Research Article Effect of Surface Forces on Ultrathin ...

Research ArticleEffect of Surface Forces on Ultrathin Film Lubrication

Prakash Chandra Mishra

School of Mechanical Engineering KIIT University Bhubaneswar India

Correspondence should be addressed to Prakash Chandra Mishra pmishrafmekiitacin

Received 4 January 2014 Accepted 24 February 2014 Published 27 May 2014

Academic Editors B A Akash and D Das

Copyright copy 2014 Prakash Chandra Mishra This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Lubricated contact with nanoscale oil film is modeled for friction Effect of the van der Waals pressure and the solvation pressureforces on such ultrathin lubricating oil film is considered while finding the friction and other parameters Hydrodynamic action isrepresented using transient thermoelastohydrodynamics Net pressure due to hydrodynamic solvation and van der Waalsrsquo actionis integrated over the contact area to find contact load Conjunctional friction due to thermal activation of such ultrathin film isderived using the Eyring model Effect of molecular dimension on friction is studied

1 Introduction

Ultrathin film transition is in between mixed and boundaryregimes of lubrication In mixed regime of lubrication thecontiguous surface geometry appears in film profile whilein boundary regime a total fluid film rupture occurs and thecontiguous solids remain in contact In between these twolubrication regimes there exists a transition where the film isin order of 05 nmndash5 nm and is termed as ultrathin film Forsuch a case the film is of about one or fewmolecular diameterthicknesses and subjected to solvation and van der Waalsrsquoaction Very few attempts weremade to know themechanismof such an ultrathin film and its lubrication performance

First Israelachvili [1] has studied the intermolecularsurface forces Henderson and Lozada-Cassou [2] developeda simplified theory to estimate the force between large spheresinside liquid considering the effect of solventThey simulatedthe alignment of the solvent dipoles in vicinity of the sphereand validated the resultant force with experimental findingEvans and Parry [3] reviewed theoretical and computersimulated studies of atomic-order-fluid film absorbed Theyfocused on wet phase transition and found that the criticalityin a continuously growing wetting film is due to capillarywave like fluctuation which was best explained Chan andHorn [4] studied the drainage of thin film between solidsurfaces They measured the transient film thickness whileit is squeezed between two mica surfaces of molecularorder smoothness In this study film thickness of 05 nm

is measured for OMTC (octamethyl-cyclotetrasiloxane) n-hexadecane and n-tetradecane For very thin film the con-tinuum Reynolds equation brakes as the drainage occurs ina series of abrupt steps whose size matches the thickness ofthe molecular layer Trace of water and its dramatic effecton drainage of nonpolar liquid between hydrophilic surfacescause the film rupture as they stated

Matsuoka and Kato [5] postulated ultrathin film lubrica-tion theory to calculate the solvation pressure for the case ofEHL contact The solvation pressure is calculated by solvingthe transformed Ornstein-Zernike equation for hard spheresin a two-phase system with Perramrsquos method and using theDerjaguin approximation They applied this new concept toelastohydrodynamic problems in which the film thicknessis very small and force due to solvation and van der Waalsrsquoaction is significant Roelands [6] developed a correlationwith viscosity temperature and pressure Mishra [7 8] usedthis correlation to analyze the thermoelastohydrodynamicsof a journal-bearing and a piston ring-cylinder liner contactrespectively

Earlier Elrod [9] developed a cavitation algorithm thatcan address the film pressure both in the fluid film and inthe cavitation region It uses a switch function to identify thefluid film and the cavitation region Swift and Stieber [10 11]proposed a boundary condition which works better thanthe Summerfield and Reynolds boundary condition Mishra[12] used this boundary condition to study a misalignedelliptic bore journal bearing Lifshitz [13] developed the

Hindawi Publishing CorporationISRN TribologyVolume 2014 Article ID 612195 9 pageshttpdxdoiorg1011552014612195

2 ISRN Tribology

Mixed regime

(a) Roughness influenced the film geometry

Zone of ultrathin film lubrication

Film span (lt50nm)

Film thickness (lt10nm)

(b) Ultrathin film due to reduced gap to nanometer order

Asperity contact

(c) Film rupture in boundary regime

Figure 1 Transient nature of lubrication with reduced oil film thickness

(a) 3D balls of OMCTSsilicone oil (b) Hexadecanecetane (c) Tetradecanealkane hydrocarbon

Figure 2 Three-dimensional molecular structure of oils

theory of molecular attractive forces between solids Thelimiting case of separation as compared to wavelength ofabsorption band of solid is studied in which the van derWaals force is becoming significant In this analysis the effectof temperature is also taken into consideration

Due to solid-solid contact the adhesion and stick-slipaffect the conjunctional performance [14] Eyring [15] cor-related viscosity plasticity and diffusion with an absolutereaction rate Such a theory yields an equation for the absoluteviscosity applicable to cases involving activation energiesThe increasing viscosity with shearing stress is explainedSimilarly the same theory yields an equation for the diffusioncoefficient which when combined with the viscosity andapplied to the results of Orr and Butler for the diffusionof heavy into light water gives a satisfactory and suggestiveinterpretation The usual theories for diffusion coefficientsand absolute electrical conductance should be replaced bythose developed here when ion and solvent molecule are ofabout the same size Briscoe and Evans [16] studied shearproperties of the Langmuir and Blodgett layers of fluid filmBowden and Tabor [17] were the first to emphasize the role ofrelatively moving solids in contactThe role of surface energyin contact of elastic solids is pointed out through the JKR(Johnson Kendall and Roberts) model [18] It improved theearlier Archardrsquos model for elastic deformation and laws offriction

Based on the literature survey it is realized that a modelof thin film lubrication will be worth presenting with theinclusion of solvation and van der Waalsrsquo action (Figure 4)

2 Theory of the Model

When the contiguous surface approaches just before asperitycontact the van der Waals and solvation pressure forcesbecome active The mechanism behind the thin film is themolecular level van der Waals force acting in directionopposite to and that of solvation pressure acting in directionof hydrodynamic pressure The molecular structure of con-tiguous metal as well as that of lubricant oil is important insuch circumstances

21 Thin Film Geometry For many types of conjunctionsthe lubrication regime transition occurs The reason is theapproaching or the separation of contiguous solid surface dueto nature or magnitude of entraining velocity The externalload that the film bears also plays a significant role Duringapproaching situation when the film thickness reduced from07 120583m to 03 120583m the roughness of the contiguous solidsneeds to be addressed while defining the film thickness forthe Reynolds equation (Figure 1) The average flow Reynolds(Patir and Chang) equation is preferred for such a mixedregime

It leads to the film rupture in the solid-solid contact caus-ing asperity interaction and wear In between two importanttransitions there would be a phase of lubrication when thefilm thickness of the lubricant would have the order of two tothree molecular diameters Figures 2(a) 2(b) and 2(c) givethe molecular structure of oils commonly used as lubricantThediameter of themolecules of these oils varies from 10 nm

