Capillary rise in Hele-Shaw models of disordered media

We study the capillary rise of a viscous liquid in large Hele-Shaw models of disordered media, both analytically and experimentally. Compared to the Fries–Dreyer and Lucas–Washburn solutions for capillary rise with and without gravity, our experimental data reveal a systematic deviation at short and intermediate times. The original pressure balance equation leading to Washburn’s results is reformulated in order to include an additional resisting term, proportional to the mean velocity of the front h˙, which appears naturally as a result of the geometry of the cell. Analytical solutions h(t  ) are found for displacements with and without gravity. These new solutions reproduce the experimental results very accurately in Hele-Shaw cells of constant gap thickness, where the capillary pressure can be approximated by a constant. In cells of fluctuating gap thickness, where the capillary pressure fluctuates in space, a small additional pressure contribution is required. This correction that depends on h˙ is also studied.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (93 K)Download as PowerPoint slideHighlights► We study capillary rise in large Hele-Shaw models of disordered media. ► Experiments are carried out for different imposed pressures and effective gravities. ► Washburn’s equation is modified to account for viscous losses at the entrance. ► Experiments in smooth cells are properly captured by this equation. ► In disordered cells another pressure drop dependent on front velocity is required.