  We develop a simple iterative scheme to include vertical turbulent mixing and
diffusion in ProDiMo thermo-chemical models for protoplanetary discs. The
models are carefully checked for convergence toward the time-independent
solution of the reaction-diffusion equations, as e.g. used in exoplanet
atmosphere models. A series of five T Tauri disc models is presented where we
vary the mixing parameter {\alpha} mix from 0 to 0.01 and take into account (a)
the radiative transfer feedback of the opacities of icy grains that are mixed
upward and (b) the feedback of the changing molecular abundances on the gas
temperature structure caused by exothermic reactions and increased line
heating/cooling. We see considerable changes of the molecular and ice
concentrations in the disc. The most abundant species (H2, CH4, CO, the neutral
atoms in higher layers, and the ices in the midplane) are transported both up
and down, and at the locations where these abundant chemicals finally
decompose, for example by photo processes, the release of reaction products has
important consequences for all other molecules. This generally creates a more
active chemistry, with a richer mixture of ionised, atomic, molecular and ice
species and new chemical pathways that are not relevant in the unmixed case. We
discuss the impact on three spectral observations caused by mixing and find
that (i) icy grains can reach the observable disc surface where they cause ice
absorption and emission features at IR to far-IR wavelengths, (ii) mixing
increases the concentrations of certain neutral molecules observable by mid-IR
spectroscopy, in particular OH, HCN and C2H2, and (iii) mixing can change the
optical appearance of CO in ALMA line images and channel maps, where strong
mixing would cause the CO molecules to populate the distant midplane.
