Session: MSNDC-04-01 Nonlinear Dynamics of Structures

Paper Number: 73908

Start Time: August 17, 11:10 AM

73908 - Slender Body Theory for Special Cosserat Rods 

The study of motion of filament-like structures in fluid media has been a topic of interest since long. It has its relevance in wide variety of industrial and biological processes such as swimming of micro-organisms like cilia and flagella; motion of semiflexible elastic filaments like DNA, actin and microtubules; study of growing elastic filaments due to liquid crystal phase transitions etc. The filament usually have very larger aspect ratio ranging from tens to several thousands in biological settings.  In this regard, slender body theory has been developed assuming the fluid flow to be stokesian which is applicable at low reynolds number. In all such developments, the filament is invariably assumed to be inextensible and unshearable. In this work, we relax the inextensibility and unshearability constraint on filaments, i.e, the filament is modeled as a special Cosserat rod which is capable of examine all modes of deformation. The incompressible stokes flow equations are recast in boundary integral framework and matched asymptotic expansion is used to derive an integral equation for the distributed fluid force and moment on the filament in terms of filament's centerline velocity and angular velocity. The resulting governing equation turns out to be complex involving elliptic functions. We further assume the shear strain to be small enough in order to come with a feasible set of equations. This formulation leads to set of integro-differential equations which reduces to the classical slender body theory under the assumption of Kirchhoff filament i.e. when shear and axial strain are set to zero. The integral equation for fluid force turns out to be singular at every arc-length. In literature, this singularity is tackled using cut-off length i.e. removing the portion of singularity in the full domain, and mollifiers such as method of regularized stokeslet. We show that the singularity is of removable type having finite but discontinuous limit. An efficient second order accurate finite difference scheme is also developed to solve the full set of governing equations. In addition to bending, deformation of the filament, our formulation also includes stretching, shearing and twisting deformation of the filament which have been neglected in all existing development.

Presenting Author: Mohit Garg IIT Delhi

Authors:

Mohit Garg IIT Delhi
Ajeet Kumar Indian Institute of Technology Delhi