ISRN Tribology 3

Contiguous solid-A OMCT lubricant Contiguous solid-B

(a) Silicon oil lubricated steel surface

Contiguous solid-A Contiguous solid-BHexadecanecetane

(b) Cetane lubricated steel surface

Contiguous solid-A Contiguous solid-BTetradecanealkane hydrocarbon

(c) Alkane hydrocarbon lubricated steel surface

Figure 3 Molecular level ultrathin film contact with different oils


Pw

Ps Ph

Force balance in ultrathin film (10minus9 m)

Film span (lt50nm)PT = Ps + Ph minus Pw

Figure 4 Ultrathin film zone and force balance

for the case of OMCTS to 025 nm in the case of alkanehydrocarbon and these are nonpolar in nature For somecases these are also used as friction protective layer or sealant

Such molecularly thin film has the tendency of dewettingdue to solvation that reduces the localized friction near theasperity tip Figure 3 represents the relatively placed oilsand the solid layer in contact where the solvation effect

is dominating Sometimes due to dewetting the metallicsurface behaves as the smooth surface to minimize theseverity of the asperity interaction

22 Solvation Solvation has a dominant effect Such anultrathin film as discussed earlier possesses the dewettingaction of solvation that prevents the formation of meniscus

4 ISRN Tribology

and reduces the chance of adhesion The solvation is moreeffective in the case of a lubricant with smaller size molecules(lt20 nm) Lubricant with longer chain molecules has negli-gible effect of solvation The solvation pressure (as given in(1)) is a function of the contact density parameter and thefilm ratio (ℎ119889

119898) with 119889

119898being diameter of the lubricant

molecule The contact density is the bulk density of the fluidwhich is the function of change in density (difference in thedensity of film in conjunction with that of film in a singlefree surface) and the Stephen Boltzmannrsquos constant and thetemperature of oil as given as follows

119875119904= minus119862119890

minusℎ119889119898 cos(2120587 ℎ

119889119898

) (1)

where119862 = 119870

119887119879120588 (ℎ 997888rarr infin)

120588 (ℎ 997888rarr infin) 997888rarr corresponding value for single surface

ℎ ge 119889119898

(2)

119879 is temperature rise in oil due to frictionThe film ratio is defined as the ratio of the film thickness

to the molecular diameter of the lubricant oil For any typeof lubricant conjunction the rise in temperature occurs dueto the rapid shear of lubricant layer The solvation effectdominates the gap which is of several molecular diameters Ithappens due to the density variation of liquid near the solidboundary The dewetting action of solvation guards againstformation of meniscus and prevents adhesion The solvationis more pronounced for small fluid molecules such as per-fluoropolyether and OMCTSoctamethyl-cyclotetrasiloxanewhich are nominally spherical molecules (1ndash15 nm) Such aneffect is negligible for long chainmolecules Table 1 representsthe molecular specification of different oils

23 Van der Waalsrsquo Pressure The van der Waals force is aweak attractive force which is mainly responsible for bindingthe organic molecule of the lubricant to asperity in thecontiguousmetal surface It is given in the following equation

119865119908= sum119875

119908119889119860 (3)

where

119875119908= minus

119860ℎ

6120587ℎ3

119860ℎ997888rarr the Hamaker constant

(4)

or

119860ℎ= 1205872

119862119886120588119898120588119897 (5)

where

119862119886= minus1199036

120596 (119903)

119860ℎlies in between (10

minus21ndash10minus19119869)

119860ℎ= 14 times 10

minus20

119869

(6)

In this case 120588119898

and 120588119897are number of atoms per unit

volume in the surfaces of metal and lubricant 119862119886is the

coefficient in particle pair interaction and is found in van derWaalsrsquo interaction The van der Waals force is effective onlyfor few hundred angstroms

24 The Casimir-Polder Pressure In lubricated contact thereis the attraction force between to contiguous solids beyondthe van derWaals limit up to fewmicrometers Such pressureis given as

119865119888

119860= 119875cas =

ℎ1198881198971205872

240ℎ4 (7)

where 119865119888is the Casimir force 119875cas is the pressure due to the

Casimir force ℎ is reduced Planckrsquos constant and 119888 is thespeed of light

25 Conjunction Friction due to the Eyring Shear Ultrathinfilm adsorbed in molecularly thin and smooth surface issubjected to shearing due to thermal activation (see (8))based chemical reactions It is non-Newtonian in natureThepotential barrier in thermal activation is given in the fol-lowing equation In this circumstance the Eyring model canbetter describe contact conjunction fluid viscosity Johnson[14] expressed the Eyring shear stress (see (9)) as function ofvelocity pressure and temperature Consider the following

119864119910= 119876 minus 119901Ω minus 120591120601

if120591120601

119870119887119879

gt 1

(8)

Potential barrier in thermal activation is given as

120591 = 120591119910+ 120585120588 (∵ 120585 =

Ω

120601) (9)

The Eyring shear stress is determined as

120591119910=

1

120601[119870119887119879 ln( 119880

V119891

) + 119876] (10)

where V119891is characteristic velocity related to frequency pro-

cess Therefore

120591119910=

119870119887119879

120601ln119880 + 120591

119910119903minus 120588119875V (11)

120591119910119903

=1

120601[119876 minus 119875VΩ + 119870

119887119879 ln V119891] (12)

In (12) the following substitution is made as follows

119870119887119879

120601≃

34

119860 120591

119910119903≃

113

119860 120585 = 016

119865 = ∬120591119910119889119909 119889119910 120591

119910gt 0

(13)

ISRN Tribology 5

Table 1 Molecular specification of several oils

Lubricanttype Compound name Chemical

formulaldquo119862rdquo valuein MPa

Moleculardiameter(nm)

Density(gmmL) Molecular structure

A OMCTSsilicon oil [Si(CH3)2O]4 172MPa 10 nm 0956

B Hexadecanecetane (C16H34) 62MPa 04 nm 077

C Tetradecanealkanehydrocarbon CH3(CH2)12CH3 49MPa 025 nm 0756

26 The Reynolds Equation The Reynolds equation is asecond-order differential equation which correlates thehydrodynamic pressure with film entraining velocity andlubricant viscosity and densityThe Reynolds equation in thiscase is given as

120597

120597119909(120588ℎ3

120578

120597119875ℎ

120597119909) +

120597

120597119910(120588ℎ3

120578

120597119875ℎ

120597119910)

= 12 119880120597119875ℎ

120597119909+ 119881

120597119875ℎ

120597119910+

120597

120597119905(120588ℎ)

(14)

It is for the full fluid film region The hydrodynamic pressurefor both fluid film and cavitation region is given as

119875ℎ= 119892120573 ln 120579 + 119875

119888 (15)

where

119892 = 1 997888rarr for full film if 120579 ge 1

0 997888rarr for cavitation region if 120579 ge 0(16)

