Capillary crack imbibition: A theoretical and experimental study using a Hele-Shaw cell

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 t hrough a hole in the bottom plate. The flow is driven purely by the force a cting on the contact lines between solid, liquid, and gas. We developed a t heoretical model for this type of flow on the basis of Darcy's law; it allo ws for the consideration of different surface conditions. We run the experiment for two surface conditions: Surfaces boiled in hydrog en peroxide to remove initial contamination, and surfaces contaminated with 2-propanol after boiling in hydrogen peroxide. The flow rate depends on th e gap aperture and on the interaction of the liquid with the air and the so lid surfaces: The smaller the aperture, the lower the flow rate due to visc ous 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 gl ass surfaces with the 2-propanol contamination. These experimental results are in agreement with our theoretical model and are confirmed by independen t measurements of the liquid-solid interaction in capillary rise experiment s under static conditions with the same Hele-Shaw cell. Another aspect of this study is the distribution of the liquid for the diff erent surface conditions. The overall shape is a circular disk, as assumed in the theoretical model. However, a pronounced contact line roughness deve lops 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 tran sition zone between stable displacement and capillary fingering, i.e., neit her viscous nor capillary fingers develop under the conditions of the exper iment. The contact line roughness and the trapped air bubbles in the contam inated cell reflect local inhomogeneities of the surface wettability.