本研究的主要目的，在建立兩接觸面間，受空氣濕度與表面粗糙度影響的黏附力理論模型。首先，本研究考慮在有濕度的情形下，針對原子力顯微鏡探針與試件表面間的黏附力機制做一探討。傳統上藉由水橋的幾何外型條件計算所得之數值結果並無法準確預測實驗量得的黏附力大小及其趨勢，亦無法證明水橋之存在及真實停留位置。本研究發現在熱力學平衡的情形下，此液氣界面上必存在一力平衡關係。藉由水橋幾何條件的限制與液氣界面間之力平衡，本研究可以準確的預估受濕度影響的黏附力大小及其行為，且其計算結果與文獻實驗結果比較亦相當符合。一般幾何模型無法計算之受濕度影響的填充角，利用此模型也可做一準確計算。本研究也推導出探針與試件之間發生黏附力的臨界間距。在探針與試件為相同的材料時，此時的黏附力與探針頭的曲率大小有關，與濕度較不相關。此外實驗結果顯示，如果考慮粗糙度效應時，黏附力在低濕度會發生一反轉的現象，數值計算結果證明液氣界面上的壓差力是主要影響的原因，而表面張力則是明顯的隨著濕度增加而增加。考慮材料親水性對黏附力的影響，具有較親水的粗糙面與較不親水的探針之組合，會導致較大黏附力。
其次，相較於傳統上僅考慮彈性變形之接觸模型，本研究結合一考慮彈性、彈塑性與塑性變形的微接觸力學模型與水膜體積守恆條件，推導出有濕度情形下，一平面與粗糙面間的新月型力與接觸力。根據數值運算的結果，水膜厚度與黏附力的大小，會隨著相對濕度與材料粗糙面變形特性之塑性指標增加而增加，隨著平均面距增加而減少。不同平均面距下的接觸力與新月形力的大小，在不同濕度與不同塑性指標下，也在此模型被準確估算。
最後，仿生學在近幾年開始盛行，研究發現所謂的蓮花效應，與其表面粗糙度間存在一關係。本研究運用一數值運算流程，探討水滴在粗糙面上的真實接觸角。利用此模型，我們可以決定一粗糙面凹槽間水膜面停留的位置，與被水濕潤與非濕潤的比例，藉由此比例與材料表面親水性有關的初始平面接觸角，我們可以得到受粗糙度影響的真實接觸角。此數值結果與實驗結果相比較，兩者相當符合。藉此，我們可以印證蓮花效應確實會受粗糙度影響，並利用受粗糙度影響的初始接觸角，重新估算黏附力。較小的初始接觸角與較大的粗糙度因子，會造成較大的黏附力。

Adhesion forces between a probe tip and a flat surface under humid conditions are usually evaluated using the geometric model of the water bridge profile. However, the force equilibrium of water/air film must exist because the film is in a stationary state and thermodynamic equilibrium. In the present study, a sophisticated numerical model, which is based on both geometry constraints and the force equilibrium of the water/air film, is proposed to compute adhesion forces. The results obtained are in good agreement with the experimental results of pull-off tests presented in literature. The maximum separation distance can be evaluated using the present model. When the contact angle of the tip equals that of the flat surface, the tip radius, rather than the humidity level, dominates the adhesion force. The capillary pressure force was found to be a major component of the adhesion force at low humidity levels. The surface tension force significantly increased when the relative humidity was increased. The adhesion forces between a semispherical probe tip and a rough surface under humid conditions are evaluated using modified method. The filling angle, which can reflect the changes in relative humidity and the hydrophilic/little hydrophilic properties of the tip and rough surface, can be precisely determined from analyses of the present model. The unusual concave curves of the adhesion force exhibited in the experimental results can be predicted by the present model. According to the results, a hydrophilic rough surface and a little hydrophilic probe tip lead to a significant increase in adhesion force.
Moreover, the model is developed to calculate the adhesion meniscus force of a rough surface with surface asperity, when in contact with a smooth, rigid flat covered by a thin water film. The original thickness of this film before surface contact is dependent upon the relative humidity of the air. Microcontact deformations of surface asperities in the elastic, elastoplastic, and fully plastic regimes are included in the present model under a normal load. The new water film thickness under the condition of microcontact deformations is considered changing with a normal load, and it is obtained from the equation developed on the basis of the volume conservation principle for the new film thickness, and the water film volume displaced by the asperities heights dipping into the film. The meniscus profile is also calculated from the balance of the surface tension force and the pressure difference force across the meniscus profile, if a new film thickness is available. Water film thickness and the meniscus force are increased by decreasing the mean separation of the two contact surfaces, or by increasing the relative humidity or the plastic index. A significant difference in the meniscus force is found between the present model and the model of literature, which is enhanced by either decreasing the mean separation, raising the plasticity index, or increasing the relative humidity. The effects of the meniscus force on the load capacity are also evaluated at different mean separations, relative humidity, and plasticity indices.
A new method that incorporates a numerical scheme is developed to investigate the adhesion behavior of a water droplet on a rough surface patterned by cyclic asperities with a fixed aspect ratio. This method is applied to determine the stagnant position of the water bridge on the lateral surface of a groove and the water bridge profile suspended at two adjacent asperities. This water bridge profile allows us to determine the real contact angle corresponding to a given initial contact angle and the hydrophobic property of the asperities. The real contact angles predicted by the present method for different asperity aspect ratios were found to have good agreement with the experimental results. The numerical behavior demonstrated by two dimensionless area parameters, D and F, related to the wetted and un-wetted areas, respectively, is discussed as a function of the initial contact angle. The real contact angle exhibited in the fully wetted and transitional regions is increased by raising the initial contact angle. An increase in the asperity’s aspect ratio creates a larger un-wetted area; an increase in the groove width leads to a larger wetted area.

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