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Problems on viscous dynamics of active and passive microfilaments


The dynamics and morphological transitions of elastic filaments and semiflexible polymers in viscous fluids underlie the complex non-Newtonian behavior of their suspensions and also play a role in many small-scale biophysical processes from ciliary and flagellar propulsion to intracellular streaming. Elucidating the physics behind the dynamic micro-structural instabilities and transitions of such elastic filaments is key to unraveling the mechanisms underlying their complex rheological behaviors, from shear thinning and normal stress differences to viscoelastic instabilities. In this work, we use slender-body-theory from low Reynolds number hydrodynamics along with tools from nonlinear stability theory and scaling analyses to understand various problems relevant to suspension dynamics and biophysics. After discussing numerical experiments that probe fluctuations in semiflexible polymers we proceed to explain morphological instabilities of passive actin filaments in simple shear flow and their role in the rheology of dilute suspensions. We then analyze a spontaneous symmetry-breaking instability of lone actin filaments in compressional flow that gives rise to chiral structures and draw similarities with classical helical buckling of elastic rods. Both of these studies are complemented by microfluidic experiments performed by collaborators as well as analytical solutions to simplified dynamical systems. We then turn to the dynamics of active filaments that are driven by molecular motors. Far from equilibrium, these filaments undergo a Hopf bifurcation leading to spontaneous oscillations that mimic the beating patterns of eukaryotic cilia and flagella. We elucidate the crucial roles of hydrodynamics and biochemical noise in their collective behavior and highlight the relevance of our model in the context of biological experiments. Finally, we study the asymptotic transport properties of Brownian filaments in 2D porous media and of passive tracers in 1D lattices. Our computations identify various modes of filament transport that involve trapping, gliding and vaulting past obstacles, and suggest a design for a chromatographic device. Studies with passive Brownian tracers in peristaltic pumping explain how dispersion is altered due to shear and the presence of entropic traps and barriers.

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