120579 is the fractional film content and 119892 is the switch functionThe Reynolds equation with cavitation inclusion turned to

120597

120597119909(120588119888ℎ3

120578119892120573

120597120579

120597119909) +

120597

120597119910(120588119888ℎ3

120578119892120573

120597120579

120597119910)

= 12 119880120597120579120588119888ℎ

120597119909+ 119881

120597120579120588119888ℎ

120597119910+

120597

120597119905(120579120588119888ℎ)

(17)

The Couette flow in the cavitation region leads to

(119880120597

120597119909+ 119881

120597

120597119910+

120597

120597119905) (120579120588119888ℎ) = 0 (18)

The Dowson and Higginson equation for density variation is

120588 = 1205880(1 +

06 times 10minus9

times 119875ℎ

1 + 17 times 10minus9 times 119875ℎ

) (19)

The viscosity variation is based on combined law as follows

120578 = 1205780119890120572119875ℎ (20)

where

120572 = (ln 1205780+ 967)

[1 + 119875ℎ198 times 10

8

119911

minus 1]

119875ℎ

119885 =1205720

51 times 10minus9 (ln 1205780+ 967)

(21)

Total conjunctional pressure at any instant of time is given as

119875119879= 119875ℎ+ 119875119908+ 119875119904 (22)

where 119875119879is the total lubrication pressure 119875

119908is the van der

Waals pressure and 119875119904is pressure due to solvationTherefore

the load bearing ability is

119882 = int119875119879119889119860 (23)

27 Solution Steps The van derWaals force and the solvationpressure force are active for film of nanometer thickness Inthis analysis we have taken the film of 20ndash30 nm (which isequivalent to three layers of oil molecule) For a film profileof this order the solvation pressure and the van der Waalspressure are calculated as per (1) and (3) Correspondinghydrodynamic pressure is calculated by solving the Reynolds

6 ISRN Tribology

0 20 40 60 80 100120140 160 180

050

100150

200

25

20

15

10Film

thic

knes

s (nm

)

Node Y Node X

140 160150

(a)

Node YNode X0 20 40 60 80 100120140 160 180

050

100150

200

0246

times106

minus2

minus4

minus6

minus8

minus10

Solv

atio

n pr

essu

re (N

m2)

(b)

minus20

minus40

minus60

minus80

Van

der W

aalsrsquo

0

Node YNode X0 20 40 60 80 100120 140 160180

050

100150

200

pres

sure

(Nm

2)

(c)

Figure 5 (a) Film profile-A (b) Solvation pressure (due to film-A) (c) Van der Waalsrsquo pressure (due to film-A)

22

24

2

12

14

16

18

1

Film

thic

knes

s (m

)

times10minus9

Node YNode X0 20 40 60 80 100 120140 160180

050

100150

200

(a)

0 20 40 60 80 100 120140 160180

050

100150

200

0246

minus2

minus4

minus6

minus8

minus10

times106

Node Y Node X

Solv

atio

n pr

essu

re (N

m2)

(b)

minus8

minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

times105

Node Y Node X0 20 40 60 80 100120 140 160180

050

100150

200

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(c)

Figure 6 (a) Film profile-B (b) Solvation pressure (due to film-B) (c) Van der Waalsrsquo pressure (due to film-B)

ISRN Tribology 7

200200 150

150 100100 5050 00Node Z Node X

minus2

minus4

minus6

minus8

0

2

4

Solv

atio

n pr

essu

re (N

m2) OMCTtimes10

7 OMCT

(a)

200200 150

150 100100

505000

Node Z Node X

minus2

minus4

6

0

2

4

Solv

atio

n pr

essu

re (N

m2)times10

6 Hexadecane

150000

(b)

180

200

150

100120140

160100

20 40 60 8050

00

Node YNode X

minus1

minus2

minus3

0

1

2

Solv

atio

n pr

essu

re (N

m2)

times103

TetradecaneTetradecane

(c)

Figure 7 Solvation pressure due to nanoscale oil film of (a) OMCT (b) hexadecane and (c) tetradecane

200

200

150150

100100

5050

00

Node Y Node X

minus8

minus6

minus4

minus2

0

times105

OMCT

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(a)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

150

Hexadecane

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(b)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

Van

der W

aalrsquos

pre

ssur

e (N

m2)

Tetradecane

150

Tetradecane

(c)

Figure 8 Van der Waalsrsquo pressure due to nanoscale oil film of (a) OMCT (b) hexadecane and (c) tetradecane

8 ISRN Tribology

0123456789

10

Fric

tion

due t

o Ey

rings

stre

ss (N

)

OMCTsilicon oilHexadecanecetane

Tetradecanealkane

Point contact Semiconformal contact Conformal contact

Figure 9 Friction for different contact due to the Eyring condition

5045403020100

minus500

minus550

minus600

minus650

minus700

minus750

minus800

minus850

Max

imum

Eyr

ings

stre

ss (N

m2)

Entraining velocity (ms)

OMCTSsilicon oilHexadecanecetane

Tetradecanealkane

Figure 10 The maximum Eyring stress variation due to entrainingvelocity

equation Load convergence and film relaxation are notrequired as the estimation is based on exact film Furtherthe Eyring stress and corresponding friction are calculated asper (11) When there is further squeezing action the film failsand the contact situation changes drasticallyThere occurs theasperity contact and boundary friction for which the wear ofcontiguous solid occurs

3 Result Analysis

Figure 5(a) shows a parabolic film profile with 25 nm thick-ness The corresponding solvation pressure and the van derWaals pressure are given in Figures 5(b) and 5(c) respectivelySuch profile matches with the slider pairs like ring linerSimilarly Figure 6(a) shows a profile which is parabolic inentraining direction with a globally deformed profile alongthe side leakage directionThe corresponding solvation pres-sure and the van der Waals pressure are plotted (Figure 8)

Node X

Casim

ir-Po

lder

rsquos p

ress

ure (

Nm

2)

0 20 40 60 80 100 120 140 160 180 20010

4

105

106

107

108

Film thickness = 25nmFilm thickness = 10nm

Film thickness = 5nm

Figure 11 Surface force beyond van der Waalsrsquo boundary up to25 nm

There is a change in the solvation and the van der Waalspressure profile due to film profile modification out of localand global deformations Figure 7 shows the 3D profile of sol-vation pressure due to ultrathin film of OMCTS hexadecaneand tetradecane respectively It predicts that different oilmolecule has different molecular structure thereby differentsolvation pressure profile

Figure 9 shows the van der Waals pressure profile for allthe three types of oils (OMCTS hexadecane and tetrade-cane) The van der Waals pressure is independent of oilmolecular arrangement Figure 9 shows the friction due tothe Eyring stress The oil with smaller molecular diameterhas less friction due to the Eyring condition Again thepoint contact causes more friction than semiconformal orconformal contact

