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We are studying the behavior of defects in a system known as printer's instability. The system is basically made up of two cylinders, one inside the other. The cylinders are acentric so that there is a small gap at the bottom of the system filled with a silicon oil. On the left is a picture of a printer's instability system. The inside cylinder is made from Delrin and the outer cylinder is made from Plexiglas. Once you set one or both of the cylinders into motion, various patterns appear. |
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We were mostly interested in a pattern of traveling fingers. Such fingers are obtained by rotating both cylinders in opposite direction to each other. If one perturbs such pattern in a special way then source and sink defects can be created. |
| Source defect separates regions of oppositely traveling waves. The waves are coming out of the source defect. Sources are stable and stationary. They can exist for a very long time so it's fairly easy to study them. |  |
| Sinks, on the other hand, are generally not stationary and it's rather difficult to create a long-living sink defect. We observed many transient sinks but in order to study them they must live for at least few minutes. Fortunately, we were able to create long-living sinks using a rubber wiper and a little bit of "magic". Sink defects also separate regions of oppositely traveling waves, but in this defect the fingers are "sinking" into the defect. |  |
In our studies we found that sources while stationary on average, exhibit irregular motion. They are stable, stationary, and symmetric (they emit waves with the same wave number on either side). However, below a certain value of the critical parameter (inner cylinder velocity in our case) they become more non-stationary and the growth of fluctuations in the core of the defect becomes more significant. It is said that the sources start to breathe.
Sinks have a mismatch in the wave number on either side and therefore have a nonzero velocity. Sinks move to achieve a phase-matching rule, that is, so that the relationship between the incoming fingers on the two sides of the defect remains fixed.
Here is a poster on the printer's instability study of sink and source defects presented at the Nonlinear Dynamics and Pattern Formation Conference in Austin, Texas, June 2000.
Relevant publications:
L. Pan and J.R. de Bruyn, "Broken-parity waves at a driven fluid-air interface",
Phys. Rev. Lett. 70, 1781 (1993).
L. Pan and J.R. de Bruyn, "Spatially uniform traveling cellular patterns at a driven interface",
Phys. Rev. E 49, 483 (1994).
L. Pan and J.R. de Bruyn, "Nonuniform broken-parity waves and the Eckhaus instability",
Phys. Rev. E 49, 2119 (1994).
J.R. de Bruyn and L. Pan, "Delayed onset of ribbing instability due to finite-size effects",
Phys. Fluids 7, 2185 (1995).
P. Habdas, M. Case, J.R. de Bruyn, "Behavior of sink and source defects in a one-dimensional
traveling finger pattern",
Phys. Rev. E 63, (2001).
