Visualization study of liquid surface stability for full reverse 3-roll coater with rigid gravure roll

Roll coating systems are widely used to coat a thin liquid layer on a moving substrate, and many publications discussing forward roll coating systems and reverse gap control coating systems are available. Recently, thinner and more uniform layers are required for use with the high-performance solutions involved. Moreover, high line speed coating is also required in order to reduce manufacturing costs. A reverse gravure roll system can coat a thin layer film at high line speed more easily than a flat roll coating system because only the liquid that enters the gravure cell is transferred to the next roll or substrate. However, the existence of the gravure cell complicates the flow between the rolls. To our knowledge, no systematic study in the literature has explored this condition in depth. In the present study, the flow between a reverse deformable roll and a solid stainless steel gravure roll is visualized in order to determine how the uniformity of coating in the high roll speed region is affected by operating parameters, that is, the speed ratio between the rolls and the properties of the coating liquid. The range for coating uniformity is compared with the case of a gap control system. The results show that the stable region can be extended by using the reverse gravure roll system.     

Process limits in two-layer reverse roll transfer

Reverse roll coating in which a thin single layer of liquid is applied onto a substrate has been used in industry for decades and has been extensively analyzed in the literature. Modern coatings, however, are often composed of more than one layer to improve the product performance and to reduce the manufacturing cost. Premetered methods such as slot, slide, and curtain coatings are typically used to produce such multilayer coatings. If the caliper of the substrate to be coated is not constant, then the coating gap and consequently the final film thickness deposited on the web will also be nonuniform. In this study, we focused on the use of reverse roll technique with slot die liquid delivery system to produce a uniform thin two-layer coating. The use of this coating technique to produce such a coating has not been previously explored. The liquid film surface as it is transferred from a rigid steel roll to a deformable urethane-covered roll was visualized to find out how the uniformity of the two-layer coating is affected by the speed ratio between two rolls, layers’ wet thicknesses, and liquid viscosities. The effect of these parameters on the ribbing frequency and amplitude was also investigated. The results show that in the two-layer coating, as in the single layer reverse transfer, there is a critical web speed above which ribbing occurs. The critical speed is determined by the bottom layer viscosity.     

Free coating of viscous and viscoelastic liquids onto a partially submerged rotating roll

Experiments are performed on the dynamics of formation of a liquid coating picked up by a cylindrical roll rotating partially submerged in a free bath. Data on coating thickness for Newtonian fluids are found to correlate according to T = H(ρg/μU)^1/2 = 0.56 for fluids whose viscosities range from 0.11 to 33 poise. Data for strongly non-Newtonian and Viscoelastic fluids (polyacrylamide solutions) can be forced to fit this correlation by defining an “equivalent coating viscosity.” It is clear that this defines a pseudo viscosity, because the “equivalent coating viscosity” is observed to increase with increasing roll speed. This suggests that strongly Viscoelastic fluids respond to the rapid deformation suddenly imposed in the dynamic meniscus near the pickup point in a distinctly elastic manner that alters the flow through the meniscus.     

Fluid absorption during forward roll coating of porous webs

Forward roll coating is a common process to deposit thin liquid films onto a continuous web. When the web is porous, some amount of the fluid is forced into the web in the nip. This removal of fluid, along with the deformation of the backing material, influences transfer in the nip as well as operational issues such as misting and coating defects. While much has been reported on forward roll coating for non-porous webs, little has been done when the web is porous.A laboratory roll coating device is used to characterize the pressure profile, the rubber deformation, and the film thickness as the fluid is in contact with a porous web. A pressure transducer is used to record the pressure profile in the nip. The film thickness on the steel roll surface and the gap between the rolls are measured with capacitance probes. Silicone oils, with three different viscosities, are used as test fluids. Three different papers are used in these tests. A model is proposed to describe the pressure profile, rubber deformation, and absorption in a forward roll coating device. The differential equations are solved to describe the nip behavior. A simplified model is also proposed, using an average nip pressure and Darcy's law, to predict penetration in the nip. The proposed models compare well with the experimental results and predict the dependence on viscosity, nip load, and paper permeability. The experimental results with low viscosity fluids show some speed dependence that is not captured by the model, but the high viscosity fluid behavior agrees well with model predictions.     

