A physical model for liquid movement into a porous substrate under the action of a pressure pulse

The dynamic behavior of ink movement under nip-pressure of a printing press has been studied. The theoretical model employed originates from the Bosanquet model that was previously applied to situations of constant or zero external pressures. In the present work, we extend the model to a printing situation where a time-dependent nip pressure presents. The general solution of the model for a simple liquid has been worked out, as in most situations the ink's continuous phase can be approached as a Newtonian fluid, e.g. mineral oil in offset and water in flexo etc. The general solution is of analytical form thanks to the possibility to expand the nip-pressure profile into a Fourier series. For illustrative purposes, simulations with three model profiles, one rectangular, one sinusoidal, and one joint sinusoidal, have been performed. It is found that the profile of the nip-pressure plays a dominant role in liquid transfer and setting.