# Wilhelmy plate

Illustration of Wilhelmy plate method. The magnitude of the capillary force ${\displaystyle F}$ on the plate is proportional to the wetted perimeter, ${\displaystyle l=2w+2d}$, and to the surface tension ${\displaystyle \gamma }$ of the liquid-air interface.

A Wilhelmy plate is a thin plate that is used to measure equilibrium surface or interfacial tension at an air–liquid or liquid–liquid interface. In this method, the plate is oriented perpendicular to the interface, and the force exerted on it is measured. Based on the work of Ludwig Wilhelmy, this method finds wide use in the preparation and monitoring of Langmuir–Blodgett films.

## Detailed description

The Wilhelmy plate consists of a thin plate usually on the order of a few square centimeters in area. The plate is often made from filter paper, glass or platinum which may be roughened to ensure complete wetting. In fact, the results of the experiment do not depend on the material used, as long as the material is wetted by the liquid.[1] The plate is cleaned thoroughly and attached to a balance with a thin metal wire. The force on the plate due to wetting is measured using a tensiometer or microbalance and used to calculate the surface tension (${\displaystyle \gamma }$) using the Wilhelmy equation:

${\displaystyle \gamma ={\frac {F}{l\cos(\theta )}}}$

where ${\displaystyle l}$ is the wetted perimeter (${\displaystyle 2w+2d}$), ${\displaystyle w}$ is the plate width, ${\displaystyle d}$ is the plate thickness, and ${\displaystyle \theta }$ is the contact angle between the liquid phase and the plate. In practice the contact angle is rarely measured, instead either literature values are used, or complete wetting (${\displaystyle \theta =0}$) is assumed.