Simulation of coating -visco-elastic liquid in the Micro-nip of metering size press
For a set of operating conditions and coating color formulations, undesirable phenomena like color spitting and coating ribs may be triggered in the Micro-nip during the coating process. Therefore, our interest in this work focus on another parameter affect on the undesirable phenomena as the vortices in the Micro-nip. The problem deals with the flow through the Micro-nip of metering size press. The flow enters and exits at a tangential velocity of 20 m/s between two rollers with diameter 80 cm and 60 mum apart. In the upper and bottom part of the domain the angular velocity is 314 rad /s. It has one sub-domain. Previous studies focus on the Micro-nip without considering the inertia and the viscoelasticity of the material. Roll coating is a technique commonly used in the coating industry to meter a thin fluid film on a moving substrate. During the film formation, the fluid is subjected to very high shear and extensional rates over a very short period of time. The fluid domain changes as a function of the hydrodynamic pressure within the nip as a result of the deformable cover usually used on one of the rolls. The free surface also adds more complexity to the flow due to the force equilibrium in the fluid gas interface. Last of all, the rheological behavior of the coating fluid is usually non-Newtonian, so the metering flow hydrodynamics is finally very difficult to describe. It is concluded that the normal forces of micro-nip increases with increasing the inhibitors. Therefore, it affects on the smoothness and creates defects. On the other hand, it can be concluded that the creation of big vortex in the middle of micro-nip affects on the coating liquid behavior.
Mathematical models for coating processes
The flow is considered of a Newtonian fluid, of viscosity η and surface tension T, in the narrow gap between a pair of rollers of radii R1 and R2, whose peripheral speeds are constant and equal to U1 and U2 respectively. The objective is to determine the coating thickness h1∞ on the upper roller as a function of the non-dimensional parameters H0/R, ηU/T and U1/U2, where H0 is the minimum gap thickness, U = ½(U1 + U2), and 2R−1 = R1−1 + R2−1. Using lubrication theory to provide an adequate description of the fluid flow, two mathematical models are derived whose essential difference lies in the specification of the boundary conditions. In the separation model it is assumed that the pressure distribution will terminate at a position which is both a stagnation point and a point of separation, whereas the Reynolds model incorporates the classical Reynolds conditions. In each case, theoretical predictions for the non-dimensional coating thickness, h1∞/H0 as a function of U1/U2 are found to compare well with experiment. However, theory does suggest that the two models are applicable to different and complementary regions of parameter space, and hence together they may form a basis for further investigations into the various features of coating processes.
Film-splitting flows in forward roll coating
A model based on the lubrication approximation is put forward for the general case of asymmetric forward roll coating of Newtonian liquids. Two more-rigorous theories are developed, one based on asymptotic expansions for small ratios of gap-to-roll diameter (H0/R), the second on Galerkin/finite-element solutions of the full Navier–Stokes equations over the relevant flow domain. The lubrication model is useful only as an approximation at high capillary numbers $(Ca\equiv \mu\overline{V}/\sigma) $. The asymptotic analysis is accurate when H0/R < 0.001 and Ca > 0.1. The ratio of the film thicknesses on the two rolls is predicted to equal the speed ratio to the 0.65 power, which is confirmed experimentally. The Galerkin/finite-element solutions give full details of the steady two-dimensional free-surface flows including complex recirculation patterns in the film-splitting region, and show how the film-splitting stagnation line becomes a static contact line in the limit as one roll surface becomes stationary.