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6. Theory
6.1 Theory of contact angle measurements
Definition
Contact angle, , is a quantitative measure of the wetting of a solid by a liquid. It is defined
geometrically as the angle formed by a liquid at the three-phase boundary where a liquid, gas and solid
intersect. As shown below it is the angle between the solid and the tangent to the drop profile at the
intersection point.
Figure 6.1. Contact angle is the angle between the drop and the surface .
Low values of indicate that the liquid spreads, or wets, well while high values indicate poor wetting. If
the angle is less than 90° the liquid is said to wet the solid. If it is greater than 90° it is said to be non-
wetting. A zero contact angle represents complete wetting.
The values of static contact angles, where the drop is not in motion, are found to depend on the recent
history of the interaction. When the drop has recently expanded the angle is said to represent the
advanced contact angle. When the drop has recently contracted the angle is said to represent the
receded contact angle. These angles fall within a range with advanced angles forming a maximum value
and receded angles forming a minimum value.
If the three-phase boundary is in actual motion the angles produced are called dynamic contact angles
and are referred to as advancing or receding angles. The difference between advanced and advancing
or receded and receding is that in the static case motion is incipient and in the dynamic case motion is
actual. Dynamic contact angles may be measured at various speeds, at low velocities they should be
equal to static angles.
Goniometry
Goniometry is the analysis of the shape of a drop of test liquid placed on a solid. The basic elements of a
goniometer include a light source, sample stage, lens and image capture. Contact angle can be
assessed directly by measuring the angle formed between the solid and the tangent to the drop surface.
Determining the tangent line which will define the contact angle is a factor that can limit the
reproducibility of contact angle measurements. Conventional goniometry relies on the consistency of the
operator in the assignment of the tangent line. This can lead to significant error and especially to
subjective error between users.