Pemodelan Matematika untuk Proses Pengeringan Lapisan Cat

Abstract

The drying process of paint layers is a crucial phenomenon in the coating industry as it significantly affects the final quality and durability of the product. One notable phenomenon observed during this process is the change in surface topography caused by uneven solvent evaporation and variations in surface tension. This study aims to develop a mathematical model that describes the dynamics of layer thickness and solvent distribution during the drying process. The model is constructed based on lubrication theory with a two-component approach, consisting of resin and solvent, and incorporates the principles of mass conservation and the Navier-Stokes equations. Through the formulation of the basic system, boundary conditions, nondimensionalization, and asymptotic analysis under thin-film assumptions, a leading-order model system is derived in the form of two nonlinear evolution equations representing the total flux and solvent flux. The results demonstrate that surface tension, pressure gradients, viscosity, and diffusion play significant roles in the drying dynamics of paint layers.