Question

What is Laplace tension equation?

Answer 1

The Laplace tension equation describes the relationship between the pressure difference across the surface of a liquid drop or bubble and the surface tension of the liquid. It is especially important in the study of fluids and plays a key role in understanding phenomena like the formation of droplets and bubbles.

The equation is:

\[
\Delta P = \frac{2 \gamma}{r}
\]

Where:
- \(\Delta P\) is the pressure difference between the inside and outside of the drop or bubble.
- \(\gamma\) is the surface tension of the liquid.
- \(r\) is the radius of the liquid drop or bubble.

### Explanation:
- **Surface tension** (\(\gamma\)) is a force that acts along the surface of a liquid, making it behave like a stretched elastic membrane.
- The **pressure difference** across the surface is higher inside the drop or bubble because of the curved shape of the surface.
- A smaller radius (smaller drop or bubble) results in a higher pressure difference, while a larger radius results in a lower pressure difference.

This equation is crucial in various applications, including understanding the behavior of bubbles in liquids, the formation of drops, and even in biological systems (like the surface tension of alveoli in the lungs).