# Washburn method

The Washburn method is a method for measuring the contact angle and the surface free energy of porous substances such as bulk powder or pigments, and absorbent materials such as paper or textiles.

###### Background

In a Washburn measurement, a glass tube with a filter base filled with powder, for example, comes into contact with a test liquid. The liquid is drawn up as a result of capillary action. The increase in mass of the tube, which is suspended from a force sensor, is determined with respect to time during the measurement. If the bulk powder is looked upon as a bundle of capillaries, then the process can be described by the Washburn equation:

m = mass; t = flow time; σ = surface tension of the liquid; c = capillary constant of the powder; ρ = density of the liquid; θ = contact angle; η = viscosity of the liquid

The constant c includes the number of micro-capillaries and their mean radius, and depends on the nature of the powder and also on that of the measuring tube.

Plotting the square of the mass m2 against time t shows a linear region, the slope of which, for known liquid properties (σ, ρ and η), only contains the two unknowns c and θ.

To determine the constant c, a measurement is carried out with an optimally wetting (spreading) liquid (e.g. n-hexane), with which the contact angle θ is 0° (cos θ = 1). The value of c is substituted in the equation in order to determine the contact angle θ with the help of other liquids. The contact angle measured in this way is an advancing angle, as it is measured in the course of wetting. The surface free energy of the powder can be calculated from the contact angle data with the help of different models.

As c depends on the bulk density, it must be ensured that the powder is packed consistently for all measurements on the same powder.

Contact angles greater than 90° cannot be measured using this method, as no wetting of the powder takes place. Alternatively, contact angle measurements can be carried out on a powder bed using drop shape analysis.

###### Bibliography

Washburn, E.W., Phys. Rev. 17, 374 (1921).