Slip Behavior in Liquid Films: Influence of Patterned Surface Energy, Flow Orientation, and Deformable Gas-Liquid Interface. Nikolai V.

Transcription

1 Slip Behavior in Liquid Film: Influence of Patterned Surface Energy, Flow Orientation, and Deformable Ga-Liquid Interface Nikolai V. Priezjev Department of Mechanical and Material Engineering Wright State Univerity Movie, Acknowledgement: NSF, ACS, WSU

2 Outline of the talk 1. Brief introduction to modeling nanoflow over heterogeneou ubtrate 2. Detail of molecular dynamic (MD) imulation (MD etup and parameter value, and movie) 3. Tranvere and longitudinal orientation of lip flow 2a 4. Tenorial lip at urface with periodic and nanocale texture 5. Liquid flow over a trapped nanobubble 2a u u U x 6. Concluion

3 Experimental meaurement of the lip length L Typically lip length of water over hydrophobic urface i about nm Poible preence of nanobubble at hydrophobic urface: L ~ 10 mm Factor that affect lip: 1) Surface roughne 2) Shear rate (= lope of the velocity profile) 3) Poor interfacial wettability (weak urface energy) 4) Nucleation of nanobubble at hydrophobic urface 5) Superhydrophobic urface (L ~ 100 mm) Rothtein, Review on lip flow over Superhydrophobic urface (2010). Porou membrane? Stroock, Dertinger, Whiteide, Ajdari, Patterning flow uing grooved urface, Analytical Chemitry 74, 5306 (2002). A micromixer for rapid mixing of two or three fluid tream

4 Part I: Poibility of large lip length on patterned urface (for imple liquid in the limit where L i hear rate independent)

5 Do ga nanobubble ignificantly enhance the lip length? Nanobubble formation in water on hydrophobic urface: Lou et al., J. Vac. Sci. Tech. B 18, 2573 (2000) Ihida et al., Langmuir 16, 6377 (2000) Tyrrell and Attard, PRL 87, (2001) Steitz et al., Langmuir 19, 2409 (2003) Continuum model of lip for urface with mixed BC Philip, J. Appl. Math. Phy 23 (1972) Lauga and Stone, JFM 489, 55 (2003) Cottin-Bizonne et al., Euro.Phy. J. E 15, 427 (2004) 1mm Tapping mode AFM of water on hydrophobic wall Steitz et al. 2a Tranvere flow configuration liquid ga olid no hear tre = infinite lip = non-wetting urface finite lip velocity = wetting urface Dependence of lip on period a and on orientation of hear flow? Comparion of MD reult with continuum prediction? N.V. Priezjev, A.A. Darhuber, S.M. Troian, Slip behavior in liquid film on urface of patterned wettability: Comparion between continuum and molecular dynamic imulation, Phy. Rev. E 71, (2005).

6 h z =20.15 h y =14.45 Detail of molecular dynamic imulation h x = U = 0.5 Top View 2a wetting, =1 y hear x non-wetting, =0.1 Total wetting/nonwetting area i the ame; different patial ditribution

7 h z =20.15 Detail of molecular dynamic imulation U velocity of the upper wall L = lip length Langevin thermotat: T=1.1 k B Vij myi myi fi i j y 1 i friction coefficient f i γ = actual hear rate V lip L γ Gauian random force V LJ Interaction potential: rcut-off 2.5 wf ( r) 4 w δ δ = 1 - wetting = non-wetting 0.8ε wall-fluid interaction fluid denity 4 wall denity fluid atom wall atom Re wf Uh r 12 6 ~ O(10) r

8 h z =20.15 Propertie of the Lennard-Jone (LJ) potential V LJ ( r) 4 wf r 12 6 r δ δ = 1 - wetting = non-wetting rcut-off 2.5

9 z/ z/ Denity and velocity profile near the tationary lower wall hear direction z 10 large period a non-wetting, =0.1 wetting, = mall period a Velocity profile mall a 2a 0 denity 5 More lip for larger period a Layering in denity and velocity profile large a 0 V(/) 0.5

