The classical imbibition models: inertial, Bosanquet and the later dominance of viscous flow, thus following the Lucas-Washburn regime, frequently are employed to characterise the imbibition behaviour of printing fluids in paper or paper-based materials. To explore the interaction relationship among these imbibition models, theoretical simulation regarding the imbibition process based on these three models is discussed and analysed in this paper under uniform physical parameters. Additionally, their mutual relationship also was displayed by means of analysis and simulation results with different radii of the equivalent capillary tube aiming at different papers or paper-based materials, with focus on coated grades. It is found that these classical imbibition models indeed have an interaction relationship in the whole imbibition process, which is that Bosanquet is a more general form to characterize imbibition behaviour both inertial and viscous, each of which describe the dominant imbibition stages during the absorption process and have an overlapping area at initial stages and times of geometrical change within the structure related to the inertial regime respectively. The overlapping point timescale changes, and is extended when the equivalent radius of capillary tube of print materials is relatively large or small. It means that the consistency of this circumstance between inertial and viscous behaviour would extend into longer periods when having a large equivalent radius of capillary tube. By contrast, if the equivalent radius is small, the inertial and viscous regimes would reach a parallel situation at an earlier point of imbibition time. It also indicates that inertial imbibition and the viscous imbibition model enable one solve the Bosanquet imbibition at the initial stage and later imbibition during some specific cases, but the permeability and viscous flow dominate at the later bulk volume imbibition stage. In addition, Bosanquet takes care of transitions between the inertial model and the L-W model due to including both effects in its expression. Thus, when the whole imbibition process needs to be characterised, the Bosanquet would be the optimal choice if the complex network structure is well characterized and the computational model available.