Work

Lie symmetry analysis of a generalized steady-state lubrication equation in thin-film dynamics

Year: 2026

Type: article

Abstract: The lubrication approximation is a fundamental framework in fluid mechanics for modeling the flow of thin liquid layers dominated by viscous and surface tension effects. We use Lie symmetry analysis to investigate the third-order ordinary differential equation y ″ ′ = y − n representing the steady-state form of the generalized lubrication equation. We examine how the parameter n affects the possibility of finding explicit solutions using invariant differentiation and by treating the equation as a first-order system. Invariant differentiation yields explicit solutions for n = 5 / 4 and n = 1 / 2 . The first-order system yields solutions via integration by quadrature for n = 5 / 2 and n = 4 / 3 . The results highlight the strong dependence of solution existence on the value of n and provide insight into the nonlinear behavior of the film profile.

Source: Communications in Nonlinear Science and Numerical Simulation

DOI: 10.1016/j.cnsns.2026.109836

Authors: Dušan Navrátil, Maria Clara Nucci

Institutions: Brno University of Technology, University of Bologna

Language: English

Topic: Fluid Dynamics and Thin Films

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,710

Funder: Vysoké Učení Technické v Brně