10 Tranvere flow configuration: Slip length dependence on period a 2a Symbol=MD reult no hear tre = infinite lip = non-wetting urface finite lip velocity = wetting urface L -2 wf Effective lip length L increae with the period a For a 30 MD recover continuum reult (imilar to rough urface!) At mall period a ~, deviation caued by effective urface roughne At mall period a ~, L maller than lip length on wettable tripe Priezjev, Darhuber and Troian, Phy. Rev. E 71, (2005). Department of Mechanical and Material Engineering Wright State Univerity

11 Longitudinal orientation: Effective lip length dependence on period a 2a L ( a) Slip length increae with the period for a20 Agreement with continuum calculation for a30 At mall period a~, deviation explained by L S(q), le order in the firt fluid layer near the wall No fitting parameter! N.V. Priezjev, A.A. Darhuber, S.M. Troian, Slip behavior in liquid film on urface of patterned wettability: Comparion between continuum and molecular dynamic imulation, Phy. Rev. E 71, (2005).

12 Longitudinal orientation: S(q) dependence on period a Structure factor: Sq ( ) exp( iqx ) j j 2 Reduction of molecular ordering above the wetting region for mall period a. Invere value of the tructure factor peak correlate well with the lip length. Thompon & Robbin, PRA, Barrat & Boucquet, PRL, 1999.

13 Important concluion: L ( a) Slip length increae with the period for a20 Excellent agreement between MD and hydrodynamic prediction for period a30, with no adjutable parameter. For the flow perpendicular to the tripe: At mall period a~, deviation from hydrodynamic caued by effective roughne of the urface potential. For the flow parallel to the tripe: At mall period a~, deviation explained by L S(q), le order in the firt fluid layer near the wall. 2a 2a N.V. Priezjev, A.A. Darhuber, S.M. Troian, Slip behavior in liquid film on urface of patterned wettability: Comparion between continuum and molecular dynamic imulation, Phy. Rev. E 71, (2005).

14 Influence of Confinement on Flow, Diffuion, and Boundary Condition in Nano Channel: A Combined Quantum Dot Imaging and Molecular Dynamic Simulation Approach Nikolai Priezjev and Manoochehr Koochefahani, Michigan State Univerity (NSF ) N. V. Priezjev, Molecular diffuion and lip boundary condition at mooth urface with periodic and random nanocale texture, Journal of Chemical Phyic 135, (2011). Microcopic jutification of the tenor formulation of the effective lip boundary condition: interfacial diffuion coefficient D correlate well with the effective lip length L( ) a a function of the hear flow direction U. Shear flow over an array of parallel tripe: L ( ) b co 2 b in 2 u u U Wetting region (high wall-fluid Nonwetting region energy) (low wall-fluid energy) a 2a x u u Leff z

15 Motivation for invetigation of lip phenomena at liquid/olid interface What i the boundary condition (BC) for liquid on olid flow in the preence of lip? Still no fundamental undertanding of lip or what i proper BC for continuum tudie. Iue i very important in micro- and nanofluidic. Contact line motion. h Top wall velocity U liquid Effective lip in flow over aniotropic textured urface O. Vinogradova and A. Belyaev, Wetting, roughne and flow boundary condition, J. Phy.: Conden. Matter 23, (2011). z u(z) L Navier lip condition u olid wall V L lip eff L γ u z u Flow over parallel tripe: L 2 ( ) b co b in 2 L ( 0 ) b L ( 90 ) b

16 Detail of molecular dynamic imulation Lennard-Jone VLJ (r ) 4 potential: r 12 r 6 y x U Fluid monomer denity: = Thermal FCC wall with denity w = Wall-fluid interaction: wf = and wf = VLJ (r ) 4 wf 6 r 12 r Nonwetting region, large lip length: 0.1 Wetting region, mall lip length: 1.0 Thermotat to thermal wall only! Langevin thermotat applied to fluid introduce a bia in flow profile near patterned wall for 0 < < 90 Friction term: m x T=1.1 kb a 0.1 Nonwetting region (low wall-fluid energy) bn Wetting region (high wall-fluid energy) bw 3.6

17 Part I: Flow over periodic tripe; longitudinal and tranvere velocity profile a = tripe period = 90 = 90 U = upper wall peed = 0 = 0 Longitudinal component: u ( z) U = 45 = 45 Tranvere component: u ( z U ) Lower patterned wall Upper wall U = 0.1 Tranvere flow u (z) i maximum when = 45

