  This paper provides an application of our hybrid continuum-particle scheme to
liquids by considering unsteady shear flows driven by wall oscillations in
nano-slots. The particle region (P) adjacent to the wall, is described at the
atomistic level by molecular dynamics, while the outer region (C), described by
a continuum equation for the transversal momentum, is solved via a finite
volume method. Both regions overlap in the ``handshaking'' region where a
two-way coupling scheme (C$\to$P and P$\to$C) is implemented. A protocol for
the C$\to$P coupling was presented in a previous paper [Delgado-Buscalioni and
Coveney, Phys. Rev. E, {\bf 67}, 046704 (2003)]; here we focus on the the
P$\to$C counterpart, that is, on the exchange of information from the
microscopic to the continuum domain. We first show how to use the finite volume
formalism to balance the momentum and mass fluxes across the P$\to$C surface in
such a way that the continuity of velocity is ensured. Then we analyse the
effect of the fluctuations of the (P) stress tensor on the stability and
accuracy of the numerical scheme. This analysis yields a condition which
establishes a restriction on the resolution of the flow field that can be
described by the hybrid method, in terms of the maximum frequency and
wavenumber of the flow.
