Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A drop of water of mass is put on a clean, flat glass plate, and a second clean glass plate is pressed down on it. The water spreads into a thin round disc between the plates, thick, wetting both plates completely (zero contact angle), as shown in the figure. The surface tension of water is and its density is . Ignore the effect of gravity on the thin film, but take for the weight of the drop.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Find the shape of the film, the pressure inside it, and from that the force. Then find the work from the change in surface energy.
Step 1. The disc (a). The volume is . Spread to a thickness , it covers of each plate. So and .
Step 2. The pressure (b). At the rim, the water surface is curved two ways. Seen edge on, it is a half circle of radius that curves into the water (water wets the glass), which lowers the pressure inside by . Seen from above, the rim is a circle of radius , which raises it by only . So the water is at below the air's pressure.
Step 3. The force (c). The air pushes on the outside of each plate with the full air pressure, and the water pushes on the inside with less. Over the wetted area the plates are pressed together by
The drop weighs only , so this is about times its weight. A thin film of water makes two plates very hard to pull apart.
Step 4. The work (d). Covering a square metre of glass with water lowers the energy by (zero contact angle), on each plate. The film covers of each plate, so its surface energy is , apart from a constant. Pushing the plates from to , the surface forces do the work
The force is the same as in (c): .
Answer: (a) . (b) . (c) . (d) .
Check. The force grows as : at it is , four times as much. The work in (d) lies between and , as it should.
Watch out. The force does not come from surface tension pulling along the rim, which is tiny. It comes from the low pressure inside the film, acting over the whole wetted area.
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