roughness amplifies natural surface chemistry three commonly used models describe different wetting states of a liquid drop resting on a solid the young relation wenzel relation and cassie baxter relation in 1805 thomas young analyzed the interaction of a fluid droplet resting on a solid surface surrounded by a gas in fig2 by performing a force balance of the interfacial forces a droplet resting on a solid surface and surrounded by a gas forms a characteristic contact angle u03b8 where the contact angle of the droplet u03b8 is shown on the left hand side of fig2 u03b3 sv is the interfacial tension between the solid and vapor u03b3 sl is the interfacial tension between the solid and liquid and u03b3 lv is the interfacial tension between the liquid and vapor if u03b3 sl lt u03b3 sv the contact angle is less than 90 u00b0 and if the liquid is water then the solid is termed hydrophilic if u03b3 sl gt u03b3 sv the contact angle is greater than 90 u00b0 and if the liquid is water then the solid is termed hydrophobic if the solid surface is rough and the liquid is in intimate contact with the solid asperities the droplet is in the wenzel state if the liquid rests on the tops of the asperities it is in the cassie baxter state in 1936 wenzel examined roughened surfaces and assumed that liquid was in intimate contact with solid asperities wenzel determined that when the liquid moves a differential distance dx the liquid experiences a change of surface energy de r u03b3 sl u03b3 sv dx u03b3 lv dx cos u03b8 where r is the ratio of the actual area to the projected area because equilibrium implies de dx 0 the increased solid area interacting with the liquid will change.