Capillary force-driven fluid flow of a wetting liquid in open grooves with different sizes

Penetration of a wetting liquid into open metallic grooves is investigated in this work. Three grooves with different depths but the same width were tested; for each groove, a gently deposited liquid droplet serves as the reservoir for liquid penetration. High-speed imaging revealed that, after the initial stage, the penetration in the grooves is in direct proportion to the square root of time and the penetration is faster in deeper grooves. The maximum penetration speed, corresponding to the moment that a droplet touches a groove, is measured to be in the neighborhood of 250-400 mm/s; the penetration speed then exponentially decreases with time. It was found that the penetration front profile remains nearly unchanged as the liquid penetrates downstream and appears to form a nearly 45° angle with respect to the groove bottom for all the three grooves tested. It is hypothesized that the capillary flow in any non-circular capillaries can be described by the Washburn's equation with the tube diameter replaced by the equivalent diameter, which is defined as the contact line length at the liquid penetration front divided by π. For the grooves tested in this work, the calculations based on the equivalent diameter match well the measurements.