18 Slip length a a function of angle between flow orientation U and tripe For tripe width a 30 MD recover continuum reult for flow either or to tripe. Priezjev, Darhuber and Troian, Phy. Rev. E 71, (2005). b b MD data 2 2 b co b in Eq.(1) L continuum prediction (red curve). Bazant and Vinogradova, J. Fluid Mech. 613, 125 (2008). Flat FCC tationary lower wall plane: U=upper wall peed. 2a U x For tripe width a / = O(10) MD reproduce lip length for aniotropic flow over an array of parallel tripe, ee Eq.(1). Non-wetting region (low wall-fluid energy, large lip length) Wetting region (high wall-fluid energy, mall lip) L ( 0 ) b L ( 90 ) b

19 Ratio of tranvere and longitudinal component of lip velocity u veru Continuum prediction (red curve) MD data u ( b b )in co 2 2 u b co b in L ( 0 ) b L ( 90 ) b For tripe width a / = O(10) MD qualitatively reproduce the ratio of tranvere and longitudinal component of the apparent lip velocity u Flat FCC tationary lower wall plane: U=upper wall peed u = lip velocity 2a u u U x Non-wetting region (low wall-fluid energy, large lip length) Wetting region (high wall-fluid energy, mall lip)

20 A correlation between interfacial diffuion coefficient D and lip length L = 90 a 2.21 r xy U = 0 = 0 r = 90 a 2 r 4D t x time Microcopic jutification of the tenor formulation of the effective lip boundary condition: interfacial diffuion coefficient D correlate well with the effective lip length a a function of the hear flow direction U. u L eff 2 ( ) b co b u z Flow over parallel tripe: L Bazant and Vinogradova, J. Fluid Mech. 613, 125 (2008). in 2

21 Part II: Slip flow over flat urface with random nanocale texture b n 156 U Additive friction from wetting and nonwetting area: x m L ( ) m m (1 ) b b w n L ( ) b n bw bn (1 ) b w (dahed curve) Homogeneou nonwetting wall 3.6 = areal fraction of wetting (δ = 1.0) lower wall atom 1 - = fraction of nonwetting (δ = 0.1) lower wall atom Wall-fluid interaction: V LJ r ( r) 4 b w 12 6 r Homogeneou wetting wall Slip length i iotropic (finite ize effect). The variation of L i determined by the total area of wetting region.

22 A correlation between interfacial diffuion coefficient D xy and lip length L U = 0 = 1.0 r 2 xy 4D xy t Trajectory for 100 = areal fraction of wetting (δ = 1.0) wall atom 1 - = fraction of nonwetting (δ = 0.1) wall atom N. V. Priezjev, Molecular diffuion and lip boundary condition at mooth urface with periodic and random nanocale texture, J. Chem. Phy. 135, (2011). When > 0.6, the lip length L i proportional to the interfacial diffuion coefficient of fluid monomer in contact with wall.

23 u L eff u z Important concluion: L 2 ( ) b co b in 2 2a u u U x Good agreement between MD and hydrodynamic reult for aniotropic flow over periodically textured urface provided length cale O(10 molecular diameter). Microcopic jutification of the tenor formulation of the effective lip boundary condition: interfacial diffuion coefficient D correlate well with the effective lip length a a function of the hear flow direction. In cae of random urface texture, the effective lip length i determined by the total area of wetting region. When > 0.6, L i linearly proportional to the interfacial diffuion coefficient of fluid monomer in contact with periodic urface potential. N. V. Priezjev, Molecular diffuion and lip boundary condition at mooth urface with periodic and random nanocale texture, J. Chem. Phy. 135, (2011). Department of Mechanical and Material Engineering Wright State Univerity

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25 Detail of molecular dynamic imulation

26 The pinning mechanim of the three-phae contact line

27 The lip velocitie and lip length for flow over urface-attached nanobubble

28 The lip velocitie and lip length for flow over urface-attached nanobubble

29 Concluion: We invetigated the behavior of the local and effective lip length that decribe hear flow over nanobubble attached to mooth olid urface uing molecular dynamic imulation. Contact line at the ga-liquid interface can be pinned by the wettability tep on a mooth ubtrate and the contact angle hyterei depend trongly on the wettability contrat. The local lip length i finite at the ga-liquid interface and it patial ditribution become aymmetric due to deformation of the nanobubble under high hear.