Reverse Roll Research Articles

Mathematical analysis of isothermal study of reverse roll coating using Micropolar fluid

This article demonstrates a mathematical model and theoretical analysis of the Micropolar fluid in the reverse roll coating process. It is important because micropolar fluids account for the microstructure and microrotation of particles within the fluid. These characteristics are significant for accurately describing the behavior of complex fluids such as polymer solutions, biological fluids, and colloidal suspensions. First, we modeled the flow equations using basic laws of fluid dynamics. The flow equations are made modified using low Reynolds number theory. The simplified equations are solved analytically. The exact expression for velocity and pressure gradient are obtained, while pressure is calculated numerically using Simpson Rule. Graphical depictions are carried out to comprehend the impact of the newly emerged physical constraints. The influence of micropolar and microrotation parameters on the velocity, pressure and pressure gradient are elaborated with the help of different graphs.

Non‐isothermal flow dynamics during reverse roll coating phenomena of non‐Newtonian polymer

AbstractRoll coating plays a major role in industrial coating, including wallpapers, plastic and photographic films, sticky tapes, magnetic recordings, wrapping magazines and books, and so on. The current study proposes a mathematical model for a non‐isothermal, incompressible Sutterby fluid flowing through a narrow gap between two heated, counterrotating rollers. Lubrication approximation theory is used to simplify nondimensional expressions. The perturbation technique provides exact results for velocity profile, temperature, flow rate, and pressure gradient, whereas the numerical technique (Simpson rule) is used to compute the pressure profile and flow rate, respectively. The effects of the involved parameters on various physical characteristics like pressure, flow rate, temperature, pressure gradient, force, and power input are depicted in graphs and tabular form. A mechanism for controlling the coating thickness, power input, flow rate, separation force, and pressure distribution is provided by the material properties involved. With variations to a Sutterby fluid parameter and the velocity ratio K, both the pressure gradient and pressure decrease. It is significant to note that the temperature distribution is controlled by the velocities ratio and Brinkman number. Moreover, the separation point is shifted towards the nip area and the coating thickness on the web reduces with increasing velocities ratio K.

Coating of micropolar fluid during non-isothermal reverse roll coating phenomena

Reverse roll coating is a high-speed coating process used in many applications. The single largest application for reverse roll coating is applying architectural paint to coils of sheet metal; however, in the converting industry reverse roll coating is used for some thermal coatings, adhesives, color laser paper receivers, wax coatings, magnetic coatings, vinyl dispersions for wallcovering, some specialty light sensitive applications, and many specialty products that require a high precision application process. This work presents a mathematical model for the steady flow of non-isothermal, incompressible, micropolar fluid in the metering nip of a reverse roll coater with velocity slip applied at both roll’s surfaces. Lubrication approximation theory (LAT) is utilized to reduce the complexity of the non-dimensional equations. Exact solutions for pressure gradient, velocity, and temperature are achieved. At the same time, numerical techniques (Simpson’s 3/8 rule with Newton Raphson method) are used to compute the pressure distribution, coating thickness, flow rate, and separation points. Effects of coupling number, slip parameter, microrotation, and velocity ratio on velocity, pressure, temperature, and pressure gradient are presented in graphs. It is observed from the current analysis that the intrinsic rotations of the fluid particles prove to be the controlling parameter of the pressure gradient, which significantly varies the coating thickness. Also, as a result of velocity slip, the flow rate declines and the coating thickness reduces as the fluid moves faster along the boundary walls.

