Langlois’ Recursive Approach to Non-Creeping Inertial Viscoelastic Corner Flow in Thin Films

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Mehboob Laraib; Maqbool Khadija; Ellahi R.; Sait Sadiq M.

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Journal Paper

Paper Information

Journal: THE JOURNAL OF COMPUTATIONAL APPLIED MECHANICS Year:2026 | Volume:57 | Issue:2 Page(s): 326-347

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Information Journal Paper

Title

Langlois’ Recursive Approach to Non-Creeping Inertial Viscoelastic Corner Flow in Thin Films

Author(s)

Mehboob Laraib | Maqbool Khadija | Ellahi R. | Sait Sadiq M. | Issue Writer Certificate

Keywords

Thin Film

Viscoelastic

Inertial forces

Corner flow

Langlois approach

Abstract

Dip coating is a key technique in thin film fabrication, widely applied in protective coatings, and material surface engineering. The coating quality depends strongly on the fluid dynamics near substrate edges, where viscoelastic effects and inertial forces can lead to stress concentration and flow instabilities. A viscoelastic fluid model is formulated based on conservation of mass and momentum, with nonlinear governing equations solved using the Langlois recursive approach and the inverse method. Analytical solutions of the stream function provide insight into velocity fields, pressure distribution, and stress behavior near the substrate surface. Results show that stresses and pressure diverge near sharp substrate corners, which can compromise coating durability. Variations in the interface angle significantly alter stress distributions on both the substrate and free surface. Furthermore, inertial forces amplify fluid velocities in the corner region, directly influencing film thickness uniformity and mechanical performance of coated layers.

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