A torque-based analysis of the reverse roll coating process

In a laboratory film coater operated at industrial speed, the torque exerted by the metering rod was used to investigate the hydrodynamics in the metering nip flow. CFD simulations were also performed taking into account the deformation of the roll cover to depict the elastohydrodynamics of the metering nip flow. From the experiments, it was found that the torque increases with transfer speed, load and viscosity. When runnability problems such as spitting were observed, the torque signal decreased. Torque measurements could also predict excessive friction between rod and roll, which may damage the elastic cover. The numerical simulations showed trends similar to the experiments. Regions of positive and negative torque values demonstrated how the fluid interacts with the rod, a phenomenon apparently related to the occurrence of secondary flows in the metering nip. Finally, the numerical results also showed that the minimum nip gap becomes constant at high loads.     

Rheology and roll coating dynamics of metallic basecoats for automotive pre-coated metal sheet

Rheological behavior and coating dynamics of solvent-based metallic basecoats using 3-roll coaters were investigated for the application process based on pre-coated metal (PCM) sheet technology that can promisingly diminish the environmental pollutants in automotive OEM line. Rheological properties of the metallic basecoats related to optical appearance and color variations were measured by altering the content of aluminum (Al) flake and temperature of the coating solution. The results showed that the basecoats exhibited a very weak shear-thinning behavior regardless of Al flake contents in this study. However, their elastic behaviors were intensified with increasing the Al flake content. From the 3-roll coating experiments with forward and reverse coating modes, the operability windows in the coating process, demarcating the uniform coating flow from defects, were established. In particular, it was possible to elucidate the relationship between the capillary number and speed ratio conditions for the desired coating thickness in roll coating systems accompanied with reverse coating mode between the pick-up and metering rolls. It was verified from the cross-sectional images of coating layers that most of Al flakes inside the basecoat layer were oriented parallel to the coating surface under the continuous roll coating flows.     

Experimental study of film thickness and free surface velocity around a rotating roll for non-newtonian fluids

Measurements are performed on film thickness and free surface velocity around a rotating roll for Newtonian, non-Newtonian inelastic, and viscoelastic fluids by using noncontact methods of a capacitance probe and a laser Doppler velocimeter probe. The film thickness decreases with increasing inspection angle for Newtonian fluids. For non-Newtonian fluids, it retains an approximately constant value, owing to shear-thinning of viscosity, except for a meniscus region development, which is dependent on fluid elasticity. Comparison of current results with the film thickness from a previous work is also made. With the increment of inspection angle, the free surface velocity increases rapidly in the meniscus region and maintains a constant value almost equal to a roll speed in the other region for viscoelastic fluids, while it increases linearly for Newtonian fluids. The shear rate at a roll surface is presented assuming that the velocity distribution in the liquid film is a polynomial equation. It is found that viscoelastic fluids exhibit different behavior from that of Newtonian and non-Newtonian inelastic fluids. Evaluation of the force acting on the liquid film for Newtonian fluids implies that the velocity gradient at a roll surface in an ascending region may be steeper than the parabolic form assumed in this study.     

Effects of shear thinning on forward roll coating

This paper described the forward mode roll coating process of generalised non-Newtonian fluids characterised by the Ellis model. The fluid in the coating bead and the free surface formation are described by the lubrication approximation and the stability is also considered using a perturbation analysis of the downstream meniscus. Results highlight the complex behaviour of this coating process and volume flow rate and film thickness results are obtained for a range of operating conditions. The stability of the downstream meniscus is observed to improve with increasing level of shear thinning when τ_1/2 (the shear stress at which the viscosity is half that of the zero shear stress viscosity) is small, however as τ_1/2 increases the meniscus stability decreases with increasing levels of shear thinning.     

Analytical prediction of roll coating with counter-rotating deformable rolls

Roll coating is a common technique for applying thin coating films on continuous substrates, e.g., papers and foils. Key advantages are the comparatively simple technology and the possibility of coating thin films using highly viscous fluids. Since roll coating is a self-metered process, the prediction of film thicknesses is of fundamental interest for industrial process control. In the present work, a new analytical approach for the prediction of the film thickness in roll coating with deformable rolls and negative gaps is developed. This method is based on the fluid dynamic theory of lubrication approximation. The film thickness is calculated depending on the geometry of the rolls (including the elasticity of the rubber), the fluid properties of the applied film and the roll velocities. This is gained by using boundary conditions for pressure and—in contrast to former literature—for force. The quality of the predicted results is validated with experimental data from literature. The comparison shows good agreement and thus the derived analytical model offers new possibilities for predicting film thickness and understanding of the associated influence parameters.     

