Modeling Moisture Distribution and Binder Migration in Drying Paper Coatings, 1995 Coating Conference Proceedings

S. X. Pan

H. T. Davis

L. E. Scriven

University of Minnesota

By setting up and solving equations that describe the pore level physics of meniscus action, water flow, vapor diffusion, binder transport and deposition, we examined how the combined actions of these mechanisms affect the pattern of drying and the distribution of binder in a simulated paper coating. The consolidated coating was modeled as a six-coordinated, rigid, non-swellable, three-dimensional network of 1000 (10x10x10) pore bodies and interconnecting pore passages. The throat diameters of the passages were randomly drawn from a representative Rayleigh distribution. The pore space was initially filled with an aqueous solution of a single non-volatile binder. The drying rate was varied from 0.1 to 1000 kg/m 2 -hr and binder diffusivity from l0 6 to 10-1 5 m 2 /s. These much broader ranges than those encountered in practice were chosen so that effects of diffusion and convection could be easily distinguished and examined relatively independently. The results indicate that ordinarily pore bodies basically empty in the order of their size and accessibility to the gas phase. Only at extremely high drying rates is there a tendency for pores to dry out exclusively from the top surface down into the coating. A capillary number is defined for drying paper coatings that characterizes the competition between the pressure resultant of surface tension in curved menisci, which drives liquid flow, and the viscous resistance to that flow. Binder tends to deposit at evaporating menisci where they pause; but the higher the binder’s mobility, the more it tends to concentrate within connected liquid clusters of pores before it deposits. A Peclet number for binder transport is defined that characterizes the competition between convection toward evaporating menisci and diffusion away from them. Whereas some of the results confirm previous computer simulations, others refute inferences about binder distribution that were drawn earlier.