Tas et al figure 1 a thin layer of liquid working as

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Unformatted text preview: of stiction. These are: Capillary Forces Hydrogen Bridging Electrostatic Forces Van der Waals forces © N. Dechev, University of Victoria 28 Stiction due to Capillary Forces Capillary forces occur when there is a liquid-solid interface. N Tas et al Consider the following example of two parallel plates with a liquid between them: d Figure 2. Liquid drop (L) on a solid (S), in air (A). θC is the contact angle between liquid and solid in air. Surface Tension Between Plates [Image from N. Tas, et al.] Figure 1. A thin layer of liquid working as an adhesive between two plates. θ is the liquid If the angle of the contact angleair, g isis lesscontact angle between is the force F than 90˚, then a and solid in #c the liquid layer thickness, and A wetted area. A force F is applied to maintain equilibrium. will exist between the two plates. C © N. Dechev, University of Victoria where γl a is the surface tension of the liquid–air interface, and r is the radius of curvature of the meniscus (negative if concave). In figure 1, the liquid is between the plates and the liquid contacts the solid at the fixed contact angle. From simple geometry it follows that r = −g /2 cos θC . In equilibrium, an external force F separating the plates must be applied to counterbalance the capillary pressure forces: F = − pl a A = 2Aγl a cos θC g Figure 3. Liquid bridging two solids. The liquid is non-spreading. The solid is only covered in the bridged area Ab . At is the total facing area. 29 (2) where A is the wetted area. Note that a positive force F corresponds to a negative Laplace pressure. The pressure inside the liquid is lower than outside and the plates are pushed together by pressure forces. For stiction calculations it is convenient to calculate the surface energy stored at the interface that is bridged by a drop of liquid [2]. Consider a drop of liquid placed on a solid, surrounded by air (figure 2). In equilibrium, the contact angle between liquid and solid is determined by the balance between the surface tensions of the three interfaces. This balance is expressed by Young’s equation [10]: Stiction due to Capillary Forces Figure 4. Liquid bridging two solids. The liquid is spreading. Outside the bridged area Ab , a thin liquid film covers the solid. The total surface the area between the plates The pressure difference between the liquid-air interface is given calculated byenergy ofthe surface tensions of the can be adding by the equation: 0<θ <π (3) γ = γ + γ cos θ solid–air, solid–liquid and liquid–air interfaces [2]. It is sa where: sl la C C where γs a is the surface tension of the solid–air interface and γs l is the surface tension of the solid–liquid interface. Young’s equation is also valid for configurations other than that of figure 2. The contact angle is the same on a curved or irregular shaped surface, inside a capillary etc. If the solid–air surface tension is smaller than the sum $pla = pressure differenceandliquid-air interface tensions, then the of the liquid–air at solid–liquid surface %la = surface tension ofis...
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