(155g) Simulation of C. elegans Swimming in Viscoelastic Fluids via the Immersed Boundary Technique

Authors: 
Guido, C., Stanford University
Binagia, J., Stanford University
Shaqfeh, E. S. G., Stanford University
The swimming behavior of microorganisms in viscoelastic fluids is of great interest since their natural fluid environments often have a rich microstructure comprised of large polymeric biological molecules. The undulating swimmer C. Elegans is an excellent case study since the microorganism’s motion resembles the behavior of many other biological structures, like cilia or flagella. Additionally, there is a well-known speed decrease as the Deborah number increases that has been experimentally observed but, to date, has not been studied numerically with a fully resolved three-dimensional simulation. In this talk, we discuss the computer simulation of the arbitrary motion of an undulating swimmer that occupies finite volume in three dimensions including the ability to specify a viscoelastic model of our choosing in the fluid. A method similar to the Immersed Finite Element Method (IFEM) presented by Zhang et al. (2007) is utilized to accomplish this task. Among the many benefits of this algorithm includes that it allows for distinct fluid and solid grids to be utilized thus reducing the need for costly re-meshing when swimmers translate. In addition, we have the capability of modelling the entire three-dimensional motion of the swimmer. In the present application, we discuss a modified version of the IFEM that allows for the simulation of deformable swimmers in viscoelastic flows with an added conformation-driven force that allows the swimmer to evolve through an arbitrary set of specified shapes. This simulation tool is validated against experimental speed data provided by Shen and Arratia (2011) and the speed reduction as a function of Deborah number is presented with good agreement for Oldroyd-B fluids. The tool is then further used to explore the underlying physical mechanism that drives swimming speed reduction in viscoelastic fluids, including comparison to other more simplified simulations/theories. It is found that many features that are neglected in previous studies contribute to the swim speed such as the value of the viscosity ratio in the Oldroyd-B fluid model and the nature of the full three-dimensional deformation gradient in the volume occupied by the solid swimmer. This latter element is a feature not resolved with common line-element models for swimmers. The simulation tool also has the capability of allowing the simulation of multiple swimmers and more complex swimming geometries opening many new possibilities for future studies of swimmers in viscoelastic fluids.
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