  Motivated by the observed coordination of nearby beating cilia, we use a
scale model experiment to show that hydrodynamic interactions can cause
synchronization between rotating paddles driven at constant torque in a very
viscous fluid. Synchronization is only observed when the shafts supporting the
paddles have some flexibility. The phase difference in the synchronized state
depends on the symmetry of the paddles. We use the method of regularized
stokeslets to model the paddles and find excellent agreement with the
experimental observations. We also use a simple analytic theory based on
far-field approximations to derive scaling laws for the synchronization time as
a function of paddle separation.
