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FLUID MECHANICS - THEORY

   

In this section, the concepts of cohesion and adhesion will be introduced, followed by a discussion of surface tension.

     


Cohesive Forces Exerted on a
Molecule in Liquid


Rubber Band Floats on Water
Click to view movie (59k)

Table: Surface Tension of Water in
Contact with Air as a
Function of the Temperature

Temperature
(oC)
Surface Tension, σ
(N/m)
0 0.0756
10 0.0742
20 0.0728
30 0.0712
40 0.0696
50 0.0679
60 0.0662
70 0.0644
80 0.0626
90 0.0608
100 0.0589
(Source: Munson, B. R., Young, D. F. and Okiishi, T. H., "Fundamentals of Fluid Mechanics," John Wiley, Inc.,
2nd ed., New York, 1994.)
  Surface Tension

 

From physics, it is known that molecules are attracted to each other through molecular forces. The force attraction between like molecules (e.g., molecules within a liquid) is called cohesion. The attraction between unlike molecules (e.g., molecules between liquid and solid) is called adhesion.

As noted in the figure at the left, the net cohesive force exerted on a molecule inside a liquid is zero; whereas there is a net inward cohesive force exerted on a molecule at the surface. As a result, this inward force holds the liquid together and forms a definite volume. In addition, the liquid surface acts like a thin stretched membrane. For example, a rubber band, which is denser than water will float on water. The weight of the rubber band is balanced by the force created by the surface tension of the water and the buoyancy force.

The force exerted on the liquid surface per unit length is referred to as the surface tension and is denoted by the Greek symbol σ. In other words, surface tension is the force (per unit length) required to change the surface shape of the liquid. The SI unit for the surface tension is N/m and the English unit is lb/ft. Surface tension is a fluid property and is generally a function of temperature and the medium in contact with the fluid. The surface tension of water in contact with air is summarized in the table to the left as a function of temperature.

The table below gives the surface tension for various liquids with air.

Material Temp
C / F
Surface Tension, σ
(N/m) (lb/ft)
Water, pure 15.6 / 60 0.0734 0.00503
Water, sea 15.6 / 60 0.0734 0.00503
Gasoline 15.6 / 60 0.022 0.0015
SAE 30W Oil 15.6 / 60 0.036 0.0025
Carbon
Tetrachloride
20 / 68 0.0269 0.00184
Mercury 20 / 68 0.466 0.0319
Glycerin 20 / 68 0.0633 0.00434
Ethyl Alcohol 20 / 68 0.0228 0.00156
     
    Surface Tension - Capillary Action


Force Balance on a Liquid Column
in a Capillary Tube

Fall of Mercury Column in a Capillary Tube



Water on a Clean and Waxed Surface


Detergent as a Surfactant

 

Surface tension can also be observed through the rise and fall of liquid in a capillary glass tube. Consider a liquid in contact with glass. If the adhesion between the liquid and glass is greater than the cohesion of the liquid molecules, then the liquid rises up the tube. The liquid is said to wet the glass surface. On the other hand, if cohesion is greater than adhesion, then the liquid falls in the tube, and it does not wet the surface. The rise and fall of liquid in small diameter tube is referred to as capillary action. For example, water wets a clean surface but tends to form droplets while in contact with a waxed or greasy surface. On the other hand, mercury does not even wet a clean glass surface because of its high surface tension.

Consider the rise of a water column in a small-diameter tube. The height of the rise (h) can be obtained by a force balance (i.e., the vertical component of the force created by surface tension must be balanced by the weight of the liquid column),

     2πRσ cosθ = ρgπ R2h

which can be simplified to yield

     h = 2σ cosθ / (ρgR)

where θ is the contact angle or wetting angle and σ is the surface tension (N/m, lb/ft). For wetting liquids, θ is less than 90°; for non-wetting liquids, θ is greater than 90°. For example, the contact angle is zero for water with a clean glass whereas the contact angle is 130° for mercury with a clean glass.

The surface tension of a liquid can be altered by a surfactant (surface active agent). Take detergent for an example. Detergent is used to reduce the surface tension of water so that water is more likely to wet the surfaces of clothing for cleaning.

     
   
 
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