Gas-driven displacement of a liquid in a partially filled radial Hele-Shaw cell

The displacement of liquids from confined geometries by using a gas phase is a problem that is relevant to many technologies. Efficient removal of the liquid phase is achieved when an extremely thin residual fluid film is produced as it is displaced. Here the dynamics of air, at constant pressure, displacing a glycerol-water drop in a radial Hele-Shaw cell is studied in this context at low Reynolds numbers. Empirically derived expressions relating the input parameters (fluid viscosity, pressure, and drop volume) to characteristic gas flow and liquid displacement rates, and the steady-state film thickness, are proposed and compared with experiments. The experiments consist of measuring cross-sectional areas of the penetrating gas (air) and displaced liquid using glycerol-water mixtures with viscosities ranging from 4 to 280 cSt and with inlet pressures ranging from 3.5 to 10.5 kPa at gap spacings of 50-100 mu m. We estimate that the system produces residual film thicknesses in the range of 5-95 mu m.