Numerical study of liquid inclusion oscillations inside a closed 1D microchannel filled with gas

The motion of a liquid inclusion inside a 1D microchannel filled with gas and externally heated is simulated. An incompressible formulation is used for the liquid, while a low Mach approximation is considered for the gas flow. Gas-liquid interfaces are captured using an Arbitrary Lagrangian Eulerian method. The whole liquid-gas system is shown to behave as a damped oscillator. Natural frequency of the linearized system and associated eigenmodes are first identified. Forced oscillations are investigated for different heating conditions (temperature or heat flux) at the microchannel ends. Detailed analyses are performed which reveal the main thermo-mechanical effects involved in the oscillations. The relevant parameters governing the dynamics are found out through a dimensionless analysis. Finally, heating conditions leading to non decaying oscillations of the liquid inclusion are proposed.