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.