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## Laminar Flow of a Fluid in a Bearing

This animation demonstrates the laminar flow of a fluid that is trapped in the space between an
solid inner cylinder and a hollow solid outer cylinder.
One might think of the fluid as the lubricant of a simple bearing.
Usually laminar flow is thought to be caused by the viscosity of the fluid. The
laminar flow here is due to the attraction of the fluid discs to the solid discs
at the inner radius of the outer cylinder and
the solid discs at the outer radius of the inner cylinder.
The fluid discs interact via a Lennard Jones force the potential of which has the form

`V(r)=4*epsilon*((sigma/r)^12-(sigma/r)^6)`

where `r` is the separation between disc centers, `sigma` has units of length, and `epsilon` is the depth
of the potential well.
The first term provides a very strong repelling force and the second term provides a weaker attractive force.
The fluid-fluid interaction is much weaker than the fluid-solid interaction.
The simulation takes several minutes to finish while storing some image and plot video frames.
I have therefore provided a movie so that the animation can be run more rapidly.
The most stable configuration of the discs is one of 6 fold symmetry where all non-border
discs have 6 nearest neighbors all at the same distance.
That causes the second nearest neighbors to be at twice this distance so that their influence of the center disc is greatly reduced.
During the rotation of a cylinder, the fluid discs become displaced from their most stable 6-fold symmetry configuration
since shear strain is occuring.
I have therefore included at option of halting the rotation so that learner can see how the discs tend to return to their most
stable configuration.
For laminar flow the tangential speed of the fluid discs is expected to vary linearly from zero at the stationary cylinder boundary
to the speed at the boundary of the rotating cylinder.
I provide a plot to demonstrate that this tends to be the case especially for the rotating outer cylinder.
Also you have the option of color coding the tangential speed of the discs which shows
that the discs near the stationary cylinder are almost stationary and the discs near the moving cylinder move at approximately the speed of that cylinder..
If you choose parameters that are too aggressive, then you might lose some of the fluid discs. Simply choose less aggressive
parameters and press the "Refresh Page" button.