larger-radius-lowers-the-pressure-jump - Fluid Mechanics and Surface Tension Step by Step

Because the pressure jump scales as 1 / R, a larger droplet has a smaller pressure difference across its surface. Flatten the curve and the surface tension has less leverage per unit area. The inverse trend is exact for the stated gamma and an ideal sphere; real interfaces vary in shape and gamma, and radius is a measured quantity with its own error.

Keeping gamma fixed while doubling radius halves the pressure jump. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Curvature pressure starts with radius and factor

The radius marker and curvature factor are both checked inputs. Neither is a caption-only explanation.

k=2\qquad R=6\ \text{m}

The pressure jump follows the exact product over radius

The table keeps every row exact. Changing radius or factor changes only the pressure value predicted by the ledger.

\begin{array}{c|c|c|c}k&\gamma&R&\Delta P\\2&6\ \text{N/m}&3\ \text{m}&4\ \text{Pa}\\2&6\ \text{N/m}&6\ \text{m}&2\ \text{Pa}\\2&6\ \text{N/m}&12\ \text{m}&1\ \text{Pa}\\\end{array}

Curvature pressure is an exact gamma over radius ledger

The diagram's radius marker, curvature factor, and pressure jump all come from the same checked source.

\Delta P=k{\gamma\over R}=2\cdot6\ \text{N/m}/6\ \text{m}=2\ \text{Pa}