Numerical analysis of the buckling and recuperation dynamics of flexible filament using an immersed boundary framework

Abstract

The dynamics of flexible filaments in viscous shear flow is of interest to biologists and engineers in a wide variety of applications involving folding and unfolding sequence of long-chain biomolecules like DNA, non-motile sperm and microalgae. It is also helpful in understanding the deformation of natural and synthetic fibers which can be applied in areas such as biotechnology. In the present work, deformation and migration behavior of non-motile unicellular phytoplankton diatoms subjected to viscous shear flow are considered. These unicellular diatoms develop into colonies which are made up of linked chains. The complex fluid-structure interaction is solved by developing a two-dimensional numerical model with an immersed boundary framework. The simulation consists of suspending an elastic filament mimicking a diatom chain in a shear flow at low Reynolds number. The governing continuity and Navier–Stokes equations are solved on a Cartesian grid arranged in a staggered manner. A forcing term is added to the momentum equation that incorporates the presence of flexible filament in the fluid domain. The discretization of the governing equation is based on a finite volume method, and a SIMPLE algorithm is used to compute pressure and velocity. A computer code is developed to perform numerical simulations, and the model is first verified with the deformation study of a tethered flexible filament in uniform fluid flow. Next, the shape deformations for flexible filament placed freely in shear flow are compared with the studies of previous researchers. Further, the present results are validated with Jeffery's equation for particles immersed in shear flow along with classification plot for filament orbit regimes. All of these comparisons provide a reasonable validity for the developed model. The effect of bending rigidity and shear rate on the deformation and migration characteristics is ascertained with the help of parametric studies. A non-dimensional parameter called Viscous Flow Forcing value (VFF) is calculated to quantify the parametric results. An optimum Viscous Flow Forcing value is determined which indicates the transition of filaments exhibiting either a recuperative (regaining original shape past deformation) or non-recuperative (permanently deformed) behavior. The developed model is successful in capturing fluid motion, diatom buckling, shape recurrences and recuperation dynamics of diatom chains subjected to shear flow. Further, the developed computational model can successfully illustrate filament-fluid interaction for a wide variety of similar problems.