With increasing velocity the Eyring stress increases(Figure 10) It is more in the case of long chain moleculesFigure 11 shows the Casimir-Polder pressure

4 Conclusion

Nanoscale film exists and performs prior to the film rupturein almost all types of lubricated contacts Combined action ofthe solvation and the van derWaals action remains dominantand governs the lubrication performance in this caseThe netpressure is the vector sum of these two pressures along withhydrodynamic pressure Such consideration has more detailof molecular and nanoscale ultrathin film performance forboth mechanical and biological contacts

Nomenclature

119860ℎ Hamakerrsquos constant (J)

119862 Solvation pressure constant (m)

119862119886 Coefficient of particle pair interaction (m)

119888119897 Speed of light (msminus1)

119889119898 Molecular diameter (m)

ISRN Tribology 9

119864119910 Barrier height for Eyring

119865 Friction force (N)

119865119888 Casimirrsquos force (N)

119865119908 Van der Waalsrsquo force (N)

119892 Switch functionℎ Film thickness (120583m)

ℎ Reduced Planckrsquos constant119870119887 Boltzmannrsquos constant (JKminus1)

119901ℎ Hydrodynamic pressure (Mpa)

119875119904 Solvation pressure (Mpa)

119875119908 Van der Waalsrsquo pressure (Mpa)

119876 Process activation energy (J)119903 Contact curvature radius (m)

119879 Temperature of the lubricant(∘C)

119880 Velocity in direction ofentrainment (msminus1)

119881 Velocity in side leakagedirection (msminus1)

V119891 Characteristic velocity related tofrequency (msminus1)

119909 Coordinate in entrainingdirection

119910 Coordinate in side leakagedirection

119882 Load bearing ability (N)

119885 Pressure viscosity index120579 Fractional film content120573 Lubricant bulk modulus120588 Lubricant density120588119897 Number of atoms per unit

volume in surface of lubricant120588119898 Number of atoms per unitvolume in surface of metal

120591 Shear stress (Mpa)120591119910 Pressure dependent shear stress(Mpa)

120591119910119903 Velocity dependent shear stress(Mpa)

120585 The Eyring model constant120601 Activation volume (m3)120578 Lubricant dynamic viscosity120572 Pressure viscosity coefficient

(Paminus1)

Conflict of Interests

The author declares that they have no conflict of interestsregarding the publication of this paper

References

[1] J N Israelachvili Intermolecular and Surface Forces AcademicPress New York NY USA 1992

[2] D Henderson and M Lozada-Cassou ldquoA simple theory for theforce between spheres immersed in a fluidrdquo Journal of Colloidand Interface Science vol 114 no 1 pp 180ndash183 1986

[3] R Evans and A O Parry ldquoLiquids at interfaces what can atheorist contributerdquo Journal of Physics B Condensed Mattervol 2 article SA15 1990

[4] D Y C Chan and R G Horn ldquoThe drainage of thin liquid filmsbetween solid surfacesrdquoThe Journal of Chemical Physics vol 83no 10 pp 5311ndash5324 1985

[5] H Matsuoka and T Kato ldquoAn ultrathin liquid film lubricationtheorymdashcalculation method of solvation pressure and its appli-cation to the EHL problemrdquo Journal of Tribology vol 119 no 1pp 217ndash226 1997

[6] C J A Roelands Correlational aspects of the viscosity-temperature-pressure relationship of lubricating oils [PhD the-sis] Technical University of Delft DelftThe Netherlands 1966

[7] P CMishra ldquoThermal analysis of elliptic bore journal bearingrdquoTribology Transactions vol 50 no 1 pp 137ndash143 2007

[8] P C Mishra ldquoTribodynamic modeling of piston compressionring and cylinder liner conjunction in high-pressure zone ofengine cyclerdquo International Journal of Advanced ManufacturingTechnology vol 66 no 5ndash8 pp 1075ndash1085 2013

[9] H G Elrod ldquoA cavitation algorithmrdquo Journal of LubricationTechnology vol 103 no 3 pp 350ndash354 1981

[10] HW Swift ldquoThe stability of lubricating oil in journal bearingsrdquoProceedings of the Institution of Civil Engineers vol 233 pp 267ndash288 1932

[11] W Stieber Hydrodynamische Theorie des Gleitlagers dasSchwimmlager VDI Berlin Germany 1933

[12] P C Mishra ldquoMathematical modeling of stability in roughelliptic bore misaligned journal bearing considering thermaland non-Newtonian effectsrdquo Applied Mathematical Modellingvol 37 no 8 pp 5896ndash5912 2013

[13] E M Lifshitz ldquoThe theory of molecular attractive forcesbetween solidsrdquo Soviet Physics-JETP vol 2 pp 73ndash83 1956

[14] K L Johnson Contact Mechanics Cambridge University PressCambridge UK 1985

[15] H Eyring ldquoViscosity plasticity and diffusion as examples ofabsolute reaction ratesrdquoThe Journal of Chemical Physics vol 4no 4 pp 283ndash291 1936

[16] B J Briscoe and D C B Evans ldquoThe shear properties ofLangmuir-Blodgett layersrdquo Proceedings of The Royal Society ofLondon A Mathematical and Physical Sciences vol 380 no1779 pp 389ndash407 1982

[17] F P Bowden and D Tabor ldquoFriction lubrication and wear asurvey of work during the last decaderdquoBritish Journal of AppliedPhysics vol 17 no 12 article 301 pp 1521ndash1544 1966

[18] K L Johnson K Kendall and A D Roberts ldquoSurface energyand the contact of elastic solidsrdquo Proceedings of the Royal Societyof London A Mathematical and Physical Sciences vol 324 pp301ndash313 1971

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2 ISRN Tribology

Mixed regime

(a) Roughness influenced the film geometry


Film span (lt50nm)

Film thickness (lt10nm)

(b) Ultrathin film due to reduced gap to nanometer order

Asperity contact

(c) Film rupture in boundary regime

Figure 1 Transient nature of lubrication with reduced oil film thickness

(a) 3D balls of OMCTSsilicone oil (b) Hexadecanecetane (c) Tetradecanealkane hydrocarbon

Figure 2 Three-dimensional molecular structure of oils

theory of molecular attractive forces between solids Thelimiting case of separation as compared to wavelength ofabsorption band of solid is studied in which the van derWaals force is becoming significant In this analysis the effectof temperature is also taken into consideration