The coating of newtonian liquids onto a rotating roll

The liquid flux picked up by a rotating roll which is partially submerged in a Newtonian liquid, and the variation of the film thickness around the per     

Coating with deformable rolls: An experimental investigation of the ribbing instability

Results from a systematic experimental investigation of deformable roll coating, operating in forward mode, are presented, with particular emphasis as to how the governing parameters of the coater (peripheral roll speed and gap setting) and the physical properties of the associated deformable roll covering (thickness, hardness and material type) influence the onset of the ribbing instability. It is found that for positive gap settings, the critical roll speed at which ribs are first observed can be increased by employing a larger gap or using a thicker covering of compliant material. For negative gap settings, explored here for the first time, ribbing is observed to be ever present over the operating range considered. However, for large negative gaps, a reduction in roll speed and the use of a thinner compliant covering are all found to produce ribs of shorter wavelength.     

A two-scale model for discrete cell gravure roll coating

A two-dimensional model for predicting the fluid pickout and coated film thickness characteristics of a discrete cell direct gravure roll coater operating in reverse mode is derived. A novel multiscale approach is adopted for this purpose and the resulting equations solved numerically for inertia-less flow conditions. A system of stiff ordinary differential equations is found to be sufficient to capture the major gross flow features, while at the cell level the analysis is based on a finite element solution of the momentum and continuity equations. It represents the first such predictive model of its kind, with particular interest placed on the nature of both the pressure distribution and web-to-roll gap profile spanning the coating bead. The effect of key operating parameters, web-to-roll speed ratio, web-tension, wrap-angle, capillary number and cell-geometry, on the degree of fluid pickout from gravure cells and the coated film thickness is explored. Although an idealised model, the trends observed show qualitative agreement with existing experimental data collected on a small-scale gravure coating rig and point the way forward to the eventual formulation of a full three-dimensional predictive model of the process.     

The coating of Newtonian liquids onto a roll rotating at low speeds

A theoretical treatment is presented for the prediction of the rate at which a liquid is entrained by a roll which is rotating partially submerged in a Newtonian liquid, and also for the prediction of the variation in the thickness of the film around the roll. The method involves the integration of the momentum equation after neglecting inertia forces in the dynamic meniscus region and the matching of the surface curvature with that derived for the static meniscus region near the liquid surface. The resulting equation allows the prediction of the relationship between a dimensionless film thickness parameter, T, and the capillary number, Ca, as a function of the radius of the roll, the withdrawal angle and the position of the roll periphery. The liquid flux on the roll can also be predicted.     

机械密封覆层密封环端面性能分析

机械密封覆层密封环能够综合利用耐磨覆层与韧性基体材料的优良特性,但其应用主要依靠经验,缺乏针对其性能的研究。利用ANSYS软件建立釜用机械密封动环、静环和静环座组成的热-结构耦合模型,综合考虑覆层端面变形、液膜反压和密封环温度之间的相互作用,并试验验证了分析模型的正确性。分析覆层结构和材料组合对密封端面最大端面比压与速度的乘积（P_bV）_max、最高端面温度T_max,覆层表面最大拉应力σ_max、主界面最大切应力τ_max、侧界面最大切应力σ_cmax和最大法向拉应力τ_cmax的影响,并确定最佳的覆层结构和材料组合。分析结果表明：覆层厚度、覆层与基体的热膨胀系数比和弹性模量比的变化主要影响覆层表面最大拉应力;覆层端面设计中,覆层厚度取值宜在0.4～0.6 mm,喷涂角度宜取15°～30°,覆层与基体的热膨胀系数比宜在0.5以上,弹性模量比宜在2.5以下。     

The effect of polymer additives on the performance of a two-roll coater

The effect of polymer additives on the performance of a two-roll coater has been examined experimentally. The coater consists of a rigid steel roll and a deformable roll with polyurethane surface. Newtonian coating solutions and solutions with polymer additives were used as test fluids. Both forward and reverse coating operations were studied. It was found that for the forward coating operation, the shear-thinning behavior of the polymer solutions can reduce the coating thickness, but the fluid elasticity can increase the coating thickness significantly and can also destabilize the coating flow. For the reverse coating operation, a small amount of polymer additives can effectively increase the wipe ratio.     

