The ribbing instability of forward roll coating is analyzed numerically by linear stability theory. The velocity ratio of two rolls is fixed to be 1/4 for practical surface coating processes. The base flows through the gap between two rolls are solved by use of powerful CFD-RC software package. A numerical program is developed to solve the ribbing instability for the package is not capable of solving the eigenvalue problem of ribbing instability. The effects of the gap between two rolls, flow viscosity, surface tension and average roll velocity on ribbing are investigated. The criterion of ribbing instability is measured in terms of critical capillary number and critical wave number. The results show that the surface coating becomes stable as the gap increases or as the flow viscosity decreases and that the surface coating is more stable to the ribbing of a higher wave number than to the ribbing of a lower wave number. The effect of average roll velocity is not determinant to the ribbing instability. There are optimum and dangerous velocities for each setup of rolling process.
