A new mathematical model for a flexible blade coater is proposed and analysed for slip and magnetohydrodynamic (MHD) effects in blade coating process. The slip is considered at the blade surface and magnetic field is imposed normal to the flow. To obtain the velocity profile, pressure, pressure gradient, volumetric flow rate and maximum pressure both exact and numerical solutions are utilized. In order to obtain the numerical solution shooting technique is applied. The interesting physical quantities like load and deflection are calculated and presented in graphical and tabulated form. The influence of the Hartman number the slip parameter and normalized coating thickness parameter on the flow and deflection are discussed graphically. In the presence of magnetic field and slip the fluid velocity and hence blade deflection can be controlled.
This article presents the blade coating analysis of viscous nanofluid passing over a porous substrate using a flexible blade coater. Water-based copper nanoparticles are considered to discuss the blade coating process. The lubrication approximation theory is applied to develop the flow equations. The analytical solution is obtained for velocity, volumetric flow rate, and pressure gradient, while shooting method is applied to obtain the pressure, thickness, and load. Different models for dynamic viscosity have been applied to observe the impact of related parameters on pressure, pressure gradient, and velocity. These results are presented graphically. Interesting engineering quantities such as load, deflection, and thickness are computed numerically and are shown in the tabulated form. It is found that nanoparticle volume fraction increases the pressure gradient, pressure and has minor effects on velocity. For model 1, an increase in the volume fraction reduces the coating thickness, load, and deflection, while model 2 has opposite effects on the mentioned quantities. Also, model 2 has a greater impact on pressure and pressure gradient when compared to model 1.
Research in the field of tribo-mechatronics has been gaining popularity in recent decades. The objective of the current research is to improve static/dynamics characteristics of hydrostatic bearings. Hydrostatic bearings always work in harsh environmental conditions that effect their performance, and which may even result in their failure. The current research proposes a mathematical model-based system for hydrostatic bearings that helps to improve its static/dynamic characteristics under varying conditions of performance-influencing variables such as temperature, spindle speed, external load, and clearance gap. To achieve these objectives, the capillary restrictors are replaced with servo valves, and a mathematical model is developed along with robust control design systems. The control system consists of feedforward and feedback control techniques that have not been applied before for hydrostatic bearings in the published literature. The feedforward control tries to remove a disturbance before it enters the system while feedback control achieves the objective of disturbance rejection and improves steady-state characteristics. The feedforward control is a trajectory-based controller and the feedback controller is a sliding mode controller with a PID sliding surface. The particle swarm optimization algorithm is used to tune the 6-dimensional vector of the tuning parameters with multi-objective performance criteria. Numerical investigations have been carried out to check the performance of the proposed system under varying conditions of viscosity, clearance gap, external load and the spindle speed. The comparison of our results with the published literature shows the effectiveness of the proposed system.
The blade coating process of a micropolar fluid using the plane and exponential coater has been studied. Equations are simplified utilizing lubrication approximation theory. The analytical expressions for flow rate, pressure gradient, and velocity are obtained, while load and coating thickness are computed numerically with the help of the shooting method. We show how the microrotation parameters and the coupling number N influence the flow characteristics, such as pressure distribution, velocity, pressure gradient and related engineering quantities such as load and thickness in the blade coating process, and they are shown graphically as well as in tabular form. We find that, for coupling number N and microrotation parameter , the pressure increases when compared to the Newtonian fluid. Moreover, the coating thickness decreases for the Newtonian case when N increases.
This article deals with the blade coating process for Johnson-Segalman (JS) fluid using plane coater. Flow equations are simplified with the Lubrication approximation theory (LAT). The equations are normalized using suitable scales. Reduced equations are solved numerically using the shooting technique. Also, for small Weissenberg numbers, a perturbation solution is obtained. How Weissenberg number and slip parameter influence the pressure gradient, velocity, pressure, load, and thickness are expressed graphically and via table. In the present work, load on the blade is crucial as it controls the thickness quality. One observes that an increased Weissenberg number decreases load, while the coating thickness increases when compared to the viscous case.
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