Development of technology for complex processing of Jerusalem artichoke

According to global analytical agencies the most promising area of development of the food industry is the enrichment of food products with physiologically functional ingredients – dietary fiber, vitamins, minerals, etc. Analysis of the market for functional ingredients indicates the prospects of organizing the production of domestic inulin and other biologically active components from various anatomical parts herbaceous tuberous plant of the Sunflower genus – Jerusalem artichoke, the distinctive features of which are high yield of tubers, unpretentiousness to cultivation conditions, resistance to diseases and pests. The purpose of the research was to develop a technology for the production of inulin and chlorophyll from Jerusalem artichoke tubers and leaves. The work used generally accepted physical and chemical methods for studying plant objects. The results of the research made it possible to establish optimal technological parameters for the process of extracting inulin from Jerusalem artichoke tubers with a 60% aqueous-alcohol solution. The technology has been proposed for the production of inulin from Jerusalem artichoke tubers, based on the fractionation of a mixture of components with different molecular weights, by passing them through polyamide composite membranes of reverse osmosis roll type. It has been established that the molecular weight of inulin isolated from Jerusalem artichoke tubers of the «Interes» variety is 5.84 kDa. It has been revealed that Jerusalem artichoke leaves contain a and b chlorophyll in amounts of 6.98 and 0.74 mg/g of wet matter. Copper chlorophyll derivatives isolated from Jerusalem artichoke leaves are promising not only as food colorings, but also as biologically active substances with a wide spectrum of action. The target products obtained using the proposed technology – inulin and copper derivatives of chlorophylls – can find wide practical application in the food industry and in public catering.

Backpropagation of Levenberg–Marquardt artificial neural networks for reverse roll coating process in the bath of Sisko fluid

Backpropagation of Levenberg–Marquardt artificial neural networks for reverse roll coating process in the bath of Sisko fluid

Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study

BackgroundThe roll-coating process plays an important role in many industries for its practical applications, such as paint, PVC-coated fabrics and plastic industries. Roll coating is commonly used to put thin coating films over continuous substrates such as foils and papers. There are several roll-to-roll coating methods, including forward and roll over web. However, the reverse roll coating study of the non-Newtonian fluid model is presented in this paper. The constitutive equation for the viscoelastic Carreau fluid model as the non-Newtonian fluid is derived using the momentum and energy equations. To simplify the nonlinear systems of partial differential equations, appropriate non-dimensional parameters are employed to convert them into systems of ordinary differential equations. MethodBy taking the Weissenberg number as a small parameter, a series solution is obtained for considerable quantities like pressure gradient, axial velocity, flow rate, pressure distribution, and temperature distribution using the perturbation method. In contrast, the numeric outcome of some quantities of engineering interest, like flow rate, coating thickness, share stresses, and separation points, are calculated. Streamlines in 2D and 3D are also drawn to observe the flow pattern. To validate the solution, the problem is also solved numerically with the BVP Midrich method. The analysis of the results demonstrates a satisfactory agreement between the analytical and numerical solutions. ResultsThe graphical investigation examines the influence of different fluid parameters on velocity profile, shear stress, pressure profile, temperature profile, and pressure gradient. A comprehensive mechanism behind these outcomes is deliberated. It has been observed that velocity rises on increasing the Weissenberg number; however, velocity decreases in the case of the velocities ratio. Further, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Moreover, the separation point and coating thickness decrease with the velocities ratio increase. The results accuracy is checked against papers that have already been published. The comparison reveals good agreement; therefore, the resultant analytical model gives new ways to forecast film thickness and explain influence parameters. Hence, these factors may help in an efficient coating process and improve the substrate life.

Finite coating thickness of Prandtl fluid in non-isothermal reverse roll coating process

PurposeThe coating process is broadly employed in the manufacturing of wallpapers, adhesive tapes, wrapping, protection of fabrics and metals, X-ray and photographic films, beautification, books and magazines, film foils, magnetic records, coated paper, etc.Design/methodology/approachIn this study, an incompressible flow of non-Newtonian fluid is modeled to inspect the rheological behavior of finite coating thickness in the reverse roll coating process. With the assistance of lubrication approximation theory (LAT), the dimensionless form of governing expressions is simplified. Exact solutions for distributions for velocity, flow rate, temperature and pressure gradient attained utilizing perturbation technique and their variation is presented as well as discussed in graphs. Meanwhile, some important factors from an engineering perspective including coating thickness and transition point were calculated mathematically and are displayed in a tabular manner. Also, streamlines are drawn to observe the flow pattern.FindingsPrandtl fluid parameters provide a controlling factor to regulate the flow rate, velocity, coating thickness, and pressure gradient leading to an efficient coating process. Moreover, the Brinkman number and Prandtl fluid parameters significantly improve the temperature distribution.Originality/valueIn the literature, this study fills a gap in the theoretical prediction of coating thickness rheologically influenced by Prandtl fluid in reverse roll coating process.

