  Nanoscale fluid transport is typically pictured in terms of atomic-scale
dynamics, as is natural in the real-space framework of molecular simulations.
An alternative Fourier-space picture, that involves the collective charge
fluctuation modes of both the liquid and the confining wall, has recently been
successful at predicting new nanofluidic phenomena such as quantum friction and
near-field heat transfer, that rely on the coupling of those fluctuations.
Here, we study the charge fluctuation modes of a two-dimensional (planar)
nanofluidic channel. Introducing confined response functions that generalize
the notion of surface response function, we show that the channel walls exhibit
coupled plasmon modes as soon as the confinement is comparable to the plasmon
wavelength. Conversely, the water fluctuations remain remarkably bulk-like,
with significant confinement effects arising only when the wall spacing is
reduced to 7 A. We apply the confined response formalism to predict the
dependence of the solid-water quantum friction and thermal boundary conductance
on channel width for model channel wall materials. Our results provide a
general framework for Coulomb interactions of fluctuating matter in nanoscale
confinement.
