Orbit Research Associates Private Limited

The Wilhelmy plate method measures:

• Surface tension (SFT) of a liquid,

• Interfacial tension (IFT) between liquids,

• Contact angle (θ) between liquid and solid.

A thin plate is dipped vertically into the liquid, and the force FFF on it is measured. The force relates to surface tension and contact angle by:

F=σ×L×cos⁡θF = \sigma \times L \times \cos \thetaF=σ×L×cosθ

• σ\sigmaσ = surface or interfacial tension,

• LLL = wetted perimeter of the plate,

• θ\thetaθ = contact angle.

For SFT/IFT:
A platinum plate is used, with contact angle ≈ 0°, so

σ=FL\sigma = \frac{F}{L}σ=LF​

For contact angle:
Dip the solid plate in a liquid with known σ\sigmaσ, then calculate

cos⁡θ=Fσ×L\cos \theta = \frac{F}{\sigma \times L}cosθ=σ×LF​

The method is static and can measure dynamic contact angles by immersing and withdrawing the plate. The wetted length LLL must be known and constant.

The Washburn method measures the contact angle and surface free energy of porous materials like powders and textiles by observing how a liquid is drawn up into the material via capillary action.

A glass tube filled with powder is dipped in a test liquid, and the liquid’s mass uptake over time is recorded. Treating the powder as many tiny capillaries, the relationship between mass squared (m2m^2m2) and time (ttt) is linear and described by the Washburn equation:

m2=cσcos⁡θηρ×tm^2 = \frac{c \sigma \cos \theta}{\eta \rho} \times tm2=ηρcσcosθ​×t

• ccc is a capillary constant related to pore size and packing,

• θ\thetaθ is the contact angle,

• σ,η,ρ\sigma, \eta, \rhoσ,η,ρ are the liquid’s surface tension, viscosity, and density.

To find ccc, measure with a fully wetting liquid (contact angle 0∘0^\circ0∘), then use this to calculate θ\thetaθ for other liquids.

Notes:

• Powder packing must be consistent since ccc depends on bulk density.

• Angles above 90° cannot be measured (no wetting). For these, drop shape analysis is used instead.