Anti-rolling analysis and resistance optimization of a new anti-rolling hydrofoil for the trimaran vessel

The roll motion performance of the trimaran vessel is not as good as expected at low forward speed in high sea conditions. A new designed anti-rolling hydrofoil is proposed, which connects the main hull and the side hull below the waterline to provide the reverse roll moment by the huge hydrodynamic pressure during the roll motion. The anti-rolling effect of four creative schemes of the hydrofoils are analyzed by a set of high-precision numerical calculation method combined with CFD and 3D potential flow theory for roll damping and roll motion in waves. The roll damping characteristics and the mechanism of the hydrofoil are analyzed in detail combined with flow field analysis. The results indicate the high anti-rolling efficiency for the trimaran vessel. In order to make this device close to the engineering application, the profile and angle of attack are optimized to reduce the resistance. Finally, the anti-rolling hydrofoil with a good comprehensive performance is obtained, providing a valuable reference for the seakeeping design of the trimaran vessel.

Perturbation based analytical and numerical solutions of non-Newtonian differential equation during reverse roll coating process under lubrication approximation theory

Reverse roll coating process are utilized for the purpose of applying a coating to a substrate or web by utilising different rollers in order to get the required coated surface. As a result of this, reverse roll coating process have found applications in a wide variety of industries, such as those dealing with food and medicine, electronic components, optical and LCD devices, and optical products. The main objective of this paper is to develop the mathematical formulation for the coating of thin film for an incompressible isothermal viscoelastic fluid between two reversely rotating rolls. Through the use of an appropriate dimensionless parameter, Non-dimensional nonlinear ordinary differential equations (ODEs) are derived from governing partial differential equations (PDEs). LAT (lubrication approximation theory) simplifies the dimensionless equations of fluid motion. The expressions for velocity of flow, pressure gradient and flow rate is obtained analytically by using regular perturbation method, while numeric solution of some mechanical parameters such as power input, coating thickness, roll separation force and separation points are calculated. The numerical validation of the analytical solution of the fundamental model of nonlinear constitutive flow laws is done in the Maple environment using the numeric technique which is based on finite difference method. The influence of numerous non-Newtonian parameters such as velocities ratio and Weissenberg number on velocity profiles, pressure gradient, power input, roll separation force, separation points and coating thickness of a non-Newtonian Johnson–Segalman (JS) fluid are explored via graphically and in tabular form. The outcomes demonstrate that on increasing the Weisenberg number and velocities ratio, the coating thickness on web is decreases. For the numerous values of velocities ratio, it is important to note that separation points shifted towards the nip region. In addition, the non-Newtonain parameter have signifcant impact on power input and roll separating force. The maximum coating thickness that is 1.0927 has been observed at the value of separation poin 0.9620. Hence, these factors may help in an efficient coating process and improve the substrate life.

