IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matte 21 !"##$% &'&(") !(*++% do,:(#.(#--.#$/*0-$-&."(.&'.&'&(") Dynamics of wetting: from inertial spreading to viscous imbibition L Courbin(,", J C Bird(, M Reyssat( and ! "tone(,* ( S1hoo2 o3 En4,nee ,n4 and A++2,ed S1,en1es5 Ha 6a d Un,6e s,ty5 Ca78 ,d4e5 MA #"(*-5 USA " IPR5 UMR CNRS '"/(5 Ca7+9s Bea92,e95 Un,6e s,t:eRennes (5 */#&" Rennes5 F an1e E-7a,2: hastone;+ ,n1eton.ed9 Recei6ed "# Ap ,2 "##$5 in <nal fo 7 $ J9ly "##$ P982,shed "$ Octo8e "##$ On2,ne at sta1=s.,o+.o 4.JPhysCM."(.&'&(") !bstract >e e+o t the ,n?9en1e o3 the nat9 e o3 8o9nda ,es on the dyna7,1s o3 @ett,n4. >e e6,e@ so7e @o = e1ently +982,shed and h,4h2,4ht ne@ eApe ,7ental obser6ations. O9 paper 8e4ins @,th the s+ ead,n4 o3 d o+s on s98st ates and de7onst ates ho@ the eA+onents o3 the s+ ead,n4 2a@s a e a33e1ted e,the 8y the s9 3a1e 1he7,st y o 8y the d o+2et sha+e. >e then d,s19ss the ,78,8,t,on o3 1o7+2ete2y and +a t,a22y @ett,n4 ?9,ds ,nto 1hanne2s and o6e 7,1 oteAt9 ed s9 3a1es. Start,ng with the one0di7ens,ona2 ,78,8,t,on o3 1o7+2ete2y @ett,n4 2,B9,ds ,n t98es and s9 3a1e teAt9 es5 we sho@ that !,% sha+e 6a ,at,ons o3 1hanne2s 1han4e the +owe 02a@ es+onse o3 the ,78,8,t,on and !,,% the 4eo7et ,1a2 +a a7ete s o3 a s9 3a1e o94hness 1han4e the s+ ead,n4 8eha6,o . Fo +a t,a22y @ett,n4 ?9,ds5 we o8se 6e d, e1t,ona22y de+endent s+ ead,n4: +o2y4ona2 @etted do7a,ns 1an 8e o8ta,ned. >e 1on129de @,th a ta892a s977a y o3 o9 <nd,n4s5 a22o@,n4 9s to d a@ 1onne1t,ons 8et@een the d,33e ent syste7s ,n6est,4ated5 and shed 2,4ht on o+en B9est,ons that e7a,n to 8e add essed. !So7e <49 es ,n th,s a t,12e a e ,n 1o2o9 on2y ,n the e2e1t on,1 6e s,on% 1. Introduction θeBH e,the 8y 1han4,n4 the s9 3a1e tens,on o3 the 2,B9,d5 γ 5 o 8y 7od,3y,n4 the s9 3a1e 1he7,st y. >hen a 2,B9,d 7a=es 1onta1t @,th any s9 3a1e5 the 1onta1t 2,ne On2y ,dea2 s9 3a1es a e s7ooth and ,t ,s @e22 =no@n 7o6es 9nt,2 the 2,B9,d.so2,d.6a+o syste7 ea1hes eB9,2,8 ,97 that 8oth s9 3a1e 1he7,stry and s9 3a1e o94hness a33e1t state. The dynam,1s on ho@ the 2,B9id ea1hes ,ts eB9,2,8 ,97 the dyna7,1s o3 @ett,n4 C'E. Unde stand,n4 the ,n?9en1e a e not t ,6,a2 and 6a y @,th s9 3a1e 1he7,st y5 s9 3a1e on