Pressure-driven displacement of gas-fluid-gas plugs in a capillary tube

This talk focuses on the study of pressure-driven displacement of gas-liquid-gas plugs in a capillary tube using theory and experiments. Several researchers have shown that in the limit of low Re, when a right circular cylindrical plug is displaced at a constant flow rate in a confined cylindrical geometry, an analytical solution can be found by solving the 4th-order stream function equation E²(E² ψ) = 0. Here, we attempt to understand the instabilities that occur in a pressure-driven displacement of a liquid plug by using perturbation analysis. We utilize the general solution to the 4th-order stream function PDE, and apply boundary conditions appropriate to the pressure-driven flow, to derive an analytical solution that is a leading-order solution of the perturbed system. This leading-order solution depicts a right circular cylindrical plug, i.e., no deformation. In this study, experiments were also performed in a capillary tube (diameter ≈ 800 μm) by displacing liquid plugs containing aqueous glycerol solution using pressurized air with a range of 0.02 psig < P < 1 psig. We study the leading-order solution at a zero capillary number to compare with low-pressure experiments.