Capillary Force-Driven Fluid Flow in Open Grooves with Different Sizes

Abstract

Penetration of a wetting liquid into open metallic grooves was investigated in this work. Three grooves with different depths but the same width were tested; for each groove, a gently deposited liquid droplet served 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, was measured to be in the neighborhood of ; 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 deg angle with respect to the groove bottom for all three grooves tested. It is hypothesized that the capillary flow in any noncircular capillaries can be described by 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 . For the grooves tested in this work, the calculations from Washburn’s equation based on the equivalent diameter match the measurements well.