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Fluid-Structure Interaction of Slender Biofilaments at Low Reynolds Numbers

  • Author(s): Mortazavi, Mehrad
  • Advisor(s): Goyal, Sachin;
  • Gopinath, Arvind
  • et al.
Creative Commons 'BY' version 4.0 license
Abstract

Some hair-like biofilaments such as cilia and flagella, experience structural instability that results in complex dynamic behaviors. They deform due to active shearing or movement of molecular motors along the filament. This is also a reason for the wave-like motion of the microorganism in its surrounding fluid. Predicting the beating pattern of such elastic slender filaments in a dissipative viscous liquid at low Reynolds numbers requires a robust computational model that can both capture the dynamics of an elastic filament as well as the hydrodynamic interactions between the structure and the fluid. To address such an elastohydrodynamic problem, we have developed a computational rod model to capture the structural dynamics of an elastic filament. We then use slender body theory (SBT) to determine the hydrodynamic interactions of the filament with the viscous fluid and combine it with our computational rod model. At low Reynolds numbers where the Stokes equations govern the motion of the fluid, viscous forces are dominant over inertial forces, which results in a linear relationship between the hydrodynamic drag force and the cross-sectional velocity of the filament. However, depending on the shape of the filament, the drag coefficient on each cross-section can vary along the centerline. Not only the shape but the presence of other no-slip boundaries such as a rigid plane wall or another nearby slender object can affect both the magnitude and the distribution of the hydrodynamic drag force across the centerline of the filament. However, the SBT model is capable of handling such nonlocal hydrodynamic interactions between the filament, the wall, and the fluid. We provide an iterative spatio-temporal procedure through which we obtain the hydrodynamic drag forces and the shape of the filament at each time step. The fluid-structure interaction model presented here can be used to mimic the motion of actual cilia, flagella. However, as an additional contribution, we analyzed the accuracy of the slender body formulations. Although SBT is computationally faster than other hydrodynamic drag models, it may not provide accurate solutions for filaments with a small length-over-radius ratio. Thus, to estimate the error associated with the SBT at different slenderness ratios, we employ a computational fluid dynamic solver (CFD) and compare the results.

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