Steady viscoelastic film flow over 2D topography: I. The effect of viscoelastic properties under creeping flow

A Modified Equation for Thickness of the Film Fabricated by Spin Coating

“…PDMS is a non-Newtonian fluid and, in [15], the authors pointed out that a study on the realistic flow for flattening of thickness through spin coating using non-Newtonian fluids. However, in [16], experiments were conducted with non-Newtonian fluids to study the applicability of non-Newtonian fluids to Newtonian fluid law.…”

Stability analysis of viscoelastic film flows over an inclined substrate with rectangular trenches

“…Traditionally in film flows, all the lengths are scaled with the flat film thickness, H * N , and all the velocity components with the mean Nusselt film velocity, U * N , defined as This scaling, for example, has been used by Pavlidis, Dimakopoulos & Tsamopoulos (2010) and Pavlidis et al (2016) for the study of the steady viscoelastic film flow over topography. It is apparent, however, that with the above scaling both the length and velocity scales are affected by the flowrate, see (2.1a,b).…”

“…The first attempt to address the interaction between fluid elasticity and inertia was made by Saprykin, Koopmans & Kalliadasis (2007), who studied the flow over a variable topography of an Oldroyd-B fluid using lubrication theory and assuming very weak fluid elasticity. Later on, Pavlidis, Dimakopoulos & Tsamopoulos (2010) and Pavlidis et al (2016) solved the 2-D momentum equations for a viscoelastic film flowing over a topography featuring rectangular trenches employing the exponential Phan-Thien Tanner (ePTT) model (Phan-Thien 1978), which introduces the most common viscoelastic properties. Recently, Pettas, Dimakopoulos & Tsamopoulos (2020) investigated the steady flow of a polymer solution over a partially coated substrate.…”

Influence of Temperature Gradient on the Stability of a Viscoelastic Film with Gradually Fading Memory over a Topography with Ridges and Furrows

“…And a nonuniform coating leads to low quality products or to manufacturing failures. Pavlidis et al [45] reported on the steady viscoelastic film flow over 2D topography with the prime objective to analyze the effect of the viscoelastic properties of polymeric solutions in spreading over and planarizing various topographical features, especially during spin-coating. Such studies are interesting and could be extended for topographies with longitudinal geometries for second-order fluids with or without invoking lubrication approximation.…”

“…Using a convected Maxwell model, Saprykin et al [44] investigated the influence of inertia and viscoelasticity on a film flowing on a stepdown topography. The effect of viscoelastic properties under creeping flow conditions was investigated by Pavlidis et al [45] considering a Phan-Thien and Tanner viscoelastic model for fluid flowing on a horizontal trench. By incorporating an asymptotic expansion of the upper-convected Maxwell model for elastic fluids, recently, Bouchut and Boyaval [46] proposed a new model for gravity-driven free-surface flows of shallow viscoelastic fluids across a topography.…”