A two-dimensional model of the pressing section of a paper machine including dynamic capillary effects

Paper production is a problem with significant importance for society; it is also a challenging topic for scientific investigation. This study is concerned with the simulation of the pressing section of a paper machine. A two-dimensional model is developed to account for the water flow within the pressing zone. A Richards-type equation is used to describe the flow in the unsaturated zone. The dynamic capillary pressure-saturation relation is adopted for the paper production process. The mathematical model accounts for the coexistence of saturated and unsaturated zones in a multilayer computational domain. The discretization is performed by the MPFA-O method. Numerical experiments are carried out for parameters that are typical of the production process. The static and dynamic capillary pressure-saturation relations are tested to evaluate the influence of the dynamic capillary effect.