* Corresponding author. Tel.: #1-514-340-4040; fax: #1-514-340- 4105. E-mail address: bertrand@urpei.polymtl.ca (F. Bertrand). Chemical Engineering Science 55 (2000) 4857}4867 Shear-induced particle migration in a short-dwell coater J.-B. Ritz, F. Bertrand*, F. Thibault, P. A. Tanguy URPEI-Paprican Chair, Department of Chemical Engineering, Ecole Polytechnique, P.O. Box 6079, Station Centre-ville, Montreal, QC, Canada HC3 3A7 Received 16 July 1999; accepted 14 February 2000 Abstract This paper aims at simulating the #ow of a pigment suspension in a short-dwell coater (SDTA), a common device used for the production of value-added paper. The process consists of depositing onto a paper web a thin coating layer, the uniformity and the quality of which depend on the short-dwell coater geometry and the coating color rheology. In order to understand the possible interactions between the hydrodynamics in the pond and the rheological behavior of the suspension, this study focuses on a phenomenon known as shear-induced particle migration, which may result in an non-homogeneous suspension. For this purpose, a numerical methodology based on a shear-induced particle migration model (Sim) and the "nite element method is presented and validated against analytical results and experimental data. This numerical approach constitutes the "rst step towards a better understanding of the hydrodynamic mechanisms that govern particle migration in a short-dwell paper coater. In this work, a parametric study of the suspension #ow behavior is carried out via the introduction of a new dimensionless number that characterizes the importance of the shear-induced migration with respect to particle convection. The proposed model is used to generate particle distribution templates. It is shown that the particle size and Reynolds number are preponderant factors that a!ect the extent at which migration occurs in the short-dwell coater. In particular, it is shown that increasing the Reynolds number ampli"es the migration phenomena and the formation of high concentration zones within a ring located in a vortex just before the nip. Such a concentration overshoot may then be dragged into the nip, resulting in runnability problems such as web breaks or coating color spitting.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Particle; Hydrodynamics; Processing; Short-dwell coater; Shear-induced particle migration; Mathematical modeling 1. Introduction The main purpose of the paper coating operation is to improve the optical properties and printability of a paper sheet by applying onto it a thin layer of a white pigment suspension called the coating color. The main challenge is to obtain a uniform and smooth coating layer, free of defects, a task that becomes more and more di$cult as the web speed and the solids content in the formulation are increased. In fact, runnability problems may appear during the process leading to a deleterious e!ect on the "nal properties of the coating "lm. Streaks on the paper, web breaks and coating color spitting are typical run- nability problems that may be triggered when speed is increased too much. From a hydrodynamical point of view, many researchers have studied the instabilities in a short-dwell coater and shown that these can be at the origin of runnability problems (Trianta"llopoulos & Aidun, 1990; Aidun, 1991). For instance, the transition between two-dimensional steady-state vortices to three- dimensional unsteady-state patterns has been related to the formation of streaks. Another problem, which has received only scant attention so far, is that of the relation- ship between hydrodynamics and the homogeneity of the suspension in the pond as well as the impact of the particle distribution on the overall process and the quality of the "nal product. We believe a better under- standing of the particle migration phenomena may help choose the best process design and coating color formu- lation to achieve high-quality coated papers. In other words, we are interested in determining how the hydro- dynamics prevailing in the short-dwell pond impact on the particle migration and the microstructure of the sus- pension. In particular, we want to assess whether par- ticles under the action of shear and transport migrate to segregated regions, which leads to inhomogeneities in the pond. One important issue is then to determine whether 0009-2509/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 1 0 6 - 8