ENVIRONMENTAL PROBLEMS CAUSED BY THE USE OF REVERSE OSMOSIS MEMBRANE ELEMENTS, AND WAYS TO SOLVE THEM

More than 70 percent of our planet is covered with water. And yet water is a scarce resource, and it is our future. According to the World Wildlife Fund, 1.1 billion people do not have access to it, and 2.7 billion experience a shortage of drinking water at least once a year. By 2025, two-thirds of the world's population may face water shortages. The shortage of drinking water and the search for renewable resources are of the most important problems in the modern world, the solution of which is directed to considerable intellectual and financial resources. Reverse osmosis is one of the most common technologies for obtaining high-quality drinking water. Technological solutions constantly improve the process of reverse osmosis and reverse osmosis spiral wound membrane elements used, science and business go hand in hand. But the price of this progress is the annual generation of a large amount of waste generated from used reverse osmosis roll membrane elements, which are usually sent to the landfill, while there are no technological solutions for their disposal. This work provides information on the available amount of such waste in the world and the dynamics of its growth in order to assess the scale of environmental damage that occurs as a result. The work collected information about the market of reverse osmosis spiral wound membrane elements in the world, and directions of their use. The structure, composition of components and technical characteristics of reverse osmosis spiral wound membrane elements are considered in detail, which makes it possible to evaluate the ways and possibilities of their utilization. The problems of surface contamination due to various types of fouling are considered. The main attention in the work is given to the reasons that cause the formation of waste. Based on the collected data, the scale of annual waste generation, which is formed due to spent reverse osmosis roll membrane elements, was analyzed. The possibility of reusing reverse osmosis spiral wound membrane elements and the main methods of their safe disposal are also considered. Summarizing the work carried out, recommendations were made on ways to solve the problem.

A Theoretical Study of Reverse Roll Coating for a Non-Isothermal Third-Grade Fluid under Lubrication Approximation Theory

The flow of non-Newtonian fluids is extremely important in a variety of industrial applications and processes, including painting, printing, and coating. The goal of this paper is to develop a mathematical model for an incompressible, non-isothermal third-grade fluid as it travels through a minor gap between two heated rolls that are revolving in the opposite direction. Using appropriate dimensionless parameters, the dimensionless version of the governing equations is constructed. To simplify the nondimensional form of the governing equations, the LAT (lubrication approximation theory) is applied. It is mentioned that the perturbation approach should be used. It is a very important tool in modern mathematical physics and practical fluid mechanics, and it is used a lot. Through perturbation techniques, exact solutions for velocity distribution, flow rate, temperature distribution, and pressure gradient are offered. To observe the flow pattern, streamlines are also drawn. Numerical outcomes of some substantial engineering quantities like flow rate, roll separation force, power input, and pressure distribution are found. Some outcomes are displayed graphically although others are presented in tabular form. We have observed that the third-grade parameters give a way to control velocity, pressure gradients, flow rate, and coating thickness. Further, increasing the velocities ratio values lowers the coating thickness on the web. Furthermore, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Both the model and the numerical calculations are in agreement with the viscous fluid model that is already present in the literature.

Reverse Swiss Roll technique for diabetic vitreous membranes.

Background:Diabetic membranes are always a challenge for a surgeon because of sticky nature and chances of iatrogenic break while removing.Purpose:To demonstrate a safe reverse swiss roll technique to dissect diabetic vitreous membranes.Synposis:Approaches and techniques for membrane dissection are segmentation, delamination and en-bloc dissection using various types of instruments and illumination. With vitreous cutte, picks and scissors, surgical steps are traditionallu performed by using classic lift and shave technique. After identifying the plane, tissue is lifted and then cut, which puts the retina at risk of break because of traction and active suction. Such a threat can be reduced by placing the cutter above the membrane thereby having the membrane itseld acting as a protective cushion to the retina. Port here, unlike lift and shave technique, doesn’t face the edge of membrane but is exactly 180 degree opposite and membrane curls into port because of suction. Also, hemostasis is maintained by continuous aspiration and cutting as the instrument is moved side to side, retracting from the edge.Highlights:Reverse swiss roll technique is safer compared to lift and shave because of the safety cushion of the membrane between the port and the retina. There is inherently less chances of retinal break because the active suction from the port is directed away from the retina. The technique also minimises traction and localised pull on the atrophic macula.Video link: https://youtu.be/WNnSsP69ZLw

Study of Slip Effects in Reverse Roll Coating Process Using Non-Isothermal Couple Stress Fluid

