ability liquid maintain contact solid surface resulting interactions brought degree determined force balance cohesive forces deals phases materials gas liquid solid center attention studies advent past decades carbon important bonding adherence materials surface forces control responsible related effects including effects types non active explanation forces liquid solid cause liquid drop spread surface cohesive forces liquid cause drop ball avoid contact surface contact angle seen figure angle liquid interface meets solid liquid interface contact angle determined result cohesive forces tendency drop spread flat solid surface increases contact angle decreases contact angle provides measure contact angle low contact angle usually indicates surface favorable fluid spread large area surface contact angles greater high contact angle generally means surface unfavorable fluid minimize contact surface form compact liquid water surface termed surface surfaces contact angles greater showing contact liquid drop surface referred lotus effect table describes varying contact angles corresponding solid liquid liquid liquid interactions term low contact angle conditions higher contact angles result similarly terms apply polar high energy low energy surfaces interact main types solid surfaces traditionally solid surfaces divided high energy low energy types relative energy solid bulk nature solid metals glasses known hard chemical bonds hold metallic strong takes large input energy break alternatively large energy required cut bulk separate surfaces high surface energy termed high energy molecular achieve complete high energy surfaces type weak molecular crystals etc molecules held essentially physical forces van der hydrogen bonds held weak forces low input energy required break termed low energy depending type liquid chosen low energy surfaces permit complete partial dynamic surfaces reported undergo changes surface energy application appropriate example surface presenting driven molecular motors shown undergo changes water contact angle switched differing surface energies low energy surfaces low energy surfaces primarily interact van der forces key findings work observed increases surface tension liquid decreased able establish linear function surface tension organic surface low termed intercept lines critical surface tension surface critical surface tension important characteristic solid knowing critical surface tension solid possible predict surface surface determined chemical groups solid differences surfaces similar structure differences packing instance surface branched chains poorer packing surface straight chains ideal solid surfaces ideal surface flat rigid perfectly smooth zero contact angle zero implies advancing contact angles equal words stable contact angle exists drop liquid placed surface characteristic contact angle formed depicted furthermore ideal surface drop return original shape disturbed following apply ideal solid surfaces valid state moving phase boundary line exists energy phases figure shows line contact phases meet net force unit length acting boundary line phases zero components net force direction given formula formula formula angles shown surface energy indicated phases relations expressed analog triangle known triangle shown figure triangle consistent restriction formula applying law law produce relations describe angles depend surface energies surface energies form sides triangle constrained triangle meaning surface tensions exceed sum surface energies follow brought contact configuration consistent figure exist geometry young relation phase replaced flat rigid surface shown figure second net force equation young equation formula relates surface tensions phases solid liquid gas subsequently contact angle liquid solid surface knowledge surface energies involved equation applies gas phase liquid liquid phase real smooth surfaces young contact angle young equation assumes perfectly flat rigid surface referred ideal surface cases surfaces far ideal situation considered case rough surfaces case smooth surfaces real rigid perfectly smooth surface drop assume wide spectrum contact angles ranging called advancing contact angle formula called contact angle formula contact angle formula calculated formula formula shown formula formula young equation spreading young equation larger sum surface energies consequence restriction prediction complete zero lack solution young equation indicator configuration contact angle situations useful spreading formula liquid surface completely complete partial occurs combining spreading definition young relation yields young equation formula physical solutions rough solid surfaces unlike ideal surfaces real surfaces perfect chemical result phenomenon called contact angle defined difference advancing contact angles formula simpler terms contact angle essentially displacement contact line figure expansion figure depicts advancing contact angles advancing contact angle maximum stable angle contact angle minimum stable angle contact angle occurs different stable contact angles found solid varying stable contact angles known states motion phase boundary involving advancing contact angles known dynamic contact line advances covering surface liquid contact angle increased generally related velocity contact line velocity contact line increased bound contact angle increases approaches gas phase thin layer liquid solid effect results contact line moving high speed complete occur known departure surface interest rough texture