Capillary Crack Imbibition: A Theoretical and Experimental Study Using a Hele-Shaw Cell

摘要

— We study the filling of horizontal cracks with constant aperture driven by capillary forces. The physical model of the crack consists of a narrow gap between two flat glass plates (Hele-Shaw cell). The liquid enters the gap through a hole in the bottom plate. The flow is driven purely by the force acting on the contact lines between solid, liquid, and gas. We developed a theoretical model for this type of flow on the basis of Darcy's law; it allows for the consideration of different surface conditions.¶We run the experiment for two surface conditions: Surfaces boiled in hydrogen peroxide to remove initial contamination, and surfaces contaminated with 2-propanol after boiling in hydrogen peroxide. The flow rate depends on the gap aperture and on the interaction of the liquid with the air and the solid surfaces: The smaller the aperture, the lower the flow rate due to viscous resistance of the liquid. The flow rate is also reduced when the glass surfaces are contaminated with 2-propanol. The contact line force per unit length is approximately 60% higher on clean glass surfaces than it is on glass surfaces with the 2-propanol contamination. These experimental results are in agreement with our theoretical model and are confirmed by independent measurements of the liquid-solid interaction in capillary rise experiments under static conditions with the same Hele-Shaw cell.¶Another aspect of this study is the distribution of the liquid for the different surface conditions. The overall shape is a circular disk, as assumed in the theoretical model. However, a pronounced contact line roughness develops in case of the surfaces contaminated with 2-propanol, and air bubbles are trapped behind the contact line. A further analysis of the flow regime using the capillary number and the ratio of the viscosities of the involved fluids (water and air) reveals that the experiments take place in the transition zone between stable displacement and capillary fingering, i.e., neither viscous nor capillary fingers develop under the conditions of the experiment. The contact line roughness and the trapped air bubbles in the contaminated cell reflect local inhomogeneities of the surface wettability.