Effect of droplet size on internal pressure due to surface tension As the diameter of a liquid droplet decreases, how does the excess pressure inside the droplet change?

Introduction / Context:
Surface tension produces a pressure jump across curved interfaces. For small droplets or bubbles, this capillary pressure becomes significant. Knowing how it scales with size is essential in atomization, emulsions, spray drying, and cloud microphysics.

Given Data / Assumptions:

• Liquid droplet (single interface), spherical.
• Surface tension T is constant (isothermal, clean interface).
• Static equilibrium (no acceleration/flow inside).

Concept / Approach:

For a spherical interface, the excess internal pressure over the outside pressure is Δp = 2 * T / r for a liquid droplet (one surface). In terms of diameter d, Δp = 4 * T / d. Hence, as size decreases (smaller r or d), Δp increases inversely with size.

Step-by-Step Solution:

Verification / Alternative check:

For a soap bubble (two interfaces), Δp_bubble = 4 * T / r = 8 * T / d, even larger for the same diameter. The inverse proportionality to size is consistent across spherical capillarity relations.

Why Other Options Are Wrong:

Decrease or no change contradicts Δp ∝ 1/r; zero or negative is physically incorrect for a clean droplet under positive T.

Common Pitfalls:

Confusing coefficients for droplet (single interface) and bubble (double interface); mixing radius and diameter forms.

Final Answer:

Increases