  The morphological dynamics, instabilities and transitions of elastic
filaments in viscous flows underlie a wealth of biophysical processes from
flagellar propulsion to intracellular streaming, and are also key to
deciphering the rheological behavior of many complex fluids and soft materials.
Here, we combine experiments and computational modeling to elucidate the
dynamical regimes and morphological transitions of elastic Brownian filaments
in a simple shear flow. Actin filaments are employed as an experimental model
system and their conformations are investigated through fluorescence microscopy
in microfluidic channels. Simulations matching the experimental conditions are
also performed using inextensible Euler-Bernoulli beam theory and non-local
slender-body hydrodynamics in the presence of thermal fluctuations, and agree
quantitatively with observations. We demonstrate that filament dynamics in this
system is primarily governed by a dimensionless elasto-viscous number comparing
viscous drag forces to elastic bending forces, with thermal fluctuations only
playing a secondary role. While short and rigid filaments perform
quasi-periodic tumbling motions, a buckling instability arises above a critical
flow strength. A second transition to strongly-deformed shapes occurs at a yet
larger value of the elasto-viscous number and is characterized by the
appearance of localized high-curvature bends that propagate along the filaments
in apparent "snaking" motions. A theoretical model for the so far unexplored
onset of snaking accurately predicts the transition and explains the observed
dynamics. For the first time, we present a complete characterization of
filament morphologies and transitions as a function of elasto-viscous number
and scaled persistence length and demonstrate excellent agreement between
theory, experiments and simulations.