Due to solid-solid contact the adhesion and stick-slipaffect the conjunctional performance [14] Eyring [15] cor-related viscosity plasticity and diffusion with an absolutereaction rate Such a theory yields an equation for the absoluteviscosity applicable to cases involving activation energiesThe increasing viscosity with shearing stress is explainedSimilarly the same theory yields an equation for the diffusioncoefficient which when combined with the viscosity andapplied to the results of Orr and Butler for the diffusionof heavy into light water gives a satisfactory and suggestiveinterpretation The usual theories for diffusion coefficientsand absolute electrical conductance should be replaced bythose developed here when ion and solvent molecule are ofabout the same size Briscoe and Evans [16] studied shearproperties of the Langmuir and Blodgett layers of fluid filmBowden and Tabor [17] were the first to emphasize the role ofrelatively moving solids in contactThe role of surface energyin contact of elastic solids is pointed out through the JKR(Johnson Kendall and Roberts) model [18] It improved theearlier Archardrsquos model for elastic deformation and laws offriction

Based on the literature survey it is realized that a modelof thin film lubrication will be worth presenting with theinclusion of solvation and van der Waalsrsquo action (Figure 4)

2 Theory of the Model

When the contiguous surface approaches just before asperitycontact the van der Waals and solvation pressure forcesbecome active The mechanism behind the thin film is themolecular level van der Waals force acting in directionopposite to and that of solvation pressure acting in directionof hydrodynamic pressure The molecular structure of con-tiguous metal as well as that of lubricant oil is important insuch circumstances

21 Thin Film Geometry For many types of conjunctionsthe lubrication regime transition occurs The reason is theapproaching or the separation of contiguous solid surface dueto nature or magnitude of entraining velocity The externalload that the film bears also plays a significant role Duringapproaching situation when the film thickness reduced from07 120583m to 03 120583m the roughness of the contiguous solidsneeds to be addressed while defining the film thickness forthe Reynolds equation (Figure 1) The average flow Reynolds(Patir and Chang) equation is preferred for such a mixedregime

It leads to the film rupture in the solid-solid contact caus-ing asperity interaction and wear In between two importanttransitions there would be a phase of lubrication when thefilm thickness of the lubricant would have the order of two tothree molecular diameters Figures 2(a) 2(b) and 2(c) givethe molecular structure of oils commonly used as lubricantThediameter of themolecules of these oils varies from 10 nm

ISRN Tribology 3









Pw

Ps Ph








4 ISRN Tribology


119898) with 119889



119875119904= minus119862119890

minusℎ119889119898 cos(2120587 ℎ

119889119898

) (1)

where119862 = 119870

119887119879120588 (ℎ 997888rarr infin)


ℎ ge 119889119898

(2)




119865119908= sum119875

119908119889119860 (3)

where

119875119908= minus

119860ℎ

6120587ℎ3


(4)

or

119860ℎ= 1205872

119862119886120588119898120588119897 (5)

where

119862119886= minus1199036

120596 (119903)



119860ℎ= 14 times 10

minus20

119869

(6)






119865119888

119860= 119875cas =

ℎ1198881198971205872

240ℎ4 (7)




119864119910= 119876 minus 119901Ω minus 120591120601

if120591120601

119870119887119879

gt 1

(8)


120591 = 120591119910+ 120585120588 (∵ 120585 =

Ω

120601) (9)


120591119910=

1

120601[119870119887119879 ln( 119880

V119891

) + 119876] (10)


cess Therefore

120591119910=

119870119887119879

120601ln119880 + 120591

119910119903minus 120588119875V (11)

120591119910119903

=1

120601[119876 minus 119875VΩ + 119870

119887119879 ln V119891] (12)


119870119887119879

120601≃

34

119860 120591

119910119903≃

113

119860 120585 = 016

119865 = ∬120591119910119889119909 119889119910 120591

119910gt 0

(13)

ISRN Tribology 5










120597

120597119909(120588ℎ3

120578

120597119875ℎ

120597119909) +

120597

120597119910(120588ℎ3

120578

120597119875ℎ

120597119910)

= 12 119880120597119875ℎ

120597119909+ 119881

120597119875ℎ

120597119910+

120597

120597119905(120588ℎ)

(14)


119875ℎ= 119892120573 ln 120579 + 119875

119888 (15)

where




120597

120597119909(120588119888ℎ3

120578119892120573

120597120579

120597119909) +

120597

120597119910(120588119888ℎ3

120578119892120573

120597120579

120597119910)

= 12 119880120597120579120588119888ℎ

120597119909+ 119881

120597120579120588119888ℎ

120597119910+

120597

120597119905(120579120588119888ℎ)

(17)


(119880120597

120597119909+ 119881

120597

120597119910+

120597

120597119905) (120579120588119888ℎ) = 0 (18)


120588 = 1205880(1 +

06 times 10minus9

times 119875ℎ


) (19)


120578 = 1205780119890120572119875ℎ (20)

where

120572 = (ln 1205780+ 967)

[1 + 119875ℎ198 times 10

8

119911

minus 1]

119875ℎ

119885 =1205720

51 times 10minus9 (ln 1205780+ 967)

(21)


119875119879= 119875ℎ+ 119875119908+ 119875119904 (22)





119882 = int119875119879119889119860 (23)


6 ISRN Tribology

0 20 40 60 80 100120140 160 180

050

100150

200

25

20

15

10Film

thic

knes

s (nm

)

Node Y Node X

140 160150

(a)

Node YNode X0 20 40 60 80 100120140 160 180

050

100150

200

0246

times106

minus2

minus4

minus6

minus8

minus10

Solv

atio

n pr

essu

re (N

m2)

(b)

minus20

minus40

minus60

minus80

Van

der W

aalsrsquo

0

Node YNode X0 20 40 60 80 100120 140 160180

050

100150

200

pres

sure

(Nm

2)

(c)


22

24

2

12

14

16

18

1

Film

thic

knes

s (m

)

times10minus9

Node YNode X0 20 40 60 80 100 120140 160180

050

100150

200

(a)

0 20 40 60 80 100 120140 160180

050

100150

200

0246

minus2

minus4

minus6

minus8

minus10

times106

Node Y Node X

Solv

atio

n pr

essu

re (N

m2)

(b)

minus8

minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

times105

Node Y Node X0 20 40 60 80 100120 140 160180

050

100150

200

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(c)


ISRN Tribology 7

200200 150

150 100100 5050 00Node Z Node X

minus2

minus4

minus6

minus8

0

2

4

Solv

atio

n pr

essu

re (N

m2) OMCTtimes10

7 OMCT

(a)

200200 150

150 100100

505000

Node Z Node X

minus2

minus4

6

0

2

4

Solv

atio

n pr

essu

re (N

m2)times10

6 Hexadecane

150000

(b)

180

200

150

100120140

160100

20 40 60 8050

00

Node YNode X

minus1

minus2

minus3

0

1

2

Solv

atio

n pr

essu

re (N

m2)

times103


(c)


200

200

150150

100100

5050

00

Node Y Node X

minus8

minus6

minus4

minus2

0

times105

OMCT

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(a)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

150

Hexadecane

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(b)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

Van

der W

aalrsquos

pre

ssur

e (N

m2)

Tetradecane

150

Tetradecane

(c)


