  This paper examines flows in the immediate vicinity of stars and compact
objects dynamically inspiralling within a common envelope (CE). Flow in the
vicinity of the embedded object is gravitationally focused leading to drag and
potential to gas accretion. This process has been studied numerically and
analytically in the context of Hoyle-Lyttleton accretion (HLA). Yet, within a
CE, accretion structures may span a large fraction of the envelope radius, and
in so doing sweep across a substantial radial gradient of density. We quantify
these gradients using detailed stellar evolution models for a range of CE
encounters. We provide estimates of typical scales in CE encounters that
involve main sequence stars, white dwarfs, neutron stars, and black holes with
giant-branch companions of a wide range of masses. We apply these typical
scales to hydrodynamic simulations of 3D HLA with an upstream density gradient.
This density gradient breaks the symmetry that defines HLA flow, and imposes an
angular momentum barrier to accretion. Material that is focused into the
vicinity of the embedded object thus may not be able to accrete. As a result,
accretion rates drop dramatically, by 1-2 orders of magnitude, while drag rates
are only mildly affected. We provide fitting formulae to the
numerically-derived rates of drag and accretion as a function of the density
gradient. The reduced ratio of accretion to drag suggests that objects that can
efficiently gain mass during CE evolution, such as black holes and neutron
stars, may grow less than implied by the HLA formalism.
