Flow around nanospheres and nanocylinders

For micro- and nanoscale problems, boundary surface roughness often means that the usual no-slip boundary condition of fluid mechanics does not apply. Here we examine the steady low-Reynolds-number flow past a nanosphere and a circular nanocylinder in a Newtonian fluid, with the no-slip boundary condition replaced by a boundary condition which attempts to account for boundary slip due to the tangential shear at the boundary. We apply the so-called Navier boundary condition and use the method of matched asymptotic expansions. This model possesses a single parameter to account for the slip, the slip length ℓ, which is made dimensionless with respect to the corresponding radius, which is assumed to be of the same order of magnitude as the slip length. Numerical results are presented for the two extreme cases, ℓ = 0 corresponding to classical theory, and graphic ℓ→ ∞ corresponding to complete slip. The streamlines for ℓ > 0 are closer to the body than for ℓ= 0, while the frictional drag for ℓ > 0 is reduced below the values for ℓ = 0, as might be expected. For the circular cylinder, results corresponding to ℓ→ ∞ are in complete accord with certain low-Reynolds-number experimental results, and this excellent agreement is much better than that predicted by the no-slip boundary condition.