IN SITU CONTROL OF FLUID MENISCI

摘要

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*].

主权项

1. A method of controlling a fluid meniscus in a non-vertical channel, comprising:
containing a fluid in a non-vertical channel so as to form a fluid meniscus having a capillary length a and a contact angle θ, the non-vertical channel in cross-section having a perimeter length |Σ| and an area |Ω|; selecting the cross-section of the non-vertical channel so as to define a constant Lagrange multiplier λ, whereλ=ΣcosθΩ; minimising a functionalΦ[Γ*]≡Γ*-cosθΣ*+1a2G*+λΩ*  to define a minimum value Φ0=MinΦ, wherein, at a critical transition where Φ0=0, the fluid defines a smooth arc of length |Γ*| that divides the cross-section of the non-vertical channel into two parts, |Ω*| is a cross-sectional area of the fluid, which has a curve of length |Σ*| in contact with the non-vertical channel, and G* represents a vertical position of a centre of mass of the fluid multiplied by the cross-sectional area |Ω*|; and controlling how far the fluid meniscus extends along the non-vertical channel by selecting one or more parameters of the functional Φ|Γ*|.