The no-slip boundary condition at the liquid/solid interface works well at the macroscale. However, this condition is an assumption and it can, in principle, be violated. The fluid velocity profile in micro and nanofluidic channels can be significantly affected by the boundary slip. The most popular Navier model relates the slip velocity at the liquid/solid interface to the shear rate via the proportionality coefficient, the so-called slip length (L0).
The magnitude of the slip length depends on several key parameters: the strength of wall-fluid interaction, fluid structure, shear rate, and surface roughness. In the case of periodic surface roughness, the effective slip length (Leff) is computed by linear extrapolation of the fluid velocity profile to zero relative to the level of the mean height of the surface roughness (see picture below).
It is well established that large amplitude (α) and small wavelength (λ) of the surface corrugation lead to a reduction of the effective slip length. In our recent paper, we have studied slipping properties of a polymer melt (N=20 beads per chain) near periodically roughened substrate with weak wall-fluid interactions. We were interested how polymer chains diffuse and orient themselves near the rough surface in the presence of slip. Below we present several animations of the dynamics of polymer chains in contact with a rough surface. For convenience, the animations display both side and top views of the same sequence simultaneously.
In a shear flow, polymer chains near the surface are forced to migrate in the shear direction. During the transition from one groove to the next, the chains stretch in the shear flow direction above the peak of the corrugation. (see the animation of the steady-state shear flow (λ=7.5σ, α=1.4σ) 7 MB and 21.5 MB). The radius of gyration Rgx above the peak is more than twice its value inside the groove. These flow conditions correspond to a negative effective slip length Leff≈-2σ.
When the wavelength of the surface corrugation is smaller than the radius of gyration, the polymer chains have to stretch significantly in the y direction to fit inside the grooves. The diffusive motion in the x direction is hindered by the surface roughness in equilibrium. The polymer chains spend most of their time inside one groove while partially or completely untangled (see the animation of the system at equilibrium (λ=3.75σ, α=1.0σ) 21.6 MB).
We find that in a shear flow, the polymer chains try to move with the mean flow velocity but their heads or tails can be trapped inside different grooves. Note that some chains are elongated partially in the y direction inside the groove, while their other end is moving with the mean flow or trapped inside another groove (see the animation of the steady-state shear flow (λ=3.75σ, α=1.0σ) 20.7 MB). For large wavenumbers, ka=2πa/λ, the magnitude of the negative effective slip length is approximately equal to the sum of the corrugation amplitude and Rgz of the polymer chains above the crests of the wavy wall.
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