Videos of twisted, bent fibers
These videos accompany the paper "The hydrodynamics of a twisting, bending, inextensible filament in Stokes flow," by Ondrej Maxian, Brennan Sprinkle, Charles Peskin, and Aleksandar Donev.
Here are videos of the relaxing fiber in Section 5.2 with zero twist modulus (top view and side view) and twist modulus = bend modulus = 1 (top view and side view). The red line shows the first material frame vector (equal to the first Bishop frame vector rotated by an angle theta). You can see how this line relaxes to straight in the case of finite twist modulus (this is better viewed from the side).
Here are videos of the twirling fiber in Section 5.3. We use a length L=2 and regularization radius a=0.02, so with the full RPY dynamics with rot-trans coupling the critical frequency of spinning is about 400 Hz (period of 0.0156 seconds after accounting for the 2π factor; this frequency is 25% lower than that predicted for ellipsoidal local drag). The period of the large scale oscillations is about 10 seconds, so there is a large separation of time scales.
For visualization purposes, the perturbation to the straight fiber is ten times larger in most of these videos than in the paper results (this does not impact the critical frequency at which the instability occurs).
- We first show a movie of stable twirling on the first time scale, where there are 50 cycles of spin shown, but the fiber endpoint moves only slightly. The green bead sits on the clamped end.
- Next, we show the fiber oscillating at the critical frequency, where the perturbation neither grows or decays (this is whirling, which will eventually become unstable).
- Further increasing the frequency, we show the instability that occurs for a spin rate 10% larger than the critical frequency. This video shows overwhirling motion, a steady state where the fiber is turned in the -y direction and spinning around its base.
- Finally, we show that, for even larger frequency, the fiber cannot reach overwhirling without crossing itself. This explains how plectomeres might form in experiments.