Spontaneous imbibition of a liquid film wetting a wall-mounted cylinder corner

Spontaneous imbibition flows within confined geometries are commonly encountered in both natural phenomena and industrial applications. A profound knowledge of the underlying flow dynamics benefits a broad spectrum of engineering practices. Nonetheless, within this area, especially concerning complex geometries, there exists a substantial research gap. This work centers on the cylinder-plane geometry, employing a combined theoretical and numerical approach to investigate the process of a wetting film wrapping a cylinder corner. It is found that the advance of the liquid front generally follows the Lucas-Washburn kinetics, i.e., t^1/2 scaling, but it also depends on the dynamics of the liquid source. Furthermore, a theoretical estimation of the timescale associated with the imbibition process is also provided, especially the merging time as an important time length characterizing the duration of the wetting process. The timescale is highly dependent on the wettability conditions and the properties of the involved liquid. The conclusion of this work lays a theoretical foundation for comprehensively understanding the capillary phenomena in complex media and shedding light on various microfluidic applications.