Multiphase capillary flows

We present here a model of the meniscus movement within uniform capillaries that explicitly accounts for the effect of the gas phase. The total momentum was assumed to change by the gravitational, viscous, surface, dissipative and boundary forces, and included dynamical effects due to variable contact angle and the reservoirs adjacent the capillary inlet and outlet. This two-phase equation was comprehensively tested against earlier models and records of two-phase systems (water, ethanol, dodecane, diethyl ether and silicon displacing air), capillary radii (0.1–4 mm), and under various gravitational accelerations (g = 9.81 m s−2 and g ≃ 0.02 m s−2). The proposed framework predicted experimental capillary rise with higher correlation coefficient (98.84–99.98%) and smaller error (0.55–2.95%) as compared to earlier single-phase equations, which achieved lower correlations (72–99.99%) and larger errors (≫1.1). Including the gas phase led to improvements up to about 6% depending on liquid characteristics. When also variable contact angle was included, the improvement increased by up to about 13% as compared to liquid-only phase and no variable contact angle. Dimensionless analyzes showed that gas-related effects were as important as inertia and reservoir effects. Supported by these results, we reject the hypothesis by which gas-related effects can be neglected in modeling capillary processes.

► Liquid and gaseous phases. ► Forces near the entrance and the reservoir retardation effects (both phases). ► Validation against earlier models and experiments.