▁contact ▁ar ises ▁from ▁the ▁consideration ▁of ▁a ▁therm od ynamic ▁equilibrium ▁between ▁the ▁three ▁phases : ▁the ▁liquid ▁phase ▁( L ), ▁the ▁solid ▁phase ▁( S ), ▁and ▁the ▁gas ▁or ▁v apor ▁phase ▁( G ) ▁( which ▁could ▁be ▁a ▁mixture ▁of ▁ambient ▁atmosphere ▁and ▁an ▁equilibrium ▁concentration ▁of ▁the ▁liquid ▁v apor ). ▁( The ▁" g ase ous " ▁phase ▁could ▁be ▁replaced ▁by ▁another ▁imm is cible ▁liquid ▁phase .) ▁If ▁the ▁solid – v apor ▁inter fa cial ▁energy ▁is ▁denoted ▁by ▁, ▁the ▁solid – liqu id ▁inter fa cial ▁energy ▁by ▁, ▁and ▁the ▁liquid – v apor ▁inter fa cial ▁energy ▁( i . e . ▁the ▁surface ▁t ension ) ▁by ▁, ▁then ▁the ▁equilibrium ▁contact ▁angle ▁ ▁is ▁determined ▁from ▁these ▁quantities ▁by ▁the ▁Young ▁equation : ▁ ▁The ▁contact ▁angle ▁can ▁also ▁be ▁related ▁to ▁the ▁work ▁of ▁ad hes ion ▁via ▁the ▁Young – D u pr é ▁equation : ▁ ▁where ▁ ▁is ▁the ▁solid ▁– ▁liquid ▁ad hes ion ▁energy ▁per ▁unit ▁area ▁when ▁in ▁the ▁medium ▁G . ▁ ▁Mod ified ▁Young ’ s ▁equation ▁ ▁The ▁earliest ▁study ▁on ▁the ▁relationship ▁between ▁contact ▁angle ▁and ▁surface ▁t ensions ▁for ▁sess ile ▁dro ple ts ▁on ▁flat ▁surfaces ▁was ▁reported ▁by ▁Thomas ▁Young ▁in ▁ 1 8 0 5 . ▁A ▁century ▁later ▁Gib bs ▁proposed ▁a ▁modification ▁to ▁Young ’ s ▁equation ▁to ▁account ▁for ▁the ▁vol um et ric ▁dependence ▁of ▁the ▁contact