The non-isothermal couple stress fluid inside a reverse roll coating geometry is considered. The slip condition is considered at the surfaces of the rolls. To develop the flow equations, the mathematical modelling is performed using conservation of momentum, mass, and energy. The LAT (lubrication approximation theory) is employed to simplify the equations. The closed form solution for velocity, temperature, and pressure gradient is obtained. While the pressure and flow rate are obtained numerically. The impact of involved parameters on important physical quantities such as temperature, pressure, and pressure gradient are elaborated through graphs and in tabular form. The pressure and pressure gradient decreases for variation of the couple stress parameter and velocity ratio parameter K. While the variation of the slip parameter increases the pressure and pressure gradient inside the flow geometry. Additionally, flow rate decreases for the variation of the slip parameter as fluid starts moving rapidly along the roller surface. The most important physical quantity which is responsible for maintaining the quality of the coating and thickness is flow rate. For variation of both the couple stress parameter and the slip parameter, the flow rate decreases compared to the Newtonian case, consequently the coating thickness decreases for the variation of the discussed parameter.

Influence of magnetohydrodynamics and heat transfer on the reverse roll coating of a Jeffrey fluid: A theoretical study

The purpose of this article is to provide a mathematical model of magnetohydrodynamic (MHD) non-isothermal flow of an incompressible Jeffrey fluid as it goes through a minimal gap between the two counter rotating rolls. The dimensionless forms of governing equations are obtained by using appropriate dimensionless parameters. The LAT (lubrication approximation theory) is utilized to simplify the dimensionless form of governing equations. Analytical solutions for the velocity, pressure gradient, flow rate, Nusselt number and temperature distribution are presented. How the Jeffrey parameters, MHD and velocities ratio influence on the flow patterns and heat transfer rate are explored. Outcomes of some significant engineering quantities such as flow rate, power input, pressure distribution and roll separation force are obtained numerically in tabular form and some are displayed graphically. We found that the MHD parameter served as a controlling parameter for different engineering quantities like velocity, temperature, flow rate, and coating thickness. Moreover, the coating thickness on the web decreases by increasing the values of velocities ratio.

Research on a Control Strategy of the Symmetrical Four-Roller Bending Process Based on Experiment and Numerical Simulation

The intelligent production of sheet metal is a comprehensive technology involving control science, computer science, and sheet metal production. Intelligent rolling is an important development in the production process of sheet metal. In this paper, a new symmetrical four-roller bending (SFRB) process is introduced, which consists of feeding, pre-bending, reverse roll bending, second bending, and forward roll bending and unloading. A control strategy is proposed for the process, including on-line monitoring of curvature, on-line identification of the springback law, on-line prediction of final reduction, and control strategy. A convenient and reliable on-line curvature monitoring method is proposed. The quantitative relationship between the reduction and the curvature, in the form of a quadratic function, was established by physical experiments and numerical simulation, and the online identification of the springback law was realized. An on-line prediction method of the final reduction is proposed, and the determination principle of the reduction of three pre-bending processes is given. Finally, the control strategy of the SFRB process was verified by physical experiments. The relative error of the curvature radius of the final formed parts can be controlled within 0.8%. This research provides new insights into intelligent rolling.

Theoretical Study of the Reverse Roll Coating of Non-Isothermal Magnetohydrodynamics Viscoplastic Fluid

This article describes the development of a mathematical model of the reverse roll coating of a thin film for an incompressible non-isothermal magnetohydrodynamics (MHD) viscoplastic fluid as it passes through a small gap between two rolls rotating reversely. The equations of motion required for the fluid added to the web are constructed and simplified using the lubrication approximation theory (LAT). Analytical results are obtained for the velocity profile, pressure gradient, and temperature distribution. The pressure distributions and flow rate are calculated numerically using the trapezoidal rule and regular false position method, respectively. Some of these results are presented graphically, while others are shown in a tabular form. From the present analysis, it has been observed that the magnitude of pressure distributions increases by increasing the value of the involved parameters. It is worth mentioning that the velocities ratio and Brickman’s number are controlling parameters for the temperature distributions. The results indicate the strong effectiveness of the viscoplastic parameter and velocities ratio for the velocity and pressure distributions. It is also concluded that the coating of Casson material has been remarkably affected by the magnetohydrodynamics effects.

