FLUIDS
AT NANOSCALES

At macroscopic scales the flow velocity of
fluids is assumed to equal that of an adjacent solid at their interface.
This boundary condition leads to singular
stresses and energy dissipation in two simple geometries. The first is contact line motion, where the
interface between two fluids advances over a solid at velocity U. The second is cavity flow, where the top of a
cavity moves at velocity U while the other walls remain stationary.
In both cases the velocity must change from U
to 0 over a distance that vanishes at the corner where two interfaces
intersect. This leads to a logarithmic
divergence in the total force and dissipation.

We developed a multiscale
approach that uses a continuum mechanics description except near the singular
corners. There, discrete atoms are
followed. The method allows particles
and heat to flow between continuum and atomistic regions. In the plots below the corners are magnified
by increasing factors from 2^{3} to 2^{11}.
The stress is resolved over 6 orders of
magnitude in length from ~nm to ~mm. The
region within ~12 atoms from the corners carries 20 to 30% of the total force.

At atomic scales deviations from the no-slip
boundary condition are observed. Our
studies revealed that these deviations can become extreme for fluid
mixtures. Large jumps in velocity arise
from gradients in interfacial energy or concentration.
A movie showing how this can be used to drive
a nanometer is at movies.html.