Page 348 - Mechanical Engineers' Handbook (Volume 4)
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2 Fundamentals  337

            2 FUNDAMENTALS
            2.1 Surface Tension
                           Surface tension is a force that operates on a surface and acts perpendicular and inward from
                           the boundaries of the surface, tending to decrease the area of the interface. As a result, a
                           liquid will tend to take up a shape having minimum area. In the case of zero gravity in
                           vacuum this liquid drop will be a perfect sphere. Surface tension can be viewed as a con-
                           sequence of attractive and repulsive forces among molecules near the interface. From a
                           thermodynamic point of view, it may be interpreted in terms of energy stored in the molecules
                           near the interface. Surface tension consists of the dispersion force and other specific forces
                           such as metallic or hydrogen bonding, i.e.,           . Surface tension in nonpolar liquids
                                                                 d
                                                                      m
                           is entirely caused by dispersion forces. In hydrogen-bonded liquids, both dispersion forces
                           and hydrogen bonding have contributions resulting in relatively larger values of surface
                           tension. In liquid metals, the metallic force combining with the dispersion force results in
                           higher values of surface tension. And it is easy to understand that the surface tensions of
                           liquid metals are higher than those of hydrogen-bonded liquid such as water, which in turn
                           are higher than those of nonpolar liquids such as pure hydrocarbons. The surface tension
                           significantly depends on the temperature. As temperature increases, the surface tension de-
                           creases. The surface tension of water, for example, decreases almost linearly with tempera-
                           ture,     75.83   0.1477T (mN/m), where T is temperature ( C).



            2.2  Contact Angle
                           A physical property that is closely related to the surface tension is the contact angle. The
                           contact angle   is defined as the angle (measured in the liquid) formed between the liquid–
                           vapor interface and the solid–liquid interface as shown in Fig. 2, which may be expressed
                           as

                                                        cos      sv  sl                          (1)

                           where   is the surface tension between the solid and vapor, and   is the surface tension
                                                                                 sl
                                 sv
                           between the solid and liquid. The surface tension between the liquid and vapor is a function
                           of temperature and decreases as the temperature increases. For a given solid surface and
                           liquid, when the surface tension between the solid and liquid is a fixed constant, the contact
                           angle will decrease as the temperature increases. When the temperature increases, the wetting
                           characteristic of a liquid on a given solid surface becomes better.



                                                                  σ
                                                  vapor

                                       σ sv                  liquid

                                                        α
                                                               σ sl
                                                                         solid
                                                      Figure 2 Contact angle.
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