surface tension (N/m)
contact angle (°)
liquid density (kg/m³)
capillary radius (mm)

Liquids (such as water, which has a density of 1000 kg/m³) that wet glass climb upward on the surfaces of their containers until the effects of surface tension and gravity balance. A concave meniscus forms. Change the surface tension, the contact angle, the liquid density, and the capillary radius with the sliders. The capillary rise increases sharply as the tube narrows.

The capillary rise is given by

h = 2 γ cos θ ρ g r

where γ = the solid–liquid surface tension (N/m),
θ = the contact angle for the meniscus (measured upward from the vertical wall),
ρ = liquid density (kg/m³),
g = the gravitational acceleration (9.81 m/s²),
r = capillary radius (mm).

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by S. M. Blinder. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.