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Cassie's law

Cassie's law describes the effective contact angle θ_c 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:

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$\cos \theta_c =\gamma_1 \cos \theta_1 + \gamma_2 \cos \theta_2 \,$

where by θ₁ is the contact angle for component 1 with areal fraction γ₁ and θ₂ is the contact angle for component 2 with areal fraction γ₂ 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:

$\cos \theta_c =\gamma_1 ( \cos \theta_1 + 1) -1 \,$

which implies that with a small γ₁ 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 very nature of the composite formed between air and feather and not by 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.