Tack, ink transfer and ink distribution on paper

We discuss the hydrodynamic flow of a half-tone dot pressed onto model porous substrates in a range of parameters representative of printing processes. We first simulate the transfer of a fluid dot onto a two-dimensional network of pores and find that, at constant porosity, fluid transfer increases with decreasing pore size and decreases with porosity at fixed pore radius. We show that the porosity and pore size can be combined as a single variable, the specific capillary pressure, to explain the ink transfer curves. We then discuss how the tack in relation to the porous structure. We show that Stefan's law, often criticised in the literature, correctly predicts how tack changes with the thickness of the ink layer. Finally, we show how ink distribution is affected by horizontal pores in the network.