Response of slot coating flows to periodic disturbances

Slot coating is a common method in the manufacture of a wide variety of products. It belongs to a class of coating method known as premetered coating: in a steady-state operation, the thickness of the coated liquid layer is set by the flow rate fed to the die and the speed of the substrate moving past, and is independent of other process variables. Thus premetered methods are ideal for high precision coating. However, even the best designed slot coating operations are subjected to small oscillations on the process conditions, such as flow rate, vacuum pressure and gap fluctuations. These oscillation may lead to unacceptable variation on the thickness of the deposited liquid layer. The effect of process condition disturbances on the coated layer has to be minimized to assure a wet thickness as uniform as possible.The effect of an imposed periodic perturbation on the liquid flow rate or on the gap clearance in the coated layer thickness is explored in this work by computer-aided analysis. The amplitude of the thickness variation is determined at different process conditions and die configurations by solving the transient, two-dimensional, viscous free surface liquid flow in the coating bead. The system of equations, with appropriate boundary conditions, was solved by the Galerkin/finite element method, and an implicit time integration. The results show the response as a function of the imposed perturbation frequency and of the die geometry. They indicate that the die geometry may be optimized in order to minimize the film thickness oscillation of a slot coating operation.     

Stability of viscoelastic liquid curtain

Thin liquid sheets occur in several practical applications. In curtain coating, a thin liquid sheet is formed and falls freely over a considerable height before it impinges onto a moving substrate. Precision curtain coating was developed for multi layer photographic films but its use has expanded to many different applications. One of the important limits of this process is the stability of the liquid curtain, which may define the minimal thickness that can be coated at a given web speed.The condition at which a low viscosity Newtonian liquid curtain breaks was first derived based on a simple balance between inertial and capillary forces. There is a critical flow rate below which the curtain becomes unstable. For viscoelastic liquids, the normal stress related to the stretching of polymer molecules as the liquid accelerates down the curtain changes the force balance. Here, the critical condition at which a viscoelastic liquid curtain breaks was determined as a function of the rheological properties of the liquid. The results show that high extensional viscosity liquids create more stable curtains. Liquid additives could be used to push the limits of curtain flow rates to smaller values and consequently to widen the operability window of the process.     

A theory of roll coating of viscous and viscoelastic fluids

A theory for roll coating of a fluid onto a moving sheet is developed utilizing the usual “lubrication approximations.” The effects of fluid and operating parameters on coating thickness and pressure distribution are determined for a Newtonian fluid, and for a purely viscous non-Newtonian fluid obeying the Power Law. The results for these cases are obtained analytically, and are rather straightforward. A viscoelastic fluid is considered, of a type which shows typical non-Newtonian shear behavior observed in polymer melts and solutions and which also exhibits normal stress behavior. Analytical solutions are not possible, but a perturbation method, using a viscoelastic perturbation parameter related to a Deborah number, yields an approximate solution. Only terms to first order in the perturbation parameter are given. Subject to that degree of approximation, the following conclusions are drawn:

• 1 Non-Newtonian shear behavior reduces the pressure distribution, and increases the coating thickness.
• 1 Elasticity of the type usually observed in polymer solutions makes only a minor contribution to the roll-separating (load-carrying) force. The contribution is positive, but smaller than the corresponding negative contribution due to the non-Newtonian shear effects.
• 1 An increase in load-carrying capacity would require a different viscoelastic fluid than the type considered here—one that is essentially Newtonian in shear but, independently, capable of developing significant normal stresses.

     

A theoretical and experimental investigation of tri-helical gravure roll coating

Tri-helical, gravure roll coating, operated in reverse mode, is investigated via a complementary experimental and theoretical approach. Flow visualisation reveals the underlying flow structure within the roll-to-web transfer region and highlights when loss of stability, that is a propensity to streaking, occurs. The latter is found to be influenced in turn by the depth of the tri-helical grooves and the capillary number. Experiments show that as the web-to-roll speed ratio is increased, so too is fluid pick-out from the grooves, although the coated film thickness may decrease. Extensive data are provided for coated film thickness, pick-out and meniscus location as a function of speed ratio, for different operating parameters. A key feature of the present investigation is the formulation of a novel complementary mathematical model for the process. The base flow within the grooves is modelled as a Poisson equation in conjunction with simplified approximations for the attendant free-surface boundary conditions. The resultant equation set is written in terms of finite Fourier sine transforms and unique solutions obtained by varying the flux until a consistent pressure distribution throughout the coating bead is obtained. Results from the model are found to be in generally good agreement with their experimental counter-parts, and are seen to predict and capture all the major features of the process over the operating range explored.     

A model for roll waves in gas-liquid flow

A liquid film flowing co-currently with a high speed gas flow often consists of a slow moving base film containing a sequence of flow surges or roll waves. Experiments have been conducted to determine the profiles of height, wall shear stress and gas pressure for individual roll waves. On the basis of these measurements a physical interpretation of roll waves is given and a mathematical model is developed. The average properties of the liquid film are given by summing the contributions from the roll waves and from the base film.