A system includes a non-vertical channel containing a fluid forming a fluid meniscus having a capillary length and a contact angle θ. The channel in cross-section has a perimeter length |Σ| and an area |Ω|. The cross-section of the non-vertical channel is selected so as to define a constant Lagrange multiplier λ, where λ=|Σ|cos θ/|Ω|. A functional Φ[Γ*]Ξ|Γ*|−cos θ|Σ*|+(1/a2)G*+λ|Ω*| is minimised to define a minimum value Φ0=MinΦ. At a critical transition where Φ=0, the fluid defines a smooth arc of length [Γ*] that divides the cross-section of the channel into two parts. |Ω*| is the cross-sectional area of the fluid, which has a curve of length |Σ*| 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 |Ω*|. How far the fluid meniscus extends along the channel is controlled by one or more parameters of the functional Φ[Γ*].
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