Abstract: A system includes a non-vertical channel containing a fluid forming a fluid meniscus having a capillary length and a contact angle ?. The channel in cross-section has a perimeter length |?| and an area |?|. The cross-section of the non-vertical channel is selected so as to define a constant Lagrange multiplier ?, where ?=|?|cos ?/|?|. A functional ?[?*]?|?*|?cos ?|?*|+(1/a2)G*+?|?*| is minimised to define a minimum value ?0=Min?. At a critical transition where ?=0, the fluid defines a smooth arc of length [?*] that divides the cross-section of the channel into two parts. |?*| is the cross-sectional area of the fluid, which has a curve of length |?*| in contact with the channel, and G* represents a vertical position of the centre of mass of the fluid multiplied by the cross-sectional area |?*|. How far the fluid meniscus extends along the channel is controlled by one or more parameters of the functional ?[?*].