8 ISRN Tribology

0123456789

10

Fric

tion

due t

o Ey

rings

stre

ss (N

)


Tetradecanealkane



5045403020100

minus500

minus550

minus600

minus650

minus700

minus750

minus800

minus850

Max

imum

Eyr

ings

stre

ss (N

m2)



Tetradecanealkane



3 Result Analysis


Node X

Casim

ir-Po

lder

rsquos p

ress

ure (

Nm

2)

0 20 40 60 80 100 120 140 160 180 20010

4

105

106

107

108







4 Conclusion


Nomenclature






ISRN Tribology 9























(Paminus1)



References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 3









Pw

Ps Ph








4 ISRN Tribology


119898) with 119889



119875119904= minus119862119890

minusℎ119889119898 cos(2120587 ℎ

119889119898

) (1)

where119862 = 119870

119887119879120588 (ℎ 997888rarr infin)


ℎ ge 119889119898

(2)




119865119908= sum119875

119908119889119860 (3)

where

119875119908= minus

119860ℎ

6120587ℎ3


(4)

or

119860ℎ= 1205872

119862119886120588119898120588119897 (5)

where

119862119886= minus1199036

120596 (119903)



119860ℎ= 14 times 10

minus20

119869

(6)






119865119888

119860= 119875cas =

ℎ1198881198971205872

240ℎ4 (7)




119864119910= 119876 minus 119901Ω minus 120591120601

if120591120601

119870119887119879

gt 1

(8)


120591 = 120591119910+ 120585120588 (∵ 120585 =

Ω

120601) (9)


120591119910=

1

120601[119870119887119879 ln( 119880

V119891

) + 119876] (10)


cess Therefore

120591119910=

119870119887119879

120601ln119880 + 120591

119910119903minus 120588119875V (11)

120591119910119903

=1

120601[119876 minus 119875VΩ + 119870

119887119879 ln V119891] (12)


119870119887119879

120601≃

34

119860 120591

119910119903≃

113

119860 120585 = 016

119865 = ∬120591119910119889119909 119889119910 120591

119910gt 0

(13)

ISRN Tribology 5










120597

120597119909(120588ℎ3

120578

120597119875ℎ

120597119909) +

120597

120597119910(120588ℎ3

120578

120597119875ℎ

120597119910)

= 12 119880120597119875ℎ

120597119909+ 119881

120597119875ℎ

120597119910+

120597

120597119905(120588ℎ)

(14)


119875ℎ= 119892120573 ln 120579 + 119875

119888 (15)

where




120597

120597119909(120588119888ℎ3

120578119892120573

120597120579

120597119909) +

120597

120597119910(120588119888ℎ3

120578119892120573

120597120579

120597119910)

= 12 119880120597120579120588119888ℎ

120597119909+ 119881

120597120579120588119888ℎ

120597119910+

120597

120597119905(120579120588119888ℎ)

(17)


(119880120597

120597119909+ 119881

120597

120597119910+

120597

120597119905) (120579120588119888ℎ) = 0 (18)


120588 = 1205880(1 +

06 times 10minus9

times 119875ℎ


) (19)


120578 = 1205780119890120572119875ℎ (20)

where

120572 = (ln 1205780+ 967)

[1 + 119875ℎ198 times 10

8

119911

minus 1]

119875ℎ

119885 =1205720

51 times 10minus9 (ln 1205780+ 967)

(21)


119875119879= 119875ℎ+ 119875119908+ 119875119904 (22)





119882 = int119875119879119889119860 (23)


6 ISRN Tribology

0 20 40 60 80 100120140 160 180

050

100150

200

25

20

15

10Film

thic

knes

s (nm

)

Node Y Node X

140 160150

(a)

Node YNode X0 20 40 60 80 100120140 160 180

050

100150

200

0246

times106

minus2

minus4

minus6

minus8

minus10

Solv

atio

n pr

essu

re (N

m2)

(b)

minus20

minus40

minus60

minus80

Van

der W

aalsrsquo

0

Node YNode X0 20 40 60 80 100120 140 160180

050

100150

200

pres

sure

(Nm

2)

(c)


22

24

2

12

14

16

18

1

Film

thic

knes

s (m

)

times10minus9

Node YNode X0 20 40 60 80 100 120140 160180

050

100150

200

(a)

0 20 40 60 80 100 120140 160180

050

100150

200

0246

minus2

minus4

minus6

minus8

minus10

times106

Node Y Node X

Solv

atio

n pr

essu

re (N

m2)

(b)

minus8

minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

times105

Node Y Node X0 20 40 60 80 100120 140 160180

050

100150

200

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(c)


ISRN Tribology 7

200200 150

150 100100 5050 00Node Z Node X

minus2

minus4

minus6

minus8

0

2

4

Solv

atio

n pr

essu

re (N

m2) OMCTtimes10

7 OMCT

(a)

200200 150

150 100100

505000

Node Z Node X

minus2

minus4

6

0

2

4

Solv

atio

n pr

essu

re (N

m2)times10

6 Hexadecane

150000

(b)

180

200

150

100120140

160100

20 40 60 8050

00

Node YNode X

minus1

minus2

minus3

0

1

2

Solv

atio

n pr

essu

re (N

m2)

times103


(c)


200

200

150150

100100

5050

00

Node Y Node X

minus8

minus6

minus4

minus2

0

times105

OMCT

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(a)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

150

Hexadecane

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(b)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

Van

der W

aalrsquos

pre

ssur

e (N

m2)

Tetradecane

150

Tetradecane

(c)


8 ISRN Tribology

0123456789

10

Fric

tion

due t

o Ey

rings

stre

ss (N

)


Tetradecanealkane



5045403020100

minus500

minus550

minus600

minus650

minus700

minus750

minus800

minus850

Max

imum

Eyr

ings

stre

ss (N

m2)



Tetradecanealkane



3 Result Analysis


Node X

Casim

ir-Po

lder

rsquos p

ress

ure (

Nm

2)

0 20 40 60 80 100 120 140 160 180 20010

4

105

106

107

108







4 Conclusion


Nomenclature






ISRN Tribology 9























(Paminus1)



References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









4 ISRN Tribology


119898) with 119889



119875119904= minus119862119890

minusℎ119889119898 cos(2120587 ℎ

119889119898

) (1)

where119862 = 119870

119887119879120588 (ℎ 997888rarr infin)


ℎ ge 119889119898

(2)




119865119908= sum119875

119908119889119860 (3)

where

119875119908= minus

119860ℎ

6120587ℎ3


(4)

or

119860ℎ= 1205872

119862119886120588119898120588119897 (5)

where

119862119886= minus1199036

120596 (119903)



119860ℎ= 14 times 10

minus20

119869

(6)






119865119888

119860= 119875cas =

ℎ1198881198971205872

240ℎ4 (7)




119864119910= 119876 minus 119901Ω minus 120591120601

if120591120601

119870119887119879

gt 1

(8)


