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Hysteresis and mode coupling in capillary bridge oscillations: observations
Wei Wei1, David B Thiessen, Philip L Marston
1Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
Nonlinear oscillations in capillary bridges show hysteresis, a phenomenon where the response depends on excitation frequency direction. This behavior is observed in low-viscosity liquids and higher-order capillary modes.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Capillary phenomena
Background:
- Capillary bridges are fundamental in fluid mechanics, exhibiting complex behaviors under external forces.
- Understanding nonlinear oscillations is crucial for various applications, from microfluidics to industrial processes.
Purpose of the Study:
- To investigate nonlinear axisymmetric oscillations of capillary bridges in density-matched, low-viscosity liquids.
- To characterize the modal frequency response and identify hysteresis in weakly damped oscillators.
- To explore hysteresis in higher-order capillary modes.
Main Methods:
- Utilizing a Plateau tank with density-matched, low-viscosity liquids.
- Exciting large amplitude oscillations using oscillating Maxwell stresses.
- Measuring modal frequency response by incrementing excitation frequency in both upward and downward directions.
Main Results:
- Observed hysteresis in the frequency response within a narrow range of excitation frequencies.
- Demonstrated that the observed hysteresis is consistent with a lumped-parameter model for mode-softening nonlinearities.
- Identified hysteresis in a higher-order capillary mode, specifically the third harmonic.
Conclusions:
- Nonlinear capillary bridge oscillations exhibit hysteresis, influenced by excitation frequency direction.
- The observed phenomenon can be modeled using nonlinear oscillator dynamics with mode-softening.
- Hysteresis is a characteristic of both fundamental and higher-order capillary modes in this system.