微通道內毛細現象的探討

Abstract

本研究以模擬與理論研究不同型態之微通道的毛細作用。毛細高度在特定尺度下可以透過Jurin’s Law來預測，在本研究中透過了Surface Evolver (SE)模擬證實了此結果。本研究亦利用能量最小化求毛細高度的方法，以SE來模擬梯形毛細管與複合型毛細管的液面毛細平衡高度，來研究樹木的輸水機制。 在梯形毛細管由液面下逐漸上升的過程中，我們由模擬觀察到液面隨管高逐漸上升，而最高高度由梯形管上管所決定，與有效體積理論相吻合，並能夠藉此推論樹木輸水的高度可能是由頂部開孔孔徑決定。在複合型毛細管當中亦與有效體積理論的預測吻合，並發現複合型毛細管中的液面最大高度會被頂部的最大管徑所限制。 此外，本研究亦以模擬、實驗、與理論的方法來研究，在毛細閥與懸垂液滴中液體被困於末端管口的現象。因為下接觸線固定於末端管口，使得接觸角得以從本質接觸角( )上升，來增加毛細力以平衡外力。我們發現，在沒有接觸角遲滯的情況下，上接觸角維持於本質接觸角 ，而有遲滯時上接觸角可以下降，來提供更多的毛細力。液滴的平衡形狀由上接觸角與下接觸角共同決定。 在毛細閥中，當上下液面壓差大於閥門壓力時，釘住於閥口的下接觸線，可以跨越管口邊界。而閥門壓差受到閥口的幾何性質與閥的本質所影響。當考慮接觸角遲滯時，因上接觸角能下降至後退角，進而提供更多的毛細力，造成閥門壓差上升。對於以重力為驅動力的懸垂液滴而言，在無接觸角遲滯情況下，當下接觸角到達180˚時，能產生最大的向上毛細力。然而，在有遲滯情況下，我們發現下接觸角能夠超過180˚，使得懸垂液滴呈現燈泡狀，這是在無遲滯效應時所沒有的現象。在我們的研究中，實驗與Surface Evolver模擬結果相當吻合。

This work investigate capillary phenomenon in different types of microchannels. Capillary rise can be described by Jurin’s Law under specific scale and the results are consistent with Surface Evolver simulation. However, capillary rise can also be studied via the energy minimization method, thus the capillary rise in the stepped tube and in composite tube are examined to model the water transportation in trees. In the process of increasing the tube height, liquid level increases with the tube height. The highest liquid level is determined by the radius of the top opening which is consistent with the effective volume theory. According to this result, we propose that the height of water transportation in trees is determined by the radius of the stomas. The simulation results of the capillary rise in a composite tube also coincide the effective volume theory. And the results of capillary rise in composite tube indicate that the highest liquid level is restricted by the max radius on the top opening of the composite tube. The liquid drop captured at the capillary end, which is observed in capillary valve and pendant drop technique, is also investigated theoretically and experimentally in this thesis. Because of contact line pinning of the lower meniscus, the lower contact angle is able to rise from the intrinsic contact angle ( ) so that the external force acting on the drop can be balanced by the capillary force. In the absence of contact angle hysteresis (CAH), the upper contact angle remains at . However, in the presence of CAH, the upper contact angle can descend to provide more capillary force. The coupling between the lower and upper contact angles determines the equilibrium shape of the captured drop. In a capillary valve, the pinned contact line can move across the edge as the pressure difference exceeds the valving pressure, which depends on the geometrical characteristic and wetting property of the valve opening. When CAH is considered, the valving pressure is elevated because the capillary force is enhanced by the receding contact angle. For a pendant drop under gravity, the maximal capillary force is achieved as the lower contact angle reaches 180˚ in the absence of CAH. However, in the presence of CAH, four regimes can be identified by three critical drop volumes. The lower contact angle can exceed 180˚ and therefore the drop takes on the shape of a light bulb, which does not exist in the absence of CAH. The comparisons between Surface Evolver simulations and experiments are quite well.