Interdisciplinary Applied Mathematics

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case of a chain molecule, the slip length depends more strongly on the value of cFS, and for cFS = 1/4 the slip length is 20.6a, in qualitative agreement with the MD simulation results of (Stevens et al., 1997) for hexadecane and also with the experimental results of (Pit et al., 2000).


Similar results were reported in (Priezjev and Troian, 2004), for shear polymer films in a Couette flow with a gap height of 24.57a. In particular, N-mer polymer chains with N up to 16 were simulated for various levels of shear rate y. The scaling law obtained in the earlier simulations of


(Thompson and Troian, 1997) for N =1, see equation (1.2), was extended for polymer chains; that is, the normalized slip length is given by


1-1


Y c



1/2



(10.7)


for shear rates 7 > 5 x 10~3r_1; pc is the critical level of shear rate above which divergence behavior is observed. It was also found that beyond N10 the molecular weight dependence of the slip length is mostly associated with the bulk viscosity.


Also, in (Barrat and Bocquet, 1999), MD simulations were performed with a Lennard-Jones potential of the form


Vlj = 4e[(r/<r) 12Cij(r/a) 6],


where Cij controls the type of interaction. The interactions between fluid atoms were defined by cFF = 1.2, while the fluid-solid interaction coefficient cFS was varied between 0.5 and 1. For cFS = 0.9 a contact angle of 100° is obtained, whereas    for    cFS    =    0.5    a contact    angle    of 150°    is    obtained, which

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