Induced free liquid surface oscillations in a visco-elastic liquid column due to angular temperature fluctuations

The response due to time-fluctuating temperature distribution applied at the free surface of a viscoelastic cylindrical liquid column with no axial dependency has been determined analytically. The amplitude of the radial- and angular velocity as well as the free liquid surface elevation has been presented as a function of the “reduced” forcing frequency of the oscillatory temperature and has numerically been evaluated for an angular temperature field proportional to sin 2φ. It was found, that visco-elasticity as described by the Maxwell model has quite some influence upon the liquid behavior. It shows for larger relaxation times besides the enlarged resonance peak additional peaks below and above resonance. This is particularly evident inside the liquid column, indicating a more pronounced elastic behavior of the liquid.