Wetting of real surfaces

189 Pages·2013·9.311 MB·English

by  Bormashenko, Edward Yu

De Gruyter Studies in Mathematical Physics 19
Editors
MichaelEfroimsky,Bethesda,USA
LeonardGamberg,Reading,USA
DmitryGitman,SãoPaulo,Brasil
AlexanderLazarian, Madison,USA
BorisSmirnov,Moscow,Russia

Edward Yu. Bormashenko
Wetting of Real Surfaces
De Gruyter
PhysicsandAstronomyClassificationScheme2010:68.08.-p,68.03.Cd,68.08.Bc,68.35.Ct,
68.08.De,68.35.Md,02.30.Xx,47.55.D-.
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Preface
ImmanuelKantsaid“Twothingsfillthemindwithevernewandincreasingadmira-
tionandawe,themoreoftenandsteadilyreflectionisoccupiedwiththem:thestarry
heavenabovemeandthemorallawwithinme.”Inmystudentdays,twosmall-scale
miracleslikewisefilledmymindwithadmiration:amightofthevariationalprinciples
ofphysics,andthefascinatingbehaviorofwaterdroplets,demonstratinganamazing
varietyofphysicalphenomena.Thisbookisdevotedtotheapplicationsofthosevari-
ationalprinciplestowettingproblems.Exploitingvariationalprinciplesallowsnatural
constructionofa general umbrella enclosinga broadvariety of wettingeffects. This
bookdemonstrates that the well-known Young, Neumann–Boruvka,Cassie–Baxter,
andWenzelequationsare actually theboundarytransversality conditionsfor theap-
propriateproblemofwetting.
My interest in wetting was stimulated by the book “Droplet”, written by my sci-
entific mentor, Professor Yakov Evseevitch Gegusin in the 1980s. Regrettably, this
book, which remains one of the best published in the field of interface science, re-
mainsunknowntoabroadreadership,becauseithasnotbeentranslatedintoEnglish.
ItakethisopportunitytohonorthememoryofProfessorGegusin,abrilliantscientist
andteacher.
Thefieldofwettingremainedunattractiveforyoungscientistsforalongtime,and
thisisinspiteofthefact thatEinstein,Schrödinger,andBohrdevotedtheirresearch
activitytothisclassofeffects.Ithasbeenlatentlysupposedthatonlyphysicsofpar-
ticlesandphenomenaoccurringinamicro-world deservetheattentionofinquisitive
minds. Several factors have revived an interest in wetting and wettability. The first
ofthesewasthediscoveryofthe“lotus”effect(orsuperhydrophobicity)byBarthlott
andNeinhuisin1997.Thesecondfactor wastherapidprogressachievedinthefield
of wetting by the scientific school leaded by P. G. de Gennes. It is noteworthy that
themainnotionsofthemoderntheoryofwetting(suchasdisjoiningpressure,super-
hydrophobicity,contactanglehysteresis,wettingtransitions)areyoungerthantheba-
sicideasofrelativityandquantummechanics.Hence,thefieldofwettingphenomena
isarapidlydevelopingfieldofmodernphysics,fullofexcitingphysicalinsights.
Itisreasonabletoask:whyonemorebookonwetting?Twoexcellentbookssum-
marizingthestateoftheartinthefieldhavebeenpublishedrecently:Capillarityand
WettingPhenomenabyP.G. deGennes, F.Brochard-Wyart andD.Quéré, andSur-
faceChemistryofSolidandLiquidInterfacesbyH.Y.Erbil,whichcouldbestrongly
recommendedtoareader.However,therapidprogressintheunderstandingofwetting
ofreal,i.e.,roughandchemicallyheterogeneoussurfacesachievedinthelastdecade
viii Preface
callsforthereviewcarriedoutinthisbook.Aspecialchapterisdevotedtothephysical
originofthecontactanglehysteresis,recently studiedintensively.Theattentionwas
devotedtosuperhydrophobicityandwettingtransitionsonroughsurfaces. Thebook
alsotreatstheelectrowetting phenomenonandso-callednonstickdroplets(including
Leidenfrost droplets and liquid marbles) studied intensively in the past decade. The
bookgenerally keepsa macroscopic approach; however, intermolecular forces were
naturallyinvolvedintheclarificationofthenotionofthesurfacetension.
The bookis intendedfor MScandPhD studentsstudyingphysics,chemical engi-
neering,andmaterialsandinterfacescience,andofcourseforresearchersworkingin
thefieldofinterfacephenomena.Fluencyintheuseofthemathematicalapparatusof
calculationofvariationsisdesirable fora reader. Anexcellenttextbook,Calculusof
Variations,byGelfand andFomin, is stronglyrecommendedfor a reader toacquire
withthecalculationofvariationsoneofthemostexcitingfieldsofcalculus.
TheauthorisindebtedtoDr.Whymanforhislongstandingfruitful cooperationin
the study of wetting phenomena. His critique and numerous remarks definitely im-
proved the text. I am thankful to Professor R. Pogreb for his contribution in under-
standingofdiversityofwettingphenomena.IamthankfultoProfessorG.Kresinfor
his help in the field of variational analysis. I am grateful to Dr. T. Stein for his co-
operationinthefieldofsuperhydrophobicity.IwanttothankmynumerousMScand
PhDstudentsfortheirresearchactivityandallegiancetoaspiritofscientificresearch.
Iamgrateful toMrs.A.Musinfor herkindhelpineditingthebook.I amespecially
indebtedtomy wife Yelena Bormashenkofor her inestimablehelp inpreparing this
book.IamgreatlythankfultoMs.HannaWeissforhervaluablehelpinEnglishedit-
ingofthisbook.Iam gratefultoDr. Z.Barkay andDr. R.Grynyovfor their helpin
SEMandESEMimaging.
Notation
a contact radius of a droplet
a critical contact radius (Section 3.4)
c
aQ characteristic length describing precursor films in dynamic
wetting (Section 4.3)
A Hamaker constant
b,c,h geometrical parameters of rough surfaces
Q
b root mean square width of the triple line (Section 3.10.3)
O
b width of a precursor film (Section 4.3)
h limiting height (scale)
m
Q
h thickness of the liquid film in the “drag-out” problem
(Section 4.10)
C capacitance
O
C curvature
Q
d characteristic thickness in the drag-out problem
(Section 4.10)
d molecular diameter, atomic scale
m
e thickness of the insulating vapor layer, thickness of the
liquid layer
eO eccentricity of the spheroidal droplet (Section 2.9)
E electric field
f fraction in the substrate surface
i
f fraction in the wetted substrate surface
s
F critical force for wetting transitions (Section 7.7)
c
g gravity acceleration
gQ geometrical factor
G free energy
O
G specific free energy
H capillary rise
I ionization potential
J moment of inertia
k wavenumber
kO D2.1(cid:2)10(cid:2)7 J the Eötvös constant
mol2=3K
k D1.38(cid:2)10(cid:2)23J the Boltzmann constant
B K