rough texture surface fall categories regime liquid fills grooves surface regime surface composite types patches important example composite surface composed patches air solid surfaces varied effects contact angles main models attempt describe surfaces apply drop size sufficiently large compared surface scale size comparable underlying pillars effect line tension considered model model describes regime seen figure defined following equation contact angle rough surface formula formula apparent contact angle corresponds stable state minimum free energy state system ratio measure surface affects surface ratio defined ratio true area solid surface apparent area young contact angle defined ideal surface equation demonstrates contact angle rough surface different contact angle describe contact angle model dealing surface model sufficient complex model needed measure apparent contact angle changes materials involved surface like seen figure explained equation law formula ratio wet surface area fraction solid surface area wet liquid important realize equation hand different surface fraction total surface area denoted formula equals total surface recast following equation formula surface tension liquid solid surface tension component solid liquid surface tension component case worth mentioning liquid drop placed substrate creates small air pockets underneath case component system denoted formula key difference notice surface tension solid second surface tension component assumption surface air exposed substrate system subsequently equation expressed equation easily derived equation experimental results surface properties versus systems showed effect pinning young angle region classified model liquid air composite system largely point sharp transition regime found drop surface edges drop precursor film advent high resolution imaging researchers started obtain experimental data led question assumptions equation calculating apparent contact angle groups believe apparent contact angle largely dependent triple line triple line contact surface rest surface like rest drop theory follow surface bending triple line unfavorable seen real world situations theory preserves equation time explaining presence energy state triple line idea precursor film film thickness advances ahead motion found triple line furthermore precursor film allows triple line bend different originally considered unfavorable precursor fluid observed environmental scanning electron surfaces pores formed bulk introduction precursor film concept triple line follow feasible correctly explaining model effect lotus effect surface enhanced different length scales red rose takes advantage hierarchy provide sufficient specifically rose collection surface turn term effect describes fact water surface rose spherical shape roll turned upside water drops maintain spherical shape contact angle roll surface high force water comparing effect lotus effect important note striking differences surface structure lotus leaf rose seen figure explain different effects lotus randomly rough surface low contact angle means water able wet spaces spikes allows air remain inside texture causing surface composed air solid result force water solid surface extremely low allowing water roll easily self cleaning phenomenon rose larger scale lotus leaf allows liquid film texture seen figure liquid enter larger scale grooves enter smaller grooves known regime liquid wet larger scale grooves force water solid high explains water fall angle turned upside effect fail volume larger balance weight surface tension surpassed transition model drop sits surface trapped air underneath transition state state air pockets longer stable liquid begins middle drop creating mushroom state seen figure penetration condition given formula critical contact angle fraction solid liquid interface drop contact surface solid flat surface penetration minimize surface energy reaches edges drop arriving state solid considered material surface phenomenon spreading called contact angles spreading occurs model valid contact angle penetration spreads drop liquid film forms surface figure depicts transition state surface film state film surface model longer applies state condition young relation yields formula fine tuning surface possible achieve transition regions generally surface spreading dynamics drop placed smooth horizontal surface generally state spreads contact radius reached partial taking account contributions drop radius function time expressed formula complete situation drop radius time spreading process given formula surface tension fluid drop volume fluid density fluid constant shape factor experimental delay time drop radius effect technological processes require control liquid spreading solid surfaces drop placed surface completely wet partially wet wet surface reducing surface tension material partially completely excess free energy drop solid surface formula liquid tension solid liquid tension solid tension area liquid interface excess pressure inside liquid radius base based equation excess free energy decreases decreases increases absorbed liquid solid liquid solid modify behavior materials reduce free energy absorbed surface polar head groups face solution tail pointing outward surfaces form solid causing dynamic drop radius characterized drop begins spread contact angle changes based following equation formula initial contact angle final contact angle transfer time scale absorbed solid surface tension increases edges drop result drop spreads
Wetting