Young–Laplace equation

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The Young–Laplace equation is a fundamental equation in the field of fluid mechanics that describes the capillary pressure difference sustained across the interface of two static fluids due to the surface tension. It is named after the British scientist Thomas Young and the French mathematician and astronomer Pierre-Simon Laplace.

Mathematical Formulation[edit | edit source]

The Young–Laplace equation is given by:

\(\Delta P = \gamma \left( \frac{1}{R_1} + \frac{1}{R_2} \right)\)

where:

  • \(\Delta P\) is the pressure difference across the fluid interface,
  • \(\gamma\) is the surface tension of the interface,
  • \(R_1\) and \(R_2\) are the principal radii of curvature of the interface.

Derivation[edit | edit source]

The derivation of the Young–Laplace equation involves considering the balance of forces at the interface of two fluids. The surface tension acts to minimize the surface area, creating a pressure difference across the interface. This pressure difference is related to the curvature of the interface, which is described by the radii of curvature \(R_1\) and \(R_2\).

Applications[edit | edit source]

The Young–Laplace equation has numerous applications in various fields, including:

Related Concepts[edit | edit source]

See Also[edit | edit source]

References[edit | edit source]

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Contributors: Prab R. Tumpati, MD