Computations of coating windows for reverse roll coating of liquid films

This paper focuses on the flow stability of reverse roll coating flows employed in practical applications to coat thin liquid films on substrates of different materials. Other coating methods are available and various computer programs are purported to predict (for each corresponding method) the set of parameters that permit stable coating conditions. The application of these programs yields so-called coating windows for each particular coating setup. Knowing these coating windows permits coating methods to be applied with preknowledge of the sets of parameters for stable coatings. For reverse roll coating, computer codes for predicting coating windows are scarce or even nonexistent, which was the reason for the present work on the analytical considerations described in this paper. The results obtained formed the basis for a reverse roll coating computer program and its applications. The program is described, and computational results are provided. These are compared with experimental data available in the literature. Good agreement was obtained for high capillary number flows, but there were discrepancies between experimental and computational results for lower capillary numbers. The experimental results for low capillary number flows also appeared less reliable, which triggered the present experimental work. Some experimental results are given for low capillary numbers and these results are also compared with corresponding numerical data. It is suggested that a test section should be built consisting of two rollers and one slot die to study experimentally the stability regions of reverse roll coating flows in a rigorous manner.

Development of a symmetrical four-roller bending process

In order to reduce the straight edge section and simplify process flow, a new symmetrical four-roller bending process is proposed, and its optimum forming process is determined. The main procedure composes of feeding, pre-bending, reverse roll bending, final bending, positive roll bending, unloading, and springback. It has advantages of less production procedure, small remaining straight edge, and simple equipment structure. Three methods are adopted to study the process, i.e., theoretical analysis, numerical simulation, and physical experiment. According to the theory of elastoplastic and geometric relation, the relationship between the reduction of the upper roller and the curvature radius before and after springback is established, and the reduction of the upper roller can be predicted. The symmetrical four-roller bending process is simulated by ABAQUS software. The distribution of stress and strain is analyzed, and the theoretical curvature radius and the simulated curvature radius are compared. The rolling part is obtained from simulation with an ovality of 0.43% and only 1.5 times the thickness of the remaining straight edge. The symmetrical four-roller bending machine is designed, and the ovality of the rolling part from experiment is less than 5%, and the minimum is only 1.74%. The error of most curvature radius is less than 0.5%. Numerical simulation and physical experiments both prove the feasibility of the method. The effect of the process parameters on the curvature after springback is studied by a single variable method. This process provides a new idea for pipe production and helps improve the rolling quality.

A semi‐analytical approach for prediction of volume flow rate in nip‐fed reverse roll coating process

AbstractReverse roll coating, one of the most widely adopted coating techniques, is considered as a self‐metered process. Its volume flow rate in the coating bead is analytically unpredictable due to the presence of the dynamic contact point. In an attempt to approximate the volume flow rate in the coating bead, the position of the dynamic contact point was numerically approximated by computational fluid dynamics (CFD) and then introduced to Navier‐Stokes equations. As a result, this semi‐analytical approach represented a non‐linear correlation of the volume flow rate with speed ratio and capillary number.

Reverse roll coating with a deformable roll operating at negative gaps

Reverse roll coating is probably the most widely used coating operation, yet its full potential has not been exploited as it is shown in this paper which considers operation with a negative gap. We demonstrate through a wide range of experimental data that such operation can yield very thin and stable films with no ribbing or cascade instabilities when low viscosity fluids are used. Typically, stable film thickness less than 5μm can be obtained at speeds up to 150m/min when a rubber roller is used at −100μm gap with fluids of viscosity in the range 10–200mPas. These film thicknesses can be made to decrease further down to 1 or 2µm with a judicious choice of speed ratios (applicator to metering roller) and rubber hardness. Such new findings make this simple coating method an attractive roll to roll technique for application in the newer coating technologies, such as in the production of solar cells and plastic electronics. The data obtained in this study have been underpinned by a model based on the classical lubrication theory, well developed for such flow situations. Essentially it is shown that the film thickness non dimensionalised with respect to the set negative gap is controlled through a single parameter, the elasticity number Ne which combines all the operating parameters. Of course, this flow problem has complexities, particularly at high speed ratios and at zero gap so the data obtained here can serve as a basis for more comprehensive modelling of this classical fluid mechanic problem.