Complex dynamics of long, flexible fibers in shear

Abstract

The macroscopic properties of polymeric fluids are inherited from the material properties of the fibers embedded in the solvent. The behavior of such passive fibers in flow has been of interest in a wide range of systems, including cellular mechanics, nutrient aquisition by diatom chains in the ocean, and industrial applications such as paper manufacturing. The rotational dynamics and shape evolution of fibers in shear depends upon the slenderness of the fiber and the non-dimensional "elasto-viscous" number that measures the ratio of the fluid's viscous forces to the fiber's elastic forces. For a small elasto-viscous number, the nearly-rigid fiber rotates in the shear, but when the elasto-viscous number reaches a threshhold, buckling occurs. For even larger elasto-viscous numbers, there is a transition to a "snaking behavior" where the fiber remains aligned with the shear axis, but its ends curl in, in opposite directions. These experimentally-observed behaviors have recently been characterized computationally using slender-body theory and immersed boundary computations. However, classical experiments with nylon fibers and recent experiments with actin filaments have demonstrated that for even larger elasto-viscous numbers, multiple buckling sites and coiling can occur. Using a regularized Stokeslet framework coupled with a kernel independent fast multipole method, we present simulations that capture these complex fiber dynamics.

Universal features of the shape of elastic fibres in shear flow

“…2018), the boundary integral technique (Peskin 2002), the method of regularized Stokeslets (Cortez, Fauci & Medovikov 2005; Nguyen & Fauci 2014; LaGrone et al. 2019), etc. We exploit the bead-spring approach for numerical simulations and the elastica model for rationalization of the numerical results (see figure 1).…”

“…2018; LaGrone et al. 2019) methods. The other limit is when, for a small , is increased to the point when the fibre bends globally along the whole length.…”

“…(2018) and LaGrone et al. (2019). This pattern of the dynamics, typical for elongated objects of a non-negligible thickness, is not reproduced by the inextensible infinitely thin Euler–Bernoulli beam (elastica), analysed e.g.…”

“…(2018) and LaGrone et al. (2019), including knotted fibres (Matthews, Louis & Yeomans 2010; Kuei et al. 2015; Narsimhan, Klotz & Doyle 2017; Soh, Klotz & Doyle 2018) and also deviations from Jeffery orbits have been studied, e.g.…”

Sedimenting pairs of elastic microfilaments

“…hydrogel micro and nano fibers [8][9][10][11] to deliver drugs, and investigations important to protect the environment, for example, waste-water treatment 12 or diatom chains in oceans. [13][14][15][16][17] Systems of elastic filaments moving in fluids exhibit interesting, complex mechanical properties, 18,19 caused by hydrodynamic interactions between segments of a single or multiple filaments. It is of special interest to investigate how elasticity affects sedimentation.…”