dyna7,1s o3 @ett,n4 o3 s9 3a1e 1he7,st y o s9 3a1e to+o4 a+hy5 and 2,B9,d + o+e t,es C(D&E. In th,s 1ont ,89t,on5 to+o4 a+hy a2one5 o s9 3a1e 1he7,st y to4ethe @,th s9 3a1e @e 3o19s on syste7s @he e the do7,nant d ,6,n4 3o 1e es92ts o94hness5 1an y,e2d ne@ 9nde stand,n4 and +otent,a2 3 o7 the ed91t,on o3 s9 3a1e ene 4y5 ,.e. the 1a+,22a y 3o 1e. a++2,1at,ons ,n6o26,n4 wett,n45 8oth stat,1s and dyna7,1s5 3o S+e1,<1a22y5 we e+o t on the @ett,n4 dyna7,1s 3o d,33e ent a 2a 4e 6a ,ety o3 s,t9at,ons5 8oth ,n nat9 e and ,n ,nd9st y. 2,B9,dDso2,d syste7s. In the 2a8o ato y5 @e 9sed so3t02,tho4 a+hy 7ethods to Fo ,dea2 s9 3a1es !,.e. s7ooth and 1he7,1a22y ho7o4e0 des,4n and 7an93a1t9 e to+o4 a+h,1a22y +atte ned5 89t 1he70 neo9s%5 a 7,n,7,Fat,on o3 the 6a ,at,on o3 the tota2 s9 3a1e ,1a22y ho7o4eneo9s5 s9 3a1es 7ade o3 +o2yd,7ethys,2oAane ene 4y needed to 7o6e the 1onta1t 2,ne a d,stan1e dx !see !PDMS% C)E. >,tho9t 39 the s9 3a1e t eat7ent5 PDMS ,s <gure (!a%% 2eads to the 3a7,2,a Yo9n4Gs e2at,on that de<nes hyd o+ho8,1 so that a @ate d o+2et +a t,a22y @ets the s9 3a1e the eB9,2,8 ,97 1onta1t an42e θeB 3o 7ed 8et@een the d o+ and @,th an eB9,2,8 ,97 1onta1t an42e θeB $#◦ (see <49 e (!8%%. the s98st ate: 1os θeB �γs6 γ s�)/γ C*E. In th,s e2at,on5 γs65 ≈ = − >e 7an93a1t9 ed s9 3a1e teAt9 es that 1ons,st o3 7,1 on0s,Fe γs� and γ denote5 es+e1t,6e2y5 the so2,d.6a+o 5 so2,d.2,B9,d and 1y2,nd ,1a2 +osts a an4ed on a sB9a e 2att,1e @,th +ost ad,, 2,B9,d.6a+o s9 3a1e tens,ons !,.e. ene 4y +e 9n,t s9 3a1e a ea%. and he,4hts5 R and H 5 and 2att,1e d,stan1es d !<49 e (!1%%. The e3ore ,3 one o3 the +hases ,s a, 5 the e a e t@o @ays to 6a y F,gure ((d% shows an eAa7ple o3 the we22 =nown I3a=, G * Present add ess: De+a t7ent o3 Mechan,1a2 and Aeros+a1e En4,nee ,n45 e33e1t: the ,n1 ease ,n s9 3a1e a ea es92t,n4 3 o7 the add,t,on P ,n1eton Un,6e s,ty5 P ,n1eton5 NJ #-/&&5 USA. o3 s9 3a1e o94hness to a s7ooth PDMS s98st ate 7a=es ,t #$/*0-$-&.#$.&'&(")J(*K*#.## ( L "##$ IOP P982,sh,n4 Ltd P ,nted ,n the UM J. Phys.: Condens. Matte 21 !"