Molecular Diffusion and Tensorial Slip at Surfaces with Periodic and Random Nanoscale Textures. Nikolai V. Priezjev

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1 Molecular Diffuion and Tenorial Slip at Surface with Periodic and Random Nanocale Teture Nikolai V. Priezjev Department of Mechanical Engineering Michigan State Univerity Movie, Acknowledgement: NSF (CBET ) N. V. Priezjev, Molecular diffuion and lip boundary condition at mooth urface with periodic and random nanocale teture, J. Chem. Phy. 135, (011).

Motivation for invetigation of lip phenomena at liquid/olid interface What i the proper boundary condition for liquid-on-olid flow in the preence of lip?

2 Motivation for invetigation of lip phenomena at liquid/olid interface What i the proper boundary condition for liquid-on-olid flow in the preence of lip? Still no fundamental undertanding of lip or what i proper boundary condition for continuum modeling. Iue i very important in microfluidic and nanofluidic. h Top wall velocity U liquid Effective lip in flow over aniotropic tetured urface O. Vinogradova and A. Belyaev, Wetting, roughne and flow boundary condition, J. Phy.: Conden. Matter 3, (011). z u(z) L Navier lip condition u olid wall V L lip eff L γ u z u Flow over parallel tripe: L ( ) b co b in L ( 0 ) b L ( 90 ) b

3 Detail of molecular dynamic imulation Lennard-Jone potential: V LJ r ( r) r y U Fluid monomer denity: = Thermal FCC wall with denity w =.3 3 Wall-fluid interaction: wf = and wf = V LJ ( r) 4 wf r 1 6 r z /σ 5 Nonwetting region, large lip length: 0.1 Wetting region, mall lip length: 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 T=1.1k B a 0.1 Nonwetting region (low wall-fluid energy) 156 b n 1.0 Wetting region (high wall-fluid energy) 3.6 b w

4 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 maimum when = 45

Fluid Mech. 613, 15 (008). Flat FCC tationary lower wall plane: U=upper wall peed.

5 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, (005). b b MD data b co b in Eq.(1) L continuum prediction (red curve). Bazant and Vinogradova, J. Fluid Mech. 613, 15 (008). Flat FCC tationary lower wall plane: U=upper wall peed. a U 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

Ratio of tranvere and longitudinal component of lip velocity u veru Continuum prediction (red curve) MD data u ( b b )in co u b co b in L ( 0 ) b L ( 90 ) b For tripe width a / = O(10) MD

6 Ratio of tranvere and longitudinal component of lip velocity u veru Continuum prediction (red curve) MD data u ( b b )in co 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 a u u U Non-wetting region (low wall-fluid energy, large lip length) Wetting region (high wall-fluid energy, mall lip)

A correlation between interfacial diffuion coefficient D and lip length

diffuion coefficient D correlate well with the effective lip length a a

7 A correlation between interfacial diffuion coefficient D and lip length L = 90 a.1 r y U = 0 = 0 r = 90 a r 4D t 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 ( ) b co b u z Flow over parallel tripe: L Bazant and Vinogradova, J. Fluid Mech. 613, 15 (008). in

$nonwetting wall 3.6 = areal fraction of wetting (δ = 1.0) lower wall atom 1 - = fraction of nonwetting (δ = 0.$

8 Part II: Slip flow over flat urface with random nanocale teture b n 156 U Additive friction from wetting and nonwetting area: L ( ) b w (1 ) b 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 1 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.

$0 r y 4D y t Trajectory for 100 = areal fraction of wetting (δ = 1.$ $0) wall atom 1 - = fraction of nonwetting (δ = 0.1) wall atom When > 0.$

9 A correlation between interfacial diffuion coefficient D y and lip length L U = 0 = 1.0 r y 4D y t Trajectory for 100 = areal fraction of wetting (δ = 1.0) wall atom 1 - = fraction of nonwetting (δ = 0.1) wall atom When > 0.6, the lip length L i proportional to the interfacial diffuion coefficient of fluid monomer in contact with wall. Department of Mechanical Engineering Michigan State Univerity

10 u L eff u z Important concluion L ( ) b co b in a u u U Good agreement between MD and hydrodynamic reult for aniotropic flow over periodically tetured 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 teture, 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 teture, J. Chem. Phy. 135, (011). Michigan State Univerity

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

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