非均匀截面毛细管中的不连续液体上升
Discontinuous liquid rise in capillaries with nonuniform cross-sections
摘要：
本文从理论上考虑了具有高度依赖性截面的毛细管中液体克服重力上升的问题。对于由疏水表面制成并浸入液体储存器中的锥形毛细管，平衡液体高度取决于锥开口角$α$、杨-杜普接触角$θ$、储存器液位处的锥半径$R_0$和毛细管长度$κ^{-1}$。随着$α$从零开始增加，弯月面的位置连续变化，直到$α$达到临界值时，弯月面跳到毛细管底部。对于亲水性表面，弯月面跳到顶部。相同的液体高度不连续性可以通过没有机械运动的电润湿来实现。基本上相同的行为被发现两个倾斜的表面。我们进一步考虑毛细管周期性半径调制，并发现有几个竞争的最小弯月面的位置。从一个到另一个的转变可以通过使用电润湿来执行。这里讨论的现象可用于需要以常规方式输送少量水"量子“（体积$<1$ nL）的微流体应用中。
英文摘要：
We consider theoretically liquid rise against gravity in capillaries with height-dependent cross-section. For a conical capillary made from a hydrophobic surface and dipped in a liquid reservoir, the equilibrium liquid height depends on the cone opening angle $α$, the Young-Dupré contact angle $θ$, the cone radius at the reservoir's level $R_0$ and the capillary length $κ^{-1}$. As $α$ is increased from zero, the meniscus' position changes continuously until, when $α$ attains a critical value, the meniscus jumps to the bottom of the capillary. For hydrophilic surfaces the meniscus jumps to the top. The same liquid height discontinuuity can be achieved with electrowetting with no mechanical motion. Essentially the same behavior is found for two tilted surfaces. We further consider capillaries with periodic radius modulations, and find that there are few competing minima for the meniscus location. A transition from one to another can be performed by the use of electrowetting. The phenomenon discussed here may find uses in microfluidic applications requiring the transport small amounts of water ``quanta'' (volume$<1$ nL) in a regular fashion.
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