The development of micro- and nanofluidic devices for actuation of liquid films, droplets and bubbles requires accurate characterization of boundary conditions at liquid/solid interfaces. The smaller the characteristic dimensions of the device, the more dominant is the influence of boundary forces on transport behavior. Of particular concern in systems subject to large surface to volume ratios is the significant frictional losses induced by the no-slip boundary condition.
The celebrated no-slip condition for liquid/solid interfaces predicates that the tangential speed of the liquid adjacent to a solid surface equal the speed of the solid substrate. Despite its simplicity, this boundary condition has proven remarkably successful in reproducing most commonplace flows. There exist, however, notable examples in non-inertial flows for which the no-slip condition leads to singular behavior including corner flows, coating flows and capillary spreading of a droplet. While a slip velocity can instead be used to regularize the shear stress singularity that arises in such flows, such models are phenomenological in origin and provide no universal understanding of the nature of momentum transport at liquid-solid interfaces. Turning to the experimental side, measurements on various systems over the past two decades have determined that liquid slippage is indeed possible at a solid boundary by application of specialized surface chemical treatments, a reduction in wall roughness and nucleation of gas nanobubbles in water films. Polymer melts of high molecular weight are also known to generate larger slip lengths in comparison to simple liquids, but the underlying cause is not completely understood nor has the possibility of a shear-dependent slip length been investigated.
By appealing to molecular dynamics (MD) simulations of liquid films in planar shear, we examine what molecular transport coefficients govern the degree of slip at liquid/solid interfaces and whether the slip length is shear rate dependent. We also discuss the role of the in-plane liquid structure factor and diffusion coefficient, the presence of wall roughness, and periodic variations in wall surface energy in establishing the degree of slip in non-inertial flows. Detailed comparison between hydrodynamic predictions and MD simulations elucidates what geometric and molecular parameters govern the slip length at different length scales. In general, we find excellent agreement between the continuum and MD results when the system size is approximately an order of magnitude larger than the molecular size of the liquid phase. We conclude this talk by a discussion of the molecular aspects which cause deviations from hydrodynamic predictions at smaller length scales.
This work is funded by the National Science Foundation, the NASA Microgravity Fluid Physics Program and the Princeton Institute for the Science and Technology of Materials.
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