  We calculate steady-state models of radiation-driven super-Eddington winds
and static expanded envelopes of neutron stars caused by high luminosities in
type I X-ray bursts. We use flux-limited diffusion to model the transition from
optically thick to optically thin, and include effects of general relativity,
allowing us to study the photospheric radius close to the star as the
hydrostatic atmosphere evolves into a wind. We find that the photospheric
radius evolves monotonically from static envelopes ($r_{\rm ph}\lesssim 50-70$
km) to winds ($r_{\rm ph}\approx 100-1000$ km). Photospheric radii of less than
$100$ km, as observed in most photospheric radius expansion bursts, can be
explained by static envelopes, but only in a narrow range of luminosity. In
most bursts, we would expect the luminosity to increase further, leading to a
wind with photospheric radius $\gtrsim 100$ km. In the contraction phase, the
expanded envelope solutions show that the photosphere is still $\approx 1$ km
above the surface when the effective temperature is only $3\%$ away from its
maximum value. This is a possible systematic uncertainty when interpreting the
measured Eddington fluxes from bursts at touchdown. We also discuss the
applicability of steady-state models to describe the dynamics of bursts. In
particular, we show that the sub to super-Eddington transition during the burst
rise is rapid enough that static models are not appropriate. Finally, we
analyze the strength of spectral shifts in our models. Expected shifts at the
photosphere are dominated by gravitational redshift, and are therefore
predicted to be less than a few percent.