##$% &'&(") L Co9 8,netal %igure 2# S1he7at,1 e+ esent,n4 the d,33e ent as+e1ts o3 @ett,n4 @e d,s19ss ,n th,s +a+e : d o+ s+ ead,n45 one0d,7ens,ona2 ,78,8,t,on5 %igure 1# !a% Pa t,a2 @ett,n4 o3 an ethano2 d o+2et on a s7ooth and @,1=,n4 o3 teAt9 es. The ,nte se1t,ons o3 the 1, 12es e7+has,Fe PDMS s98st ate. Inset: 12ose09+ o3 the 1onta1t 2,ne the d o+ 7a=es the 1onne1t,ons that eA,st 8et@een to+,1s: the sha+e o3 a 8o9nda y @,th the s98st ate sho@,n4 Yo9n4Gs 1onst 91t,on. !8% A d o+ o3 @ate 7atte s 3o d o+ s+ ead,n4 and one0d,7ens,ona2 ,78,8,t,on5 the deposited on smooth hyd opho8,1 PDMS 7a=es an eB9,2,8 ,97 eB9,2,8 ,97 1onta1t angle a33e1ts the dyna7,1s o3 d o+2ets and 1onta1t an42e 12ose to θeB $#◦. !1% M,1 o+atte ned s9 3a1e 7ade o3 @,1=,n4 o3 s9 3a1e teAt9 es5 and 8oth one0 and t@o0d,7ens,ona2 ≈ PDMS and s1he7at,1 de+,1t,n4 the to+o4 a+h,1a2 3eat9 es. !d% A ,78,8,t,on o3 7,1 oteAt9 ed s9 3a1es a e ,n?9en1ed 8y the d o+ o3 @ate de+os,ted on a o94h PDMS !s9+e hyd o+ho8,1% to+o4 a+h,1 3eat9 es o3 a s9 3a1e o94hness. >ett,n4 ,s the 1ent a2 s98st ate !as sho@n ,n !1%% ado+ts a nea 2y s+he ,1a2 sha+e5 the7e o3 these a eas. θ (/#◦. The +,1t9 es o3 d o+s a e ada+ted 3 o7 C/E. eB ≈ 8e4,n 8y e6,e@,n4 ho@ a d o+ s+ eads on a d y5 1o7+2ete2y s9+e hyd o+ho8,15 θ (/# . In th,s I3a=, G state5 a d o+ @ett,n4 s9 3a1e !eB9,2,8 ,97 1onta1t an42e θeB #◦%. Next5 eB ◦ = o3 @ate ado+ts a nea 2y≈ s+he ,1a2 sha+e and eas,2y o22s o33 the @e des1 ,8e ho@ the ea 2y @ett,n4 8eha6,o ,s 7od,<ed @hen s98st ate C'5 -E. In 1ont ast5 1o7+2ete @ett,n45 ,.e. θeB #◦5 the s9 3a1e ,s +a t,a22y @ett,n4 !θeB > #◦%. This @o = on 1an 8e a1h,e6ed 8y 9s,n4 a d o+2et o3 o,2 that 1o7+2ete2y≈ wets +artia2 wettin4 adds a 3e@ additional details to ou ecent a s7ooth PDMS s98st ate. +a+e C$E. F,na22y5 we sha e ne@ o8se 6at,ons and ana2yt,1a2 He e @e d,s19ss the ,n?9en1e o3 8o9nda y 1ond,t,ons 1ons,de at,ons 3o the ,n?9en1e o3 the ,n,t,a2 d o+ sha+e on the on the dyna7,1s o3 wetting o3 drops on smooth s9 3aces, ea 2y t,7e s+ ead,n4 dyna7,1s. In +a t,192a 5 8y a++2y,n4 an and 7o6,n4 2,B9,d 3 onts ,n s7ooth t98es and 7,1 oteAt9 ed e2e1t ,1a2 +otent,a2 a1 oss the d o+5 @e a e a82e to 1han4e the s98st ates. >e 8e4,n ,n se1t,on " 8y des1 ,8,n4 the de+enden1e sha+e o3 the d o+ 3 o7 s+he ,1a2 to 1on,1a2 + ,o to 1onta1t o3 the s+ ead,n4 dyna7,1s o3 d o+s on θeB and on the sha+e o3 @,th the s9 3a1e.