Resumen
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*].
Reivindicaciones
1. Claims 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 channel in cross-section having a perimeter length |∑| and an area |Ω| ; selecting the cross-section of the non-vertical channel so as to define a I∑| cos0 constant Lagrange multiplier λ, where λ = ^— ; minimising a functional φ[Γ *]≡ |Γ *|— cos0|∑ *| + G * +λ|Ω *| to define a i minimum value Φ<0>=ΜίηΦ, wherein, at a critical transition where Φ<0>=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 |∑ *| 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*| ; and controlling how far the fluid meniscus extends along the channel by selecting one or more parameters of the functional Φ[Γ*]. 2. The method of claim 1 , comprising selectively emptying the fluid from the channel by controlling one or more parameters so that Φ<0>< 0. 3. The method of claim 1 , comprising controlling the how far the fluid meniscus extends along the channel without emptying. 4. The method of any preceding claim, wherein selecting the cross-section of the channel comprises varying the size, shape and/or orientation of the channel. 5. The method of any preceding claim, wherein controlling how far the fluid meniscus extends along the channel comprises changing the contact angle Θ. 6. The method of claim 5, wherein changing the contact angle Θ comprises adjusting a material parameter of the fluid. 7. The method of claim 5 or 6, wherein changing the contact angle Θ comprises adjusting a material parameter of the channel. 8. The method of claim 7, wherein changing the contact angle Θ comprises modifying the wetting properties of at least a region of the channel surface, for example by applying an electric field. 9. The method of any preceding claim, wherein controlling how far the fluid meniscus extends along the channel comprises changing the capillary length a by altering the fluid. 10. The method of claim 9, wherein changing the capillary length a comprises adjusting the temperature of the fluid. 1 1. The method of claim 9 or 10, wherein changing the capillary length a comprises adjusting the density of the fluid. 12. The method of claim 9, 10 or 1 1 , wherein changing the capillary length a comprises adjusting the composition of the fluid. 13. The method of any preceding claim, wherein controlling how far the fluid meniscus extends along the channel comprises changing the gravitational acceleration. 14. The method of any preceding claim, wherein selecting the cross-section of the channel comprises changing the rotational orientation of the channel in a horizontal plane. 15. The method of any preceding claim, wherein selecting the cross-section of the channel comprises changing the cross-sectional shape in at least one dimension. 16. The method of any preceding claim, wherein the channel comprises a flexible material and selecting the cross-section of the channel comprises applying a pressure to the channel. 17. The method of any preceding claim, wherein the channel comprises a piezoelectric material and selecting the cross-section of the channel comprises applying an electric field to the channel. 18. A system comprising a non-vertical channel containing a fluid forming a fluid meniscus having a capillary length a and a contact angle θ , the channel in cross-section having a perimeter length |∑| and an area |Ω| ; the cross-section of the non-vertical channel being selected so as to define a constant Lagrange multiplier ; <img class="EMIRef" id="295236164-imgf000015-0001" /> a functional φ[Γ *]≡ |Γ *|— cos0|∑ *| + G * +λ|Ω *| being minimised to i define a minimum value Φ<0>=ΜίηΦ, wherein, at a critical transition where Φ<0>=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 |∑*| 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*|; wherein, how far the fluid meniscus extends along the channel is controlled by one or more parameters of the functional Φ[Γ*]. 19. The system of claim 18, wherein the fluid is selectively emptied from the channel by one or more parameters being controlled so that Φ<0>< 0. 20. The system of claim 18, wherein one or more parameters are controlled so that the fluid meniscus does not extend outside the channel. 21. The system of any of claims 18-20, comprising means to modify the cross- section of the channel. 22. The system of any of claims 18-21 , comprising means to modify the contact angle Θ. 23. The system of claim 22, wherein the contact angle Θ is modified by adjusting a material parameter of the fluid. 24. The system of claim 22 or 23, wherein changing the contact angle Θ comprises adjusting a material parameter of the channel. 25. The system of claim 24, wherein the contact angle Θ is modified by changing the wetting properties of at least a region of the channel surface, for example by applying an electric field. 26. The system of any of claims 18-25, comprising means to modify the capillary length a by altering the fluid. 27. The system of claim 26, comprising means to modify the temperature of the fluid. 28. The system of claim 26 or 27, comprising means to modify the density of the fluid. 29. The system of claim 26, 27 or 28, comprising means to modify the composition of the fluid. 30. The system of any of claims 18-29, comprising means to modify the gravitational acceleration. 31. The system of any of claims 18-30, comprising means to modify the rotational orientation of the channel in a horizontal plane. 32. The system of any of claims 18-31 , comprising means to modify the cross- section of the channel in at least one dimension. 33. The system of any of claims 18-32, wherein the channel comprises a flexible material and the system comprises means to apply a pressure to the channel to change the cross-section. 34. The system of any of claims 18-33, wherein the channel comprises a piezoelectric material and the system comprises means to apply an electric field to the channel to change the cross-section.
