Linear stability analysis for the meniscus instability of a viscous fluid between elastic sheets

Abstract

When two parallel plates confining a viscous fluid in a narrow gap between their plates separate from each other at a constant velocity, the free surface of the fluid disturbs like a dendrite or fingers. This phenomenon is referred to as meniscus instability. In the present study, the meniscus instability of a viscous fluid between two elastic sheets bonded to rigid substrates was examined theoretically and experimentally. Linear stability analysis was performed to obtain the wavelength of disturbances on free surface of the fluid. The elastic sheet was modeled by a linear spring in order to take into account of the deformation of elastic sheets. The wavelength was measured by using a video camera in experiment. These results were well agreed with each other by considering a normal viscous stress at the interface and the effect of the thickness of fluid film remaining on the plates. The minimum wavelength predicting from the theory was about 3.2 times larger as the initial film thickness of the fluid, and the experimental ones were about 3.0 to 5.0 times. The experimental wavelength in the elastic sheets was smaller than that in the parallel plates like as theoretical ones. This result suggests that deformation of the elastic sheets destabilizes the free surface of the fluid.

Keywords

• meniscus instability
• elastic sheet
• capillary number
• hele-shaw flow