Harishankar Manikantan

The sedimentation of flexible filaments

Author(s): Li, L; Manikantan, H; Saintillan, D; Spagnolie, SE | Abstract: The dynamics of a flexible filament sedimenting in a viscous fluid are explored analytically and numerically. Compared with the well-studied case of sedimenting rigid rods, the introduction of filament compliance is shown to cause a significant alteration in the long-time sedimentation orientation and filament geometry. A model is developed by balancing viscous, elastic and gravitational forces in a slender-body theory for zero-Reynolds-number flows, and the filament dynamics are characterized by a dimensionless elasto-gravitation number. Filaments of both non-uniform and uniform cross-sectional thickness are considered. In the weakly flexible regime, a multiple-scale asymptotic expansion is used to obtain expressions for filament translations, rotations and shapes. These are shown to match excellently with full numerical simulations. Furthermore, we show that trajectories of sedimenting flexible filaments, unlike their rigid counterparts, are restricted to a cloud whose envelope is determined by the elasto-gravitation number. In the highly flexible regime we show that a filament sedimenting along its long axis is susceptible to a buckling instability. A linear stability analysis provides a dispersion relation, illustrating clearly the competing effects of the compressive stress and the restoring elastic force in the buckling process. The instability travels as a wave along the filament opposite the direction of gravity as it grows and the predicted growth rates are shown to compare favourably with numerical simulations. The linear eigenmodes of the governing equation are also studied, which agree well with the finite-amplitude buckled shapes arising in simulations.

Buckling transition of a semiflexible filament in extensional flow.

An analytical expression for the fluctuation-rounded stretch-coil transition of semiflexible polymers in extensional flows is derived. The competition between elasticity and tension is known to cause a buckling instability in filaments placed near hyperbolic stagnation points and the effect of thermal fluctuations on this transition has yet to receive full quantitative treatment. Motivated by the findings of recent experiments as well as our simulations, we solve for the amplitude of the first buckled mode near the onset of the instability. This reveals a stochastic supercritical bifurcation, which is in excellent agreement with full numerical simulations.

Subdiffusive transport of fluctuating elastic filaments in cellular flows

The dynamics and transport properties of Brownian semiflexible filaments suspended in a two-dimensional array of counter-rotating Taylor-Green vortices are investigated using numerical simulations based on slender-body theory for low-Reynolds-number hydrodynamics. Such a flow setup has been previously proposed to capture some of the dynamics of biological polymers in motility assays. A buckling instability permits elastic filaments to migrate across such a cellular lattice in a “Brownian-like” manner even in the athermal limit. However, thermal fluctuations alter these dynamics qualitatively by driving polymers across streamlines, leading to their frequent trapping within vortical cells. As a result, thermal fluctuations, characterized here by the persistence length, are shown to lead to subdiffusive transport at long times, and this qualitative shift in behavior is substantiated by the slow decay of waiting-time distributions as a consequence of trapping events during which the filaments remain in a particular cell for extended periods of time. Velocity and mass distributions of polymers reveal statistically preferred positions within a unit cell that further corroborate this systematic shift from transport to trapping with increasing fluctuations. Comparisons to results from a continuum model for the complementary case of rigid Brownian rods in such a flow also highlight the role of elastic flexibility in dictating the nature of polymer transport.

Effect of flexibility on the growth of concentration fluctuations in a suspension of sedimenting fibers: Particle simulations

Three-dimensional numerical simulations are performed to study the stability of a sedimenting suspension of weakly flexible fibers. It is well known that a suspension of rigid rods sedimenting under gravity at low Reynolds number is unstable to concentration fluctuations owing to hydrodynamic interactions. Flexible fibers, however, reorient while settling and even weak flexibility can alter their collective dynamics. In our recent work [Manikantan et al., “The instability of a sedimenting suspension of weakly flexible fibres,” J. Fluid Mech. 756, 935–964 (2014)], we developed a mean-field theory to predict the linear stability of such a system. Here, we verify these predictions using accurate and efficient particle simulations based on a slender-body model. We also demonstrate the mechanisms by which flexibility-induced reorientation alters suspension microstructure, and through it, its stability. Specifically, we first show that the anisotropy of the base state in the case of a suspension of flexible fib...