Computers and Chemical Engineering 33 (2009) 1427–1437 Contents lists available at ScienceDirect Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng Modelling of forward roll coating flows with a deformable roll: Application to non-Newtonian industrial coating formulations H.A. Lécuyer a , J.P. Mmbaga b , R.E. Hayes b,∗ , F.H. Bertrand a,∗∗ , P.A. Tanguy a a Department of Chemical Engineering, Ecole Polytechnique de Montréal, Montréal, Québec, Canada H3T 1J7 b Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G6 article info Article history: Received 18 December 2008 Accepted 10 April 2009 Available online 21 April 2009 Keywords: Roll coating flows Elastic deformation Finite element method Free surface Newtonian fluid Non-Newtonian fluid abstract This paper describes the development of a model of the application nip of a forward roll coater and its use to investigate the hydrodynamics of non-Newtonian industrial coating formulations. The focus of the work is on the simulation of the roll deformation and its relationship with the hydrodynamics in the nip. The free surface movement of the fluid domain is included in the model, and is coupled to the deformation of the elastomer-covered roll for the case of a negative gap. An iterative approach is used, whereby the free surface movement is adjusted according to the normal velocity component along the boundary. The governing equations are solved with the finite element method and adaptive re-meshing of the domain between iterations. The elastomer deformation is modeled using a two-dimensional approach, where the elastomer/liquid interface is updated using the force balance at the surface. The solid and fluid problems are solved in a de-coupled manner, in which each problem is solved separately and alternately until final overall convergence is obtained. A comparison with recently obtained data shows a close match between experiment and simulation. Finally, the methodology is applied to investigate the effect on the pressure profile of the properties of non-Newtonian Kaolin-latex coating formulations and roll speeds typical of those in the industry. The results show that the proposed model can help gain insight into the mechanisms that govern this type of coating process. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction The production of high quality paper often involves a coating process, which is carried out to improve optical and mechanical properties such as smoothness, brightness, gloss, and opacity, as well as to reduce ink absorption during printing. In paper coat- ing, the base paper sheet is coated with an aqueous concentrated suspension of pigments, called the coating colour. Many types of coating processes are used, with the metered size press (MSP) being a technology that is growing in popularity, in part because of some perceived advantages over, for example, blade coating. The MSP is an example of roll coating, which in general uses a pair of counter- rotating rolls to perform the coating operation. They may operate in a flooded regime, where the incoming film thickness exceeds the minimum clearance between the rolls, or in a starved regime where the thickness of the incoming film is either equal to or less than the ∗ Corresponding author. ∗∗ Corresponding author at: Department of Chemical Engineering, Ecole Polytech- nique de Montréal, P.O. Box 6079, Station Centre-ville, Montréal, Québec, Canada H3C 3A7. Tel.: +1 514 340 4711; fax: +1 514 340 4105. E-mail address: francois.bertrand@polymtl.ca (F.H. Bertrand). minimum clearance. The roll surfaces may be either rigid or cov- ered with a thin deformable elastomer. Fig. 1 shows a schematic of an MSP. The MSP consists of a metering rod, a transfer roll and an application roll. As seen in the figure, the coating colour is first pre-metered onto the transfer roll using the metering rod, which is a small diameter rod that rotates in the same direction as the transfer roll (co-rotating). The space between the metering rod and the transfer roll is referred to as the metering nip. The transfer roll then carries the pre-metered layer of fluid to the application nip, which is defined as the space between the transfer roll and the backing roll (also called the application roll). The backing roll brings the paper to be coated to the application nip. The backing roll is usually rigid, being made from chromium plated stainless steel. The transfer roll is usually covered with a soft deformable elastomer to reduce the risk of clashing that would exist if two hard rolls were used. It also allows the achievement of thinner coated layers and may reduce or delay the formation of process instabilities (Carvahlo, 1996). A deformable cover also allows oper- ation with a negative gap, which occurs when the centre-to-centre spacing of the two rolls is less than the sum of the two roll radii. Operation with a negative gap is standard for the MSP. Because a negative gap is used, the MSP operates with a flooded application nip, where a bank of coating colour builds up at the inlet to the 0098-1354/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2009.04.001