Richard R. Eley

Numerical Modelling of Liquid Withdrawal from Gravure Cavities in Coating Operations

A numerical model is presented for the simulation of cell emptying behaviour when an engraved roller is used to transfer a liquid coating onto a moving substrate. The three-dimensional unsteady liquid motion is calculated where the flow domain is bounded above by a stress-free surface and bounded below by a moving substrate with a complex pattern of indentations. The physical model is simplified through use of the long-wave or lubrication approximation appropriate to flow in thin liquid layers. Specific predictions are made for particular cells and patterns. Cell size is found to be the principal determinant of emptying behaviour with larger cells emptying more completely. Modelling is currently restricted to the flow domain beneath the receding meniscus and drainage due to gravity. There are limitations on the dimensionless measures of coating speed. It is found that both surface tension and cell orientation are also significant in controlling the rate of drainage. Both Newtonian and shear-thinning flows are considered.

Interaction of rheology, geometry, and process in coating flow

A final coating of uniform thickness implies good leveling and the avoidance of defects during film formation. Though generally desired, this objective is often unmet. The outcome of a coating process depends on the nonlinear interaction of the rheology, process variables, and substrate geometry. Understanding the role of rheology is complicated by difficulties in linking fundamental rheological properties with coating performance. During a coating process, forces of varying type, magnitude and duration act on the fluid film. For non-Newtonian coatings the viscosity varies with both time and position within the coating layer, making predictions of flow behavior quite difficult. One answer is computer simulation, using numerical techniques to solve a set of nonlinear differential equations governing the flow. The rheological and other physical properties are parameter values for the program.We present results of mathematical modeling and numerical simulation of a coating imperfection known as a “dripmark.” The model includes non-Newtonian rheology, substrate shape, surface tension, and gravity. We compare theoretical prediction with experimental observation in a study of two architectural paints. We also describe a new method of quantitatively measuring the surface profile of a coating defect.

Flow of architectural coatings on complex surfaces; theory and experiment

A mathematical model is developed to predict the three-dimensional time-dependent flow of a non-Newtonian shear-thinning liquid coating on a non-planar substrate. The model employs the lubrication approximation and other simplifications. Results are compared with experimental observation of the drainage flow out of an axisymmetric indentation in a vertical substrate. A straightforward experimental method is developed to capture quantitative measurements of the evolving free-surface shapes. Two different architectural paints are used. The agreement between theory and experiment is good overall; however, agreement is better for one of the paints, presumably due to inadequate rheological modeling of the other. Improved understanding of the coating flow of these liquids can be expected to lead to improved products and processes.

RHEOLOGY AND COATING FLOWSa

Heraclitus ( 1 ) proclaimed “παντα ϱɛι” (everything flows), and Deborah accurately prophesied that even “mountains flow before the Lord” ( 2 ), suggesting the pervasive nature of flow phenomena in natural processes. Not only do apparently solid mountains flow, resulting in the synclines and anticlines of geologic strata, but so also must the fluids vital to the functioning of a living body, and the viscoelastic properties of blood, mucus, synovial (joint) fluid b and the vitreous humor of the eye c are important for their proper function. Among man-made materials, flow behavior, often complex, can be a crucial element of commercial success. Paints and industrial coatings, creams and lotions, inks, adhesives, ceramic slips, solder pastes, foods, medicines, etc. , are examples of the range of materials whose commercial viability depends on having the “right” rheology. In turn, the required rheological properties must be defined with due regard to the flow or stress conditions which prevail during processing and application.