120591 = 120591119910+ 120585120588 (∵ 120585 =

Ω

120601) (9)


120591119910=

1

120601[119870119887119879 ln( 119880

V119891

) + 119876] (10)


cess Therefore

120591119910=

119870119887119879

120601ln119880 + 120591

119910119903minus 120588119875V (11)

120591119910119903

=1

120601[119876 minus 119875VΩ + 119870

119887119879 ln V119891] (12)


119870119887119879

120601≃

34

119860 120591

119910119903≃

113

119860 120585 = 016

119865 = ∬120591119910119889119909 119889119910 120591

119910gt 0

(13)

ISRN Tribology 5










120597

120597119909(120588ℎ3

120578

120597119875ℎ

120597119909) +

120597

120597119910(120588ℎ3

120578

120597119875ℎ

120597119910)

= 12 119880120597119875ℎ

120597119909+ 119881

120597119875ℎ

120597119910+

120597

120597119905(120588ℎ)

(14)


119875ℎ= 119892120573 ln 120579 + 119875

119888 (15)

where




120597

120597119909(120588119888ℎ3

120578119892120573

120597120579

120597119909) +

120597

120597119910(120588119888ℎ3

120578119892120573

120597120579

120597119910)

= 12 119880120597120579120588119888ℎ

120597119909+ 119881

120597120579120588119888ℎ

120597119910+

120597

120597119905(120579120588119888ℎ)

(17)


(119880120597

120597119909+ 119881

120597

120597119910+

120597

120597119905) (120579120588119888ℎ) = 0 (18)


120588 = 1205880(1 +

06 times 10minus9

times 119875ℎ


) (19)


120578 = 1205780119890120572119875ℎ (20)

where

120572 = (ln 1205780+ 967)

[1 + 119875ℎ198 times 10

8

119911

minus 1]

119875ℎ

119885 =1205720

51 times 10minus9 (ln 1205780+ 967)

(21)


119875119879= 119875ℎ+ 119875119908+ 119875119904 (22)





119882 = int119875119879119889119860 (23)


6 ISRN Tribology

0 20 40 60 80 100120140 160 180

050

100150

200

25

20

15

10Film

thic

knes

s (nm

)

Node Y Node X

140 160150

(a)

Node YNode X0 20 40 60 80 100120140 160 180

050

100150

200

0246

times106

minus2

minus4

minus6

minus8

minus10

Solv

atio

n pr

essu

re (N

m2)

(b)

minus20

minus40

minus60

minus80

Van

der W

aalsrsquo

0

Node YNode X0 20 40 60 80 100120 140 160180

050

100150

200

pres

sure

(Nm

2)

(c)


22

24

2

12

14

16

18

1

Film

thic

knes

s (m

)

times10minus9

Node YNode X0 20 40 60 80 100 120140 160180

050

100150

200

(a)

0 20 40 60 80 100 120140 160180

050

100150

200

0246

minus2

minus4

minus6

minus8

minus10

times106

Node Y Node X

Solv

atio

n pr

essu

re (N

m2)

(b)

minus8

minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

times105

Node Y Node X0 20 40 60 80 100120 140 160180

050

100150

200

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(c)


ISRN Tribology 7

200200 150

150 100100 5050 00Node Z Node X

minus2

minus4

minus6

minus8

0

2

4

Solv

atio

n pr

essu

re (N

m2) OMCTtimes10

7 OMCT

(a)

200200 150

150 100100

505000

Node Z Node X

minus2

minus4

6

0

2

4

Solv

atio

n pr

essu

re (N

m2)times10

6 Hexadecane

150000

(b)

180

200

150

100120140

160100

20 40 60 8050

00

Node YNode X

minus1

minus2

minus3

0

1

2

Solv

atio

n pr

essu

re (N

m2)

times103


(c)


200

200

150150

100100

5050

00

Node Y Node X

minus8

minus6

minus4

minus2

0

times105

OMCT

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(a)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

150

Hexadecane

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(b)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

Van

der W

aalrsquos

pre

ssur

e (N

m2)

Tetradecane

150

Tetradecane

(c)


8 ISRN Tribology

0123456789

10

Fric

tion

due t

o Ey

rings

stre

ss (N

)


Tetradecanealkane



5045403020100

minus500

minus550

minus600

minus650

minus700

minus750

minus800

minus850

Max

imum

Eyr

ings

stre

ss (N

m2)



Tetradecanealkane



3 Result Analysis


Node X

Casim

ir-Po

lder

rsquos p

ress

ure (

Nm

2)

0 20 40 60 80 100 120 140 160 180 20010

4

105

106

107

108







4 Conclusion


Nomenclature






ISRN Tribology 9























(Paminus1)



References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 5










120597

120597119909(120588ℎ3

120578

120597119875ℎ

120597119909) +

120597

120597119910(120588ℎ3

120578

120597119875ℎ

120597119910)

= 12 119880120597119875ℎ

120597119909+ 119881

120597119875ℎ

120597119910+

120597

120597119905(120588ℎ)

(14)


119875ℎ= 119892120573 ln 120579 + 119875

119888 (15)

where




120597

120597119909(120588119888ℎ3

120578119892120573

120597120579

120597119909) +

120597

120597119910(120588119888ℎ3

120578119892120573

120597120579

120597119910)

= 12 119880120597120579120588119888ℎ

120597119909+ 119881

120597120579120588119888ℎ

120597119910+

120597

120597119905(120579120588119888ℎ)

(17)


(119880120597

120597119909+ 119881

120597

120597119910+

120597

120597119905) (120579120588119888ℎ) = 0 (18)


120588 = 1205880(1 +

06 times 10minus9

times 119875ℎ


) (19)


120578 = 1205780119890120572119875ℎ (20)

where

120572 = (ln 1205780+ 967)

[1 + 119875ℎ198 times 10

8

119911

minus 1]

119875ℎ

119885 =1205720

51 times 10minus9 (ln 1205780+ 967)

(21)


119875119879= 119875ℎ+ 119875119908+ 119875119904 (22)





119882 = int119875119879119889119860 (23)


6 ISRN Tribology

0 20 40 60 80 100120140 160 180

050

100150

200

25

20

15

10Film

thic

knes

s (nm

)

Node Y Node X

140 160150

(a)

Node YNode X0 20 40 60 80 100120140 160 180

050

100150

200

0246

times106

minus2

minus4

minus6

minus8

minus10

Solv

atio

n pr

essu

re (N

m2)

(b)

minus20

minus40

minus60

minus80

Van

der W

aalsrsquo

0

Node YNode X0 20 40 60 80 100120 140 160180

050

100150

200

pres

sure

(Nm

2)

(c)


22

24

2

12

14

16

18

1

Film

thic

knes

s (m

)

times10minus9

Node YNode X0 20 40 60 80 100 120140 160180

050

100150

200

(a)

