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# Cassie's law

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:

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

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.

## References

1. ^  Cassie A.B.D., S. Baxter, Trans. Faraday Soc., 1944, 40, 546