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On the displacement of fluid bridges from solid surfaces in viscous pressure-driven flows

The yield conditions for the displacement of three-dimensional fluid bridges from solid boundaries are studied in pressure-driven Stokes flows. The study seeks the optimal shape of the contact line that yields the maximum flow rate for which a fluid bridge can adhere to the surfaces. The contact line contours show fore-and-aft asymmetry with a distorted shape not well represented by simple circular/elliptical planforms. The critical shear rate is shown to be sensitive to viscosity ratio; as the viscosity of the bridge increases, the critical shear rate decreases facilitating the displacement. The effects of the contact angles are found to be similar for both viscous and inviscid bridges, in direct contrast with our earlier results for drop displacement from a single substrate. The critical flow rate is strongly affected by the plate spacing; bridges with moderate height are shown to withstand the highest flow rate. This behavior is readily explained employing scaling analysis.