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

Abstract

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 liquidgas 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.

A numerical method for the simulation of low Mach number liquid–gas flows

“…In this way, the interfaces between liquid and gas are real discontinuities, and there are no errors that could be attributed to the front-tracking method and the existence of a mixing zone. Using an accurate discretization, we can consider the results given by this code as reference results (see [10] for more details about the ALE procedure).…”

“…This effect is entirely due to the gas compressibility and was analyzed in detail in [10]. The corresponding thermodynamic pressure history is shown in Fig.…”

“…In the gas, the density at steady state is unchanged, T f = T w everywhere, and P f = P 0 ÁT f /T 0 = 128,976.37 Pa following the perfect gas equation of state. This test case was treated in [10], based on a Arbitrary Lagrangian Eulerian (ALE) method (moving mesh). In this way, the interfaces between liquid and gas are real discontinuities, and there are no errors that could be attributed to the front-tracking method and the existence of a mixing zone.…”

“…This case was investigated in detail in [10], using an ALE approach where liquid and gaseous domains were considered separately. The thermodynamic pressures in the gaseous zones are P 1 (t) and P 2 (t).…”

“…In the microfluidic context, some operations like pumping or mixing rely on the gas dilatability to impose the liquid motion. We have shown that in such configurations the complete description of the flow in the gas is indeed necessary [7,10].…”