# Cassie's law

(Redirected from Cassie-Baxter equation)

Cassie's law describes the effective contact angle θc for a liquid on a composite surface.[1] The law explains how simply roughing up a surface increases the apparent surface angle. The law is stated as:

${\displaystyle \cos \theta _{c}=f_{1}\cos \theta _{1}+f_{2}\cos \theta _{2},}$

where θ1 is the contact angle for component 1 with area fraction f1, and θ2 is the contact angle for component 2 with area fraction f2 present in the composite material. This equation takes on special meaning when in a 2-component system one component is air with a contact angle of 180°. With cosine(180) = −1, the equation reduces to:

${\displaystyle \cos \theta _{c}={\mathit {f}}_{1}(\cos \theta _{1}+1)-1,}$

which implies that with a small f1 and a large θ1, it is possible to create surfaces with a very large contact angle. Cassie's research pointed out that the water-repelling quality of ducks is due to the nature of the composite formed between air and feather and not to other causes, such as the presence of exceptional proofing agents like oils. Water striders also exploit this phenomenon. Artificial superhydrophobic materials such as nanopin film exist in the laboratory that also make use of this law.