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Molecular Dynamics Simulations of the Slip Boundary Condition

Overview. I. Intro to basic concepts

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Molecular Dynamics Simulations of the Slip Boundary Condition

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    1. Molecular Dynamics Simulations of the Slip Boundary Condition Jon Horek ME 438-2: Nanofluidics January 23, 2003

    2. Overview I. Intro to basic concepts – Slip, L/J

    3. Intro to Concepts (pg. 1/2 ) Brief Review of Velocity Slip BC Recall, velocity u often vanishes at wall (No slip BC). Certain parameters (i.e. – fluid/wall interactions, MFP, ?) can create “slip” or “stick” of a certain length ? Slip BC.

    4. Intro to Concepts (pg. 2/2 ) Lennard-Jones (L-J) Potential Common model of intermolecular potential ? force field e (particle interaction energy scale) ? ewf is wall-fluid s (particle interaction length scale)? swf is wall-fluid ?w (Wall density of particles) also important parameter Parameters are varied to simulate cohesiveness.

    5. Thompson/Troian (pg. 1/3) Conditions for Molecular Dynamics computer experiments in Couette cell. Lennard-Jones interface parameters ?w, ewf, swf varied in sets. Speed of Couette cell wall, u = U, varied for each set of (?w, ewf , swf).

    6. Thompson/Troian (pg. 2/3) Results of MD Experiments in Couette Cell for constant U Constant U ? one no slip, and two slip profiles. Main result: S/L momentum transfer ? as surface energy corrugation ?. Wall density down and/or ewf up ? no slip. Why? Stronger interaction.

    7. Thompson/Troian (pg. 3/3 ) Results of MD Experiments in Couette Cell for variable wall-speed Several wall speeds, for each of four L-J interface parameter sets Velocity profiles converted to shear rates Slip length (normalized) vs. Shear Rate (normalized) plotted Normalized Curve collapses to a generalized slip BC!

    8. Barrat / Bocquet (pg. 1/4 ) Conditions for MD computer experiments of nonwetting fluid between walls Recall, nonwetting case ? L-J Potential utilized Contact angle written in terms of minimum pressure to enter pore: 90o < ? <140o for this experiment Couette (shear-driven) and Poiseuille (pressure-driven) cases studied

    9. Barrat / Bocquet (pg. 2/4 ) Result of MD Experiment in Couette cell Plotted results for upper wall speed = U = .5. Within one length scale from wall, profile matches the analytical result of Couette flow with slip BC ? Obtained by altering d and zw , the hydrodynamic position of the walls.

    10. Barrat / Bocquet (pg. 3/4 ) Result of MD Experiment in Poiseuille case Pressure grad created by adding external force to each particle. MD Fits analytical results with slip BC; no fit with no slip BC.

    11. Barrat / Bocquet (pg. 4/4 ) Main Result Normalized slip length versus reduced pressure (i.e. – contact angle) General decay of slip length, as ? ? hydrophilic Data taken for different values of L-J interaction parameters.

    12. Conclusions (pg. 1/1) Summary of results Navier slip BC is a special, low shear rate case of a general nonlinear slip BC. Hydrophobic liquid flow in pores modeled by slip BC Slip length of hydrophobic liquid decays as ?? 90o

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