Immersed Fibre Dynamics

My work in this area centers around understanding the flow of incompressible fluids in the presence of moving, elastic fibres, using the Immersed Boundary Method. The approach I have taken is three-fold:

• using linear stability analyses to study the behaviour of solution modes corresponding to oscillations of the immersed fibre, and hence explain the stability and stiffness properties of immersed fibres;
• applying these analyses to designing better numerical methods for solving problems with immersed boundaries;
• using numerical experiments to study physically- or industrially-relevant examples of moving boundary problems.

1. Analysis of parametrically-excited immersed boundaries:

I am investigating the parametric excitation of an immersed boundary through a periodically-modulated elastic stiffness, with the results summarized in this paper. The technique used is closely related to the classical analysis of the Mathieu equation (for more details, see the description of parametric resonance in the ``Pendulum Lab''). This work is a natural extension of the static linear stability analysis I performed in my thesis.

2. Model computations in 2D:

The following three simulations are representative of what I use in my model computations to test analytical results and changes to the numerical scheme. Refer to Chapters 3 and 4 of my thesis for more information ('sigma' refers to the fibre stiffness parameter, with more flexible fibres having a smaller value of 'sigma').

• Flat fibre (stable, sigma=10,000)
• Flat fibre (unstable, sigma=10,000)
• Star-shaped fibre (sigma=1,000)

3. Pulp fibre simulations in 2D:

In an exhaustive series of experiments done on wood pulp suspensions in the 1950's, a wide range of differing orbital motions is observed, depending on the stiffness of the fibre and the flow shear rate. In the following series of 2D simulations, I have reproduced all of the planar orbit classes by varying the fibre stiffness parameter, sigma:

• Rigid rotation
• Springy rotation
• Snake turn
• Complex rotation
• Snake turn (streamline plot)

See Chapter 5 of my thesis for more information on pulp fibres.

4. Pulp fibre simulations in 3D:

This is recent work done in collaboration with Nathaniel Cowen (Tulane University). I have collected a series of QuickTime animations to illustrate the results.