Tsori Yoav
Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel.
Langmuir. 2006 Oct 10;22(21):8860-3. doi: 10.1021/la061605x.
We consider theoretically liquid rise against gravity in capillaries with height-dependent cross-sections. 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 alpha, the Young-Dupré contact angle theta, the cone radius at the reservoir's level R(0), and the capillary length kappa(-)(1). As alpha is increased from zero, the meniscus' position changes continuously until, when alpha 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 discontinuity 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. Finite pressure difference between the two sides of the liquids can be incorporated as well, resulting in complicated phase-diagrams in the alpha-theta plane. 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.
我们从理论上考虑了液体在横截面随高度变化的毛细管中克服重力上升的情况。对于由疏水表面制成并浸入液体储液器中的锥形毛细管，平衡液体高度取决于锥顶角α、杨氏 - 杜普雷接触角θ、储液器液面处的锥半径R(0)以及毛细长度κ⁻¹。当α从零开始增加时，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。对于亲水表面，弯月面跳到顶部。通过电润湿且无机械运动也可实现相同的液体高度不连续性。对于两个倾斜表面，本质上发现了相同的行为。我们进一步考虑了半径具有周期性调制的毛细管，发现弯月面位置存在几个相互竞争的最小值。通过使用电润湿可以实现从一个最小值到另一个最小值的转变。也可以纳入液体两侧的有限压差，从而在α - θ平面中产生复杂的相图。这里讨论的现象可能在微流体应用中有用，这些应用需要以规则的方式传输少量的水“量子”（体积<1 nL）。
