Young–Laplace equation

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The Young–Laplace equation is a fundamental equation in the field of fluid mechanics and capillarity. It describes the pressure difference across the interface of a curved surface due to the surface tension of the liquid. This equation is named after the British scientist Thomas Young and the French mathematician and astronomer Pierre-Simon Laplace.

Mathematical Formulation

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 interface,
• \(\gamma\) is the surface tension of the liquid,
• \(R_1\) and \(R_2\) are the principal radii of curvature of the surface.

Derivation

The derivation of the Young–Laplace equation involves considering the balance of forces at the interface of a curved liquid surface. The surface tension acts to minimize the surface area, creating a pressure difference between the inside and outside of the curved surface.

Applications

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

• Bubbles and droplet formation,
• Capillary action,
• Biophysics (e.g., the shape of cell membranes),
• Microfluidics.

Related Concepts

• Surface tension
• Capillary action
• Fluid mechanics
• Curved surface
• Thomas Young (scientist)
• Pierre-Simon Laplace

See Also

• Laplace's equation
• Capillary pressure
• Meniscus (liquid)
• Contact angle