Thin Film Instability Analysis

@omkumarsingh1

Hi there, You need independent validation of your thin-film evolution equations to confirm Marangoni destabilization and the dual role of steepness without wasting time on re-derivation. The risk is that a standard solver might smooth out the delicate uphill stabilizing versus downhill destabilizing asymmetry found in your model. Here is the plan: - Implement the specific evolution equation (Eq. 52) using a pseudospectral method to generate the figures. - Validate the linear stability thresholds and reproduce the reported trends for spatial and temporal instabilities. - Produce clean, publication-quality plots confirming the instability thresholds. I previously validated a nonlinear lubrication model for coating flows, matching analytical growth rates with 0.5% error. I can complete this validation in 3-4 days. Would you like me to reproduce the spatial growth rate plot for Mn = 0.4 as a quick free sample? Best, Om Kumar Singh

@yuvarajy3

I have already derived the long-wave model governing a thin viscous film flowing down a heated, undulated incline and identified Marangoni-driven destabilisation together with the competing influence of substrate steepness. What I now require is independent validation and controlled extension of these results, rather than a re-derivation of the theory or preparation of a full LaTeX manuscript. Using the specific evolution equations, travelling-wave reductions, and weakly nonlinear formulations provided in the paper, you would: • reproduce the linear and weakly nonlinear stability results and verify the instability thresholds and growth rates; • implement a numerical solver (pseudospectral or high-order finite difference) solely to generate figures directly from the given equations and parameter values; • confirm the Marangoni-induced destabilisation and the dual stabilising/destabilising role of substrate steepness; • produce publication-quality figures (stability maps, wave profiles, time traces) consistent with the reported trends. The goal is verification and figure-level agreement, not reformulation of the model. Analytical and numerical results should agree in the small-amplitude limit, and the numerical results must recover the uphill/downhill asymmetry observed in the study. This task is best suited to someone already experienced with lubrication theory, nonlinear travelling waves, and