  We present an analysis of physical conditions in planetary nebulae (PNe) in
terms of collisionally-excited line (CEL) and optical-recombination line (ORL)
profiles. We aim to investigate whether line profiles could be used to study
the long-standing CEL/ORL abundance-discrepancy problem in nebular
astrophysics. Using 1D photoionization models and their assumed velocity
fields, we simulate the line profiles of various ionic species. We attempt to
use our model to account for the observed CEL and ORL profiles. As a case study
we present a detailed study of line profiles of the low-excitation planetary
nebula (PN) IC 418. Our results show that the profiles of classical temperature
and density diagnostic lines, such as [O III] 4363,5007, [S II] 6716,6731, and
[Ar IV] 4711,4740, provide a powerful tool to study nebular temperature and
density variations. The method enables the CEL/ORL abundance-discrepancy
problem to be studied more rigorously than before. A pure photoionization model
of a chemically-homogeneous nebula seems to explain the observed disagreements
in the profiles for the [O III] 4363 and the 5007 lines, but cannot account for
the differences between the [O III] CELs and the O II ORLs. We also investigate
the temperature and density variations in the velocity space of a sample of
PNe, which are found to be insignificant.
