relative to elasticity. The tumbling motion seen in weak flows and typical of rigid Brownian rods gives way to elastoviscous buckling followed by a tank-treading regime. We characterize these transitions using microfluidic experiments with F-actin along with numerical simulations and a reduced-order theoretical model, which provides a prediction for the onset of tank-treading with no fitting parameter. In uniaxial compressional flow, buckling also occurs above a critical flow strength and is found to give rise to helicoidal morphologies for high elastoviscous numbers. This phenomenon is also characterized in detail and explained using a weakly nonlinear model based on the post-buckling nonlinear interaction of linearly unstable planar deformation modes. I will conclude by discussing the implications of these instabilities for the rheology of elastic polymer suspensions, where the onset of buckling is found to enhance shear-thinning and normal stress differences.