Mathematical simulation of the calendering process for non-Newtonian polymers

Javed, Muhammad Asif; Nasir, Sarah; Ali, Nasir; Arshad, Sabeen

doi:10.1177/87560879211066900

Cited by 6 publications

(5 citation statements)

References 27 publications

(33 reference statements)

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“…Equation (19) shows that p depends exclusively on x. Hence by putting equation ( 21) in ( 18) and ( 20), we get…”

Section: Mathematical Formulationmentioning

confidence: 97%

“…Reverse roll coating process was examined by Shahzad et al 18 by adopting couple stress liquid and reported the variation of coating thickness under material parameter and slip. Javed et al 19 adopted the Carreau-Yasuda model to numerically study the exiting sheet thickness during calendering process by applying Matlab’s built-in-bvp4c routine. Javed et al 20 studied the non-Newtonian polymer in calendering phenomena with velocity slip.…”

Section: Introductionmentioning

confidence: 99%

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Final sheet thickness variation during the non-isothermal calendering process of rheological Prandtl fluid polymer

Abbas,

Khaliq,

Ihsan

et al. 2023

Journal of Plastic Film & Sheeting

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Industries widely use the calendering process to create coated fabrics, thermoplastic films, plastic sheeting, and textile fabrics to procure the prerequisite surface smoothness plus texture. This article inspects the non-isothermal calendering phenomena with heat transfer mechanism to report the rheological behavior of Prandtl fluid on the sensitivity of sheet thickness with velocity slip at roll’s surface. Lubrication theory is utilized to simplify the governing expressions before normalization. We obtained the zeroth plus first order perturbative solutions for the velocity profile, pressure gradient, pressure distribution, temperature, and sheet thickness. And other mechanical properties are evaluated with a numerical solution. Through graphs and tabular data, how material parameters influence the various flow and engineering parameters are reported. As it can be seen, the material parameters are the main parameters that control the pressure gradient, leading to different final sheet thickness and separating force. As the material parameters increased, sheet thickness and separating force increased.

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“…Equation (19) shows that p depends exclusively on x. Hence by putting equation ( 21) in ( 18) and ( 20), we get…”

Section: Mathematical Formulationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Final sheet thickness variation during the non-isothermal calendering process of rheological Prandtl fluid polymer

Abbas,

Khaliq,

Ihsan

et al. 2023

Journal of Plastic Film & Sheeting

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show abstract

“…Integrating equation (24) with respect to "y" and applying the boundary conditions in (25), the exact velocity profile solution is…”

Section: Numerical Solutionmentioning

confidence: 99%

“…Mughees et al 23 studied the second grade fluid to be coated on moving porous substrate in blade coating technique. Javed et al 24 studied tangent hyperbolic fluid to report the calendering technique of non-Newtonian polymers. Most recently, Khaliq and Abbas 25 examined the Upper-convected Jeffery’s material to study the impact of material parameters on the coating thickness and other mechanical quantities.…”

Section: Introductionmentioning

confidence: 99%

Analytical study of isothermal blade coating process using Rabinowitsch fluid model

Abbas

Khaliq

Murtaza

et al. 2022

Journal of Plastic Film & Sheeting

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Blade coating process is widely applied in the industry for its practical applications in photographic films, paint industries, and magnetic storage devices. Also for manufacturing newspaper, metal coating, electronic circuit boards, and textile fibers. The blade coating process passes a fluid into the gap between the moving substrate and blade. This study uses the Rabinowitsch model which represents the Newtonian, shear thickening, and shear thinning effects by changing a non-linear parameter. Lubrication theory is used to simplify the dimensionless governing expressions. Then perturbation technique is used up to second order to solve the resultant system and validated by the numerical shooting technique. The graphs and tables present how the non-linear parameter affects the dimensionless velocity, pressure profile, coating thickness, and blade load. The non-linear model parameter proves to be the controlling parameter for the coating thickness, blade load, and pressure distribution, helping in determining the coating efficiency and improving the substrate life. This paper provides the theoretical framework for engineers to be applied in many industrial applications. In future, further validation of results can be done through experiments.

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“…It is essential to make advantage of the structure of the problem when dealing with issues that include a parameter that is either extremely large or extremely small in order to produce the most accurate approximation. These methods are extremely helpful when dealing with converging and diverging geometries, such as coating flow problems [39,40]. Due to the fact that equation ( 30) is a nonlinear differential equation, finding a solution in closed form can be challenging.…”

Section: Solution Of the Problemmentioning

confidence: 99%

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

Ali¹,

Hou²,

Zahid³

et al. 2022

Phys. Scr.

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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.

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Mathematical simulation of the calendering process for non-Newtonian polymers

Cited by 6 publications

References 27 publications

Final sheet thickness variation during the non-isothermal calendering process of rheological Prandtl fluid polymer

Final sheet thickness variation during the non-isothermal calendering process of rheological Prandtl fluid polymer

Analytical study of isothermal blade coating process using Rabinowitsch fluid model

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

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