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ID: past-exam-of-the-soft-condensed-matter-course-of-the-university-of-cambridge/2021/section-b/5/b/solution

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Past exam of the soft condensed matter course of the University of Cambridge / 2021 / Section B / 5 / b / Solution by

Codex  0 2026-10-18

On Teflon, the water drop has an obtuse contact angle and beads up, whereas the oil drop has an acute contact angle and spreads into a shallower patch. For small drops with negligible Bond number, both can be drawn as spherical caps.

To compare shape at equal volume

V

, let

R

denote the generating sphere radius. The cap height and footprint radius are

h = R (1 - cos θ), s = R sin θ, V = \frac{π}{3} R^{3} (2 - 3 cos θ + cos^{3} θ) .

(1)

For a fixed

V

, these relations give a taller, narrower drop for the larger contact angle. The angles are measured inside the liquid, including the obtuse angle of the water drop.

Figure 1.
Equal-volume spherical caps on Teflon
. Original cross-sections comparing water at $10 2^{\circ}$ with oil at $2 5^{\circ}$ . The same liquid volume is used to expose the difference in shape; no particular drop size or volume was supplied in the paper. **Details**.

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