0 20 40 60 80 100 120140 160180

050

100150

200

0246

minus2

minus4

minus6

minus8

minus10

times106

Node Y Node X

Solv

atio

n pr

essu

re (N

m2)

(b)

minus8

minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

times105

Node Y Node X0 20 40 60 80 100120 140 160180

050

100150

200

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(c)


ISRN Tribology 7

200200 150

150 100100 5050 00Node Z Node X

minus2

minus4

minus6

minus8

0

2

4

Solv

atio

n pr

essu

re (N

m2) OMCTtimes10

7 OMCT

(a)

200200 150

150 100100

505000

Node Z Node X

minus2

minus4

6

0

2

4

Solv

atio

n pr

essu

re (N

m2)times10

6 Hexadecane

150000

(b)

180

200

150

100120140

160100

20 40 60 8050

00

Node YNode X

minus1

minus2

minus3

0

1

2

Solv

atio

n pr

essu

re (N

m2)

times103


(c)


200

200

150150

100100

5050

00

Node Y Node X

minus8

minus6

minus4

minus2

0

times105

OMCT

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(a)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

150

Hexadecane

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(b)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

Van

der W

aalrsquos

pre

ssur

e (N

m2)

Tetradecane

150

Tetradecane

(c)


8 ISRN Tribology

0123456789

10

Fric

tion

due t

o Ey

rings

stre

ss (N

)


Tetradecanealkane



5045403020100

minus500

minus550

minus600

minus650

minus700

minus750

minus800

minus850

Max

imum

Eyr

ings

stre

ss (N

m2)



Tetradecanealkane



3 Result Analysis


Node X

Casim

ir-Po

lder

rsquos p

ress

ure (

Nm

2)

0 20 40 60 80 100 120 140 160 180 20010

4

105

106

107

108







4 Conclusion


Nomenclature






ISRN Tribology 9























(Paminus1)



References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









6 ISRN Tribology

0 20 40 60 80 100120140 160 180

050

100150

200

25

20

15

10Film

thic

knes

s (nm

)

Node Y Node X

140 160150

(a)

Node YNode X0 20 40 60 80 100120140 160 180

050

100150

200

0246

times106

minus2

minus4

minus6

minus8

minus10

Solv

atio

n pr

essu

re (N

m2)

(b)

minus20

minus40

minus60

minus80

Van

der W

aalsrsquo

0

Node YNode X0 20 40 60 80 100120 140 160180

050

100150

200

pres

sure

(Nm

2)

(c)


22

24

2

12

14

16

18

1

Film

thic

knes

s (m

)

times10minus9

Node YNode X0 20 40 60 80 100 120140 160180

050

100150

200

(a)

0 20 40 60 80 100 120140 160180

050

100150

200

0246

minus2

minus4

minus6

minus8

minus10

times106

Node Y Node X

Solv

atio

n pr

essu

re (N

m2)

(b)

minus8

minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

times105

Node Y Node X0 20 40 60 80 100120 140 160180

050

100150

200

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(c)


ISRN Tribology 7

200200 150

150 100100 5050 00Node Z Node X

minus2

minus4

minus6

minus8

0

2

4

Solv

atio

n pr

essu

re (N

m2) OMCTtimes10

7 OMCT

(a)

200200 150

150 100100

505000

Node Z Node X

minus2

minus4

6

0

2

4

Solv

atio

n pr

essu

re (N

m2)times10

6 Hexadecane

150000

(b)

180

200

150

100120140

160100

20 40 60 8050

00

Node YNode X

minus1

minus2

minus3

0

1

2

Solv

atio

n pr

essu

re (N

m2)

times103


(c)


200

200

150150

100100

5050

00

Node Y Node X

minus8

minus6

minus4

minus2

0

times105

OMCT

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(a)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

150

Hexadecane

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(b)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

Van

der W

aalrsquos

pre

ssur

e (N

m2)

Tetradecane

150

Tetradecane

(c)


8 ISRN Tribology

0123456789

10

Fric

tion

due t

o Ey

rings

stre

ss (N

)


Tetradecanealkane



5045403020100

minus500

minus550

minus600

minus650

minus700

minus750

minus800

minus850

Max

imum

Eyr

ings

stre

ss (N

m2)



Tetradecanealkane



3 Result Analysis


Node X

Casim

ir-Po

lder

rsquos p

ress

ure (

Nm

2)

0 20 40 60 80 100 120 140 160 180 20010

4

105

106

107

108







4 Conclusion


Nomenclature






ISRN Tribology 9























(Paminus1)



References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 7

200200 150

150 100100 5050 00Node Z Node X

minus2

minus4

minus6

minus8

0

2

4

Solv

atio

n pr

essu

re (N

m2) OMCTtimes10

7 OMCT

(a)

200200 150

150 100100

505000

Node Z Node X

minus2

minus4

6

0

2

4

Solv

atio

n pr

essu

re (N

m2)times10

6 Hexadecane

150000

(b)

180

200

150

100120140

160100

20 40 60 8050

00

Node YNode X

minus1

minus2

minus3

0

1

2

Solv

atio

n pr

essu

re (N

m2)

times103


(c)


200

200

150150

100100

5050

00

Node Y Node X

minus8

minus6

minus4

minus2

0

times105

OMCT

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(a)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

150

Hexadecane

Van

der W

aalsrsquo

pres

sure

(Nm

2)

(b)

200

200

150150

100100

5050

00Node Y Node X

minus8

minus6

minus4

minus2

0

times105

Van

der W

aalrsquos

pre

ssur

e (N

m2)

Tetradecane

150

Tetradecane

(c)


8 ISRN Tribology

0123456789

10

Fric

tion

due t

o Ey

rings

stre

ss (N

)


Tetradecanealkane



5045403020100

minus500

minus550

minus600

minus650

minus700

minus750

minus800

minus850

Max

imum

Eyr

ings

stre

ss (N

m2)



Tetradecanealkane



3 Result Analysis


Node X

Casim

ir-Po

lder

rsquos p

ress

ure (

Nm

2)

0 20 40 60 80 100 120 140 160 180 20010

4

105

106

107

108







4 Conclusion


Nomenclature






ISRN Tribology 9























(Paminus1)



References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









8 ISRN Tribology

0123456789

10

Fric

tion

due t

o Ey

rings

stre

ss (N

)


Tetradecanealkane



5045403020100

minus500

minus550

minus600

minus650

minus700

minus750

minus800

minus850

Max

imum

Eyr

ings

stre

ss (N

m2)



Tetradecanealkane



3 Result Analysis


Node X

Casim

ir-Po

lder

rsquos p

ress

ure (

Nm

2)

0 20 40 60 80 100 120 140 160 180 20010

4

105

106

107

108







4 Conclusion


Nomenclature






ISRN Tribology 9























(Paminus1)



References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 9























(Paminus1)



References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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