Atomic hydrodynamics of the moving contact line

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The no-slip limit condition and the moving contact line problemThe summed up Navier limit condition (GNBC) from atomic elements (MD) simulationsImplementation of the new slip limit condition in a continuum hydrodynamic model (stage field formulation)Comparison of continuum and MD resultsA variational inference of the continuum model, for both the mass comparisons and the limit cond

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Slide 1

Atomic hydrodynamics of the moving contact line Tiezheng Qian Mathematics Department Hong Kong University of Science and Technology as a team with Ping Sheng ( Physics Dept, HKUST ) Xiao-Ping Wang ( Mathematics Dept, HKUST ) SISSA – Trieste – Italy, May 2007

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The no-slip limit condition and the moving contact line issue The summed up Navier limit condition (GNBC) from sub-atomic progression (MD) reenactments Implementation of the new slip limit condition in a continuum hydrodynamic model (stage field definition) Comparison of continuum and MD comes about A variational induction of the continuum show, for both the mass conditions and the limit conditions, from Onsager's standard of minimum vitality dispersal (entropy generation)

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Wetting marvels: All this present reality complexities we can have! Moving contact line: All the improvements we can make and every one of the recreations, atomic and continuum , we can complete! Numerical tests Offer a negligible model with answer for this traditional liquid mechanical issue, under a general standard overseeing thermodynamic irreversible procedures

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? No-Slip Boundary Condition , A Paradigm

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(1823) from Navier Boundary Condition to No-Slip Boundary Condition : shear rate at strong surface : slip length , from nano-to micrometer Practically, no slip in perceptible streams

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Young's condition (1805):

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speed irregularity and wandering worry at the MCL

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The Huh-Scriven display for 2D stream (linearized Navier-Stokes condition) 8 coefficients in An and B, controlled by 8 limit conditions Shear stress and weight fluctuate as

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Dussan and Davis, J. Liquid Mech. 65 , 71-95 (1974): Incompressible Newtonian liquid Smooth unbending strong dividers Impenetrable liquid interface No-slip limit condition Stress peculiarity: the digressive drive applied by the liquid on the strong surface is unbounded. Not even Herakles could sink a strong ! by Huh and Scriven (1971). a) To build a continuum hydrodynamic model by evacuating condition (3) or potentially (4). b) To make correlation with atomic elements recreations

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Numerical trials accomplished for this exemplary liquid mechanical issue Koplik, Banavar and Willemsen, PRL (1988) Thompson and Robbins, PRL (1989) Slip saw in the region of the MCL Boundary condition ??? Continuum conclusion of atomic elements !

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Immiscible two-stage Poiseuille stream The dividers are moving to one side in this reference outline, and far from the contact line the liquid speed close to the divider corresponds with the divider speed. Close to the contact lines the no-slip condition seems to come up short , be that as it may.

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Slip profile no slip finish slip The disparity between the minuscule anxiety and recommends a breakdown of neighborhood hydrodynamics .

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The dynamic model by Blake and Haynes: The part of interfacial pressure A fluctuating three stage zone . Adsorbed atoms of one liquid trade with those of the other liquid. In harmony the net rate of trade will be zero. For a three-stage zone moving with respect to the strong divider, the net uprooting, is expected to a nonzero net rate of trade , driven by the uneven Young anxiety The vitality move because of the lopsided Young anxiety prompts to two distinct rates

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Two classes of models proposed to portray the contact line movement: An Eyring approach: Molecular adsorption/desorption forms at the contact line (three-stage zone); Molecular scattering at the tip is predominant. T. D. Blake and J. M. Haynes, Kinetics of fluid/fluid uprooting , J. Colloid Interf. Sci. 30, 421 (1969). A hydrodynamic approach: Dissipation ruled by thick shear stream inside the wedge; For wedges of little (obvious) contact point, a grease guess used to rearrange the estimations; A (sub-atomic scale) cutoff acquainted with evacuate the logarithmic peculiarity in gooey dispersal. F. Brochard-Wyart and P. G. De Gennes, Dynamics of fractional wetting , Advances in Colloid and Interface Science 39 , 1 (1992).

