  We study the linearized hydrodynamics of a two-component fluid membrane near
a repulsive wall, via a model which incorporates curvature- concentration
coupling as well as hydrodynamic interactions. This model is a simplified
version of a recently proposed one [J.-B. Manneville et al. Phys. Rev. E, 64,
021908 (2001)] for non-equilibrium force-centres embedded in fluid membranes,
such as light-activated bacteriorhodopsin pumps incorporated in phospholipid
(EPC) bilayers. The pump/membrane system is modeled as an impermeable,
two-component bilayer fluid membrane in the presence of an ambient solvent, in
which one component, representing active pumps, is described in terms of force
dipoles displaced with respect to the bilayer midpoint. We first discuss the
case in which such pumps are rendered inactive, computing the mode structure in
the bulk as well as the modification of hydrodynamic properties by the presence
of a nearby wall. We then discuss the fluctuations and mode structure in steady
state of active two-component membranes near a repulsive wall. We find that
proximity to the wall smoothens membrane height fluctuations in the stable
regime, resulting in a logarithmic scaling of the roughness even for initially
tensionless membranes. This explicitly non-equilibrium result, a consequence of
the incorporation of curvature-concentration coupling in our treatment, also
indicates that earlier scaling arguments which obtained an increase in the
roughness of active membranes near repulsive walls may need to be reevaluated.
