curvature-pressure-radius-factor-cross-scan - Surface Tension and Capillarity Step by Step

Curvature pressure is scanned across inverse radius and direct factor. 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 has a radius input and a surface-count factor

The radius marker is visible in the diagram. The factor is a checked integer that distinguishes a droplet-style surface from a two-sided film surface.

\Delta P=k{\gamma\over R}=2\cdot6\ \text{N/m}/3\ \text{m}=4\ \text{Pa}

Increasing radius lowers the pressure jump

Gamma and factor are fixed here. The three radius rows expose the inverse relationship without decimal approximations.

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

Increasing the curvature factor raises the pressure jump

The factor rows keep radius fixed. A two-sided film factor gives a larger pressure jump than a one-sided training case.

\begin{array}{c|c|c|c}k&\gamma&R&\Delta P\\1&6\ \text{N/m}&3\ \text{m}&2\ \text{Pa}\\2&6\ \text{N/m}&3\ \text{m}&4\ \text{Pa}\\4&6\ \text{N/m}&3\ \text{m}&8\ \text{Pa}\\\end{array}