Dual effects of pressure difference for long-wave stratified flow in horizontal microchannels

In this work, the linear stability analysis combining with energy balance theory is performed to clarify the suppressing and boosting long-wave instabilities driven by pressure difference in horizontal microchannels as well as its corresponding physical meanings. It is found that, for a specific fluid combination, there exists a certain relative liquid film thickness (hN,c) at which the disturbance work done by interfacial shear stress over unit wavelength (denoted by ISS) is exactly equal to the total viscous dissipation rate over unit wavelength within both phase bulk flows (denoted by DIStot). When the liquid film thickness (hN) exceeds hN,c, ISS is smaller than DIStot, indicating that the initial disturbance energy cannot be replenished from the primary flow until its completely disappear due to the viscosity dissipation. Conversely, ISS is larger than DIStot, indicating that the initial disturbance can acquire energy from the primary flow and grow up. The strength of suppressing and boosting effect can be influenced by liquid film thickness, flow rate, and channel height. However, the demarcation of the dual effects remains unchanged. An analytical expression of hN,c with respect to the viscosity ratio is established by means of long-wave approximation method, which matches well with the numerical results. The energy balance mechanisms revealed in the present study provide a new insight into the wave mode in the confined space and help the design of microfluidic systems.