Flexible fibers in shear flow approach attracting periodic solutions

Abstract

The dynamics of a single flexible fiber in shear flow is evaluated numerically, in the absence of inertia and Brownian motion. A wide range of ratios A of bending to hydrodynamic forces and hundreds of initial configurations are considered. We demonstrate that flexible fibers in shear flow exhibit much more complicated evolution patterns than in case of extensional flow, where transitions to higher-order modes of characteristic shapes are observed when A exceeds consecutive threshold values. In shear flow, we identify the existence of different families of attracting periodic and close to periodic motions which, together with a highly ordered steady mode, dominate the typical longtime evolution of fiber shapes, depending on A and the initial orientation. The most common transient motions, typical for the relaxation phase, are also determined, including close to periodic oscillations. For dilute suspensions of flexible fibers, within a narrow range of A, the existence of a highly ordered phase is predicted, with the fibers stretched and oriented parallel to the vorticity direction.

Universal features of the shape of elastic fibres in shear flow

“…2015; Słowicka et al. 2015, 2020), cylinder-hinge models (Schmid & Klingenberg 2000; Férec et al. 2009), slender-body and inextensible Euler–Bernoulli beam (elastica) approaches (Becker & Shelley 2001; Tornberg & Shelley 2004; Nazockdast et al.…”

“…(1999), Joung, Phan-Thien & Fan (2001), Wang et al. (2012), Zhang, Lam & Graham (2019), Zhang & Graham (2020) and Słowicka, Stone & Ekiel-Jeżewska (2020).…”

“…Słowicka et al. (2020) demonstrated that in the shear flow, for a wide range of values of the bending stiffness ratio , elastic fibres often tend to the flow–gradient plane if initially located out of it. More precisely, in Słowicka et al.…”

“…More precisely, in Słowicka et al. (2020), fibres were initially straight, and hundreds of their three-dimensional (3-D) initial orientations spanned the whole range of 3-D directions. It turned out that, in most cases, fibres perform effective time-dependent Jeffery orbits and are (exponentially in time) attracted to spinning along the vorticity direction or tumbling motion in the flow–gradient plane.…”

“…(1997), Lindström & Uesaka (2007), Słowicka et al. (2012, 2013, 2015, 2020), Harasim et al. (2013), Nguyen & Fauci (2014), Farutin et al.…”