(550d) Buckling and Transport of Heterogeneously Stiff Elastic Fibers in Microscale Flows

The dynamic behavior of flexible filaments in Stokesian fluids plays a critical role in our understanding of non-Newtonian systems arising in macro-scale biological processes and engineering problems. However, previous work has only considered and studied these filaments with homogenous structural properties. The filament backbone has a non-uniform rigidity in many biological systems like microtubules, where the association and dissociation of proteins can potentially lead to spatial and temporal changes in structural rigidities. The consequences of such non-uniformities in the configurational stability and transport of these fibers have yet to be revealed. Here, we use slender-body theory and Euler-Bernoulli elasticity in numerical simulations coupled with various heterogeneous rigidity profiles to study their buckling instability properties and transport dynamics. We observe more pronounced buckling in areas of reduced rigidity in our simulations. We show that these shapes are predictable using linear stability analysis and we present a framework to analyze arbitrary non-uniform filament rigidity. In shear flows, the unique buckling patterns that materialize from non-uniform rigidity give rise to fluid-filament interactions that have not been previously reported. We also illustrate strategies to determine optimal rigidity profiles to mitigate filament buckling. Non-uniform buckling leads to configurations that permit migration across streamlines, and filament transport properties change strikingly from those with a uniform rigidity. We also examine cross-streamline migration and quantify the role of elastic backbone heterogeneity in the transverse transport of elastic filaments. Collectively, these results suggest that the distinct rigidity profiles we explored can drastically alter the fluid-structure interactions in physiologically relevant settings, providing a foundation for further elucidating the interplay between hydrodynamics and the complex structural properties of biopolymers.