Investigation on the Dynamics of Flexible Filaments in Viscous Fluid

Abstract

Many chemical and biological systems have applications involving fluid-structure interaction (FSI) of flexible filaments in viscous fluid. The dynamics of single and multiple filament interaction is of interest to engineers and biologists working in the area of DNA fragmentation, protein synthesis, polymer segmentation etc. Some other important applications involve mixing enhancement, fluid pumping, flow rate control and drug delivery. The FSI simulations related to these applications are challenging to numerically implement. In this direction, techniques like immersed boundary method (IBM) have proved to be quite successful. In the present study, two-dimensional computational models based on finite volume immersed boundary method is developed in order to understand the dynamics and interaction of flexible filaments in different fluid flow conditions like uniform flow, shear flow and oscillatory flow. However, in order to familiarize with the implementation of immersed boundary method, a preliminary work is done to study the fluid flow behaviour in straight and wavy rigid walled channels by modelling the walls as immersed boundaries. In the preliminary study, the continuity and Navier-Stokes equations governing the flow are solved by fractional step based finite volume method on a staggered Cartesian grid system. Fluid variables are described by Eulerian co-ordinates and solid boundary by Lagrangian co-ordinates. A four-point Dirac delta function is used to couple both the coordinate variables. A momentum forcing term is added to the Navier-Stokes equation in order to impose the no-slip boundary condition on the rigid wavy wall. A computer code is developed to perform numerical simulations. Parametric study is carried out to analyse passive mixing effects and fluid flow characteristics by varying amplitude and wavelength of wavy wall configurations for different Reynolds number. Configurations of wavy walls having larger amplitude (A = 0.14) and intermediate wavelength (WL = 1.0) are preferred. From this work, it is evident that incorporating rigid wavy walled passive modulators prove to be good and robust method for enhancing mixing in bio-medical devices. The preliminary computational model is extended by modelling flexible filament with additional structural forces like stretching/compression and bending. The fractional stepviii method is also replaced by SIMPLE algorithm to solve the fluid velocity and pressure terms of the governing equations. With the help of this extended model, simulations are carried out in various phases depending on the interaction of flexible filament with incoming fluid under different channel flow conditions. In the first phase, the flexible filament is modelled as diatom chain interacting in oceanic shear flow. The computational 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. Finally, 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 present 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 VFF value is determined which indicates the transition of filaments exhibiting either a recuperative (regaining original shape past deformation) or non-recuperative (permanently deformed) behaviour. The present model is thus successful in capturing fluid motion, buckling, shape recurrences and recuperation dynamics of diatom chains subjected to shear flow. In the second phase, two cases of oscillatory flow conditions are used with the flexible filament tethered at the centre of bottom channel wall. The first case is sinusoidal oscillatory flow with phase shift (SOFPS) and second case is sinusoidal oscillatory flow without phase shift (SOF). The simulation results are validated with filament dynamics studies of previous researchers. Further, parametric analysis is carried to study the effect of filament length, filament bending rigidity and Reynolds number on the complex deformation and behaviour of flexible filament interacting with nearby oscillating fluid motion. It is found that selection of right filament length and bending rigidity is crucial for fluid mixing scenarios. The phase shift in fluid motion is also found to critically effect filament displacement dynamics especially for rigid filaments. Symmetric deformation isix observed for filaments subjected to SOFPS condition irrespective of bending rigidity whereas medium and low rigidity filaments placed in SOF condition show severe asymmetric behaviour. Two key findings of this study are - 1) Symmetric filament conformity without appreciable bending produces sweeping motion in fluid flow which is highly suited for mixing application and 2) Asymmetric behaviour shown by the filament depicts antiplectic metachronism commonly found in beating cilia. As a result, it is possible to pin point the type of fluid motion governing fluid mixing and fluid pumping. In the third phase, two-dimensional numerical simulation of flexible membrane fixed at two end points and subjected to uniform fluid flow is carried out at low Reynolds number in a rectangular channel. The model is validated using previous research work and numerical simulations are carried out for different parametric test cases. Different membrane conformations or mode shapes are observed due to the complex interplay between the hydrodynamics and structural elastic forces. Since the membrane undergoes deformation with respect to inlet fluid conditions, a variation in flow rate past the flexible structure is confirmed. It is found that, by changing the membrane length, bending rigidity and its initial position in the channel, flow rate can be controlled. Also, for membranes that are placed at the channel mid-plane undergoing self-excited oscillations there exists a critical dimensionless membrane length condition L > =1.0 that governs this behaviour. Also, an artificial neural network (ANN) model is developed that successfully predicts flow rate in the channel for different membrane parameters. Finally, the dynamics and mutual interaction of two flexible filaments placed sideby-side in shear flow is studied. Viscous flow forcing value (VFF) and fractional contraction terms are incorporated so as to effectively categorize filament motion into various deformation regimes. A detailed analysis is carried out to study the effects of tumbling motion on the filament migration and recuperative aspects. Also, an artificial neural network (ANN) model is developed from the immersed boundary simulation results to predict tumbling counts for different filament parameters.