Transient two-dimensional coating flow of a viscoelastic fluid film on a substrate of arbitrary shape
type: Item
instance of: scholarly article
title: Transient two-dimensional coating flow of a viscoelastic fluid film on a substrate of arbitrary shape
zbMATH Open document ID: 0995.76006
DOI: 10.1016/S0377-0257(00)00174-9
published in: Journal of Non-Newtonian Fluid Mechanics
publication date: 2002-10-21T00:00:00Z
review text: This paper examines transient two-dimensional flows of a thin film of Oldroyd-B fluid on a stationary solid substrate of arbitrary shape. The fluid is driven by a pressure gradient in a channel from which it emerges. The investigation is motivated by the fact that in coating process, for example, the orgin of some problems may appear at the early stages before steady state is achieved, if it is achieved at all. In particular, the investigation focuses on the effects of viscosity, elasticity, inertia, gravity and substrate topography, under the lubrication assumption. As for the mathematical technique, the film equations are solved by expanding the flow field in Fourier series in the height direction. The Galerkin projection method is then applied to derive the equations governing the expansion coefficients. Finally, a time-stepping implicit finite difference discretization, together with a sixth-order Runge-Kutta scheme, is utilized to calculate the evolution of the shape of free surface and the flow field with time. In analyzing the results, the author finds that the viscosity ratio, fluid elasticity, gravity and substrate topography can have a significant effect on transient behavior. However, these effects depend on the level of fluid inertia. For low inertia the fluid tends to accumulate near the channel exit, exhibiting a standing wave that grows with time. The topography of the substrate affects the flow significantly. In the presence of a bump, for example, the flow of a high-inertia fluid can generate a secondary wave that moves downstream of the primary wave.
Mathematics Subject Classification ID: 76A10
Mathematics Subject Classification ID: 76A20
Mathematics Subject Classification ID: 76M25
zbMATH DE Number: 1556243
zbMATH Keywords: thin film
zbMATH Keywords: Oldroyd-B fluid
zbMATH Keywords: stationary solid substrate of arbitrary shape
zbMATH Keywords: pressure gradient
zbMATH Keywords: coating process
zbMATH Keywords: lubrication
zbMATH Keywords: Fourier series
zbMATH Keywords: Galerkin projection method
zbMATH Keywords: time-stepping implicit finite difference discretization
zbMATH Keywords: sixth-order Runge-Kutta scheme
zbMATH Keywords: free surface
zbMATH Keywords: viscosity ratio
zbMATH Keywords: fluid elasticity
zbMATH Keywords: gravity
zbMATH Keywords: substrate topography
zbMATH Keywords: fluid inertia
zbMATH Keywords: secondary wave
author: Roger E. Khayat
reviewed by: H. Ramkissoon
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1556243