Simulation of the consolidation of paper coating structures: probabilistic versus deterministic models

Two categories of mathematical models were compared for the simulation of consolidation of paper coating structures, that is for the packing of pigments on a paper substrate under dewatering conditions. The first category uses probabilistic methods, relying on a random number generator to either determine the initial position of the pigments or their motion. The second category uses deterministic methods based on force balances. In this work, two probabilistic models and two deterministic models are described and their respective advantages and drawbacks are critically reviewed. Simulation results obtained using three of these methods are compared for the case of monodisperse and bidisperse spherical suspensions. Porosity calculations of the numerical packings obtained with the (deterministic) discrete element method (DEM) and two probabilistic methods, the Monte-Carlo (MCD) and the steepest descent (SDD) deposition methods, are compared with experimental data from the literature. These calculations reveal significant differences in the pore volume obtained with these three models. An analysis based on the bridging and relaxation phenomena that prevail in the flow of such particulate systems provide an explanation for these differences and show the strong potential of the discrete element method. The choice of the simulation method depends on the objective of the simulations. DEM will provide more accurate predictions of macroscopic quantities such as the porosity or the roughness, but requires very long computational times. MCD or SDD will only provide qualitative trends, but is computationally far less intense. A combination of strategies might be appropriate, using MCD (or SDD) to provide guidelines and DEM to enhance the results predicted by MCD. (C) 2004 Elsevier Ltd. All fights reserved.