We use a model for the evolution of galaxies in the far-IR based on the LambdaCDM cosmology to make detailed predictions for upcoming cosmological surveys with the Herschel Space Observatory. We use the combined GALFORM semi-analytical galaxy formation model and GRASIL spectrophotometric code to compute galaxy SEDs including the reprocessing of radiation by dust. The model, which is the same as that in Baugh et al. (2005), assumes two different IMFs: a normal solar neighbourhood IMF for quiescent star formation in disks, and a very top-heavy IMF in starbursts triggered by galaxy mergers. We have shown previously that the top-heavy IMF appears necessary to explain the number counts and redshifts of faint sub-mm galaxies. In this paper, we present predictions for galaxy luminosity functions, number counts and redshift distributions in the Herschel imaging bands. We find that source confusion will be a serious problem in the deepest planned surveys. We also show predictions for physical properties such as star formation rates and stellar, gas and halo masses, together with fluxes at other wavelengths (from the far-UV to the radio) relevant for multi-wavelength follow-up observations. We investigate what fraction of the total IR emission from dust and of the high-mass star formation over the history of the Universe should be resolved by planned surveys with Herschel, and find a fraction ~30-50%, depending on confusion. Finally, we show that galaxies in Herschel surveys should be significantly clustered.
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