Rounded-corners-induced re-entrant non-occlusion in a horizontal tube

Keeping a tube from being plugged by a fluid is an important process in applications. An interesting re-entrant phenomenon for the capillary state with the occluding state sandwiching the non-occluding state from both the high- and low-Bond-number regions can appear by inserting a rod into a horizontal tube at an eccentric position (Tan et al., J. Fluid Mech, vol. 946, 2022, A7). Containers with rounded corners are very common. We theoretically investigate a situation for a horizontal open tube with rounded corner(s). The results show that a re-entrant non-occlusion at a contact angle can also appear without the insertion of any object. The competition between the rounded corner wetting/non-wetting effect and gravity effect can lead to a re-entrant non-occlusion. The re-entrant non-occlusion is affected by the shape and orientation of the rounded corner(s). For a tube with only one rounded corner, the re-entrant non-occlusion exists when the rounded corner has a not-so-large corner radius and is not in a landscape orientation. For a tube with two (or more) rounded corners, the corner(s) with the strongest corner effect will determine the existence or non-existence of the re-entrant non-occlusion. This paper provides an effective scheme for designing a high-performance capillary with corners that are not easily occluded by a fluid and removing fluid blockage from a capillary in optofluidic/microfluidic applications.