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F. Brochard-Wyart and P. G. De Gennes, Dynamics of halfway wetting , Adv. in Colloid and Interface Sci. 39 , 1 (1992). To compress: a total exchange of the flow would on a fundamental level require both terms in Eq. (21). (21) grease estimate: hydrodynamic term for the thick scattering in the wedge sub-atomic term because of the motor adsorption/desorption Wedge : Molecular cutoff acquainted with the gooey dispersal Dissipation Tip : Molecular dissipative coefficient from dynamic system of contact-line slip

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No-slip limit condition ? G. I. Taylor; K. Moffatt; Hua & Scriven; E.B. Dussan & S.H. Davis; L.M. Selling; P.G. de Gennes; Koplik, Banavar, Willemsen; Thompson & Robbins; and so forth Apparent Violation seen from the moving/slipping contact line Infinite Energy Dissipation (unphysical peculiarity) No-slip limit condition separates ! Nature of the genuine B.C. ? (minuscule slipping component) If slip happens inside a length scale S in the region of the contact line, then what is the greatness of S ? Qian, Wang & Sheng, Phys. Rev. E 68 , 016306 (2003) Qian, Wang & Sheng, Phys. Rev. Lett. 93 , 094501 (2004)

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Molecular progression recreations for two-stage Couette stream System estimate Speed of the moving dividers Fluid-liquid sub-atomic associations Fluid-strong sub-atomic communications Densities (fluid) Solid divider structure (fcc) Temperature

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Two indistinguishable liquids: same thickness and consistency, however when all is said in done diverse liquid strong cooperations Smooth strong divider: strong iotas put on a crystalline structure No contact point hysteresis!

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Modified Lennard-Jones Potentials for like atoms for particles of various species for wetting property of the liquid

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liquid 2 liquid 1 liquid 1 dynamic arrangement f-1 f-2 f-1 f-1 f-2 f-1 symmetric lopsided static setups

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limit layer extraneous energy transport Stress from the rate of distracting force transport per unit range

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schematic representation of the limit layer liquid constrain measured by standardized circulation of divider compel

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The Generalized Navier limit condition The worry in the immiscible two-stage liquid: gooey part non-thick part interfacial drive GNBC from continuum finding static Young segment subtracted >>> uncompensated Young anxiety A digressive compel emerging from the deviation from Young's condition

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got by subtracting the Newtonian thick segment strong circle: static symmetric strong square: static hilter kilter exhaust circle: dynamic symmetric purge square: dynamic awry

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non-thick part gooey part Slip driven by uncompensated Young anxiety + shear thick anxiety

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Uncompensated Young Stress missed in Navier B. C. Net compel because of hydrodynamic deviation from static constrain adjust (Young's condition) NBC NOT fit for portraying the movement of contact line Away from the CL , the GNBC suggests NBC for single stage streams .

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Continuum Hydrodynamic Model: Cahn-Hilliard (Landau) free vitality utilitarian Navier-Stokes condition Generalized Navier Boudary Condition (B.C.) Advection-dispersion condition First-arrange condition for unwinding of (B.C.) supplemented with incompressibility impermeability B.C. impermeability B.C.

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Phase field displaying for a two-segment framework

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supplemented with

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GNBC : a condition of unrelated constrain adjust

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Dussan and Davis, JFM 65, 71-95 (1974): Incompressible Newtonian liquid Smooth inflexible strong dividers Impenetrable liquid interface No-slip limit condition Stress peculiarity: the digressive compel applied by the liquid on the strong surface is interminable. Condition (3) >>> Diffusion over the liquid interface [Seppecher, Jacqmin, Chen - Jasnow - Vinals, Pismen - Pomeau, Briant - Yeomans] Condition (4) >>> GNBC Stress peculiarity, i.e., vast unrelated constrain applied by the liquid on the strong surface, is expelled.

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Comparison of MD and Continuum Results Most parameters decided from MD straightforwardly M and advanced in fitting the MD comes about for one design All ensuing correlations are without customizable parameters . M and ought not be viewed as fitting parameters, Since they are utilized to understand the interface imperviousness condition, as per the MD recreations.

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sub-atomic positions anticipated onto the xz plane Symmetric Couette stream Asymmetric Couette stream Diffusion versus Slip in MD

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close entire slip at moving CL Symmetric Couette stream V=0.25 H=13.6 no slip

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profiles at various z levels symmetric Couette stream V=0.25 H=13.6 deviated CCouette stream V=0.20 H=13.6

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symmetric Couette V=0.25 H=10.2 symmetric Couette V=0.275 H=13.6

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hilter kilter Poiseuille stream g ext =0.05 H=13.6

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Power-law rot of fractional disappear from the MCL from finish slip at the MCL to no slip far away, represented by the NBC and the asymptotic 1/r push

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The continuum hydrodynamic model for the moving contact line A Cahn-Hilliard Navier-Stokes framework supplemented with the Generalized Navier limit condition , initially revealed from sub-atomic flow recreations Continuum forecasts in concurrence with MD comes about. Presently got from the guideline of least vitality dispersal , for irreversible thermodynamic procedures ( dissipative straight reaction, Onsager 1931). Qian,

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