# Surface Tension

The molecules in the middle of a fluid exert an attractive force on each other, called cohesion. This is what holds the fluid together. The molecules at the surface of the fluid, however, experience a cohesive force directed into the fluid. If the surface becomes bent for some reason, there is a restoring force making the surface smooth or flat. The larger the distortion, the larger the force, up to a maximum:

 Fmax = Î³L ...(11)

where Î³ is the surface tension (a function of the fluid) and L is the length of the edge of the object in contact with the fluid. This will become clearer with some examples.

Example-1

Water has a surface tension of 7.2 x 10â€“2 N/m at 25Ëš C. A six-legged water bug stands on the surface of the water. The radius of each foot is 2 x 10â€“4 m. What is the maximum force on the bug due to the water? That is, what is the maximum weight the water surface tension can support?

Solution

In this case, L is the circumference of a foot. (See Figure 10-7.) Applying the formula yields
Fmax = 6Î³ (2Ï€r) = 5 x 10â€“4 N, where 6 is the number of legs on the bug.

Figure 10-7

Example-2

A needle floats on the surface of the water as shown in Figure 10-8. Its length is l = 3 cm, and its width is very small. What is the maximum force exerted on the needle by the surface tension of the water?

Figure 10-8

Solution

In this case, L is the circumference of the dimple, that is, the length of distorted surface around the needle or the length of the dashed line in Figure 10-8. Notice the similarity between Figures 10-7 and 10-8. We use the formula for the perimeter of a rectangle:

L = 2l + 2w â‰ˆ 2l

since the width w is very small. Thus we have

Fmax = Î³(2l) = 4.3 x 10â€“3 N

Example-3

A straight piece of wire has loops at both ends, and the two hoops fit on the arms of a U-shaped frame. A water film fills the interior of the U-shape. (See Figure 10-9.) In this case the surface tension exerts its maximum force.

If the length of the wire is l and the width of the film is w, what is the force of surface tension?

Figure 10-9

Solution

The circumference is the distance around the wire, as in the previous example. In Figure 10-9 we measure the length of the wire along the front of the page and then along the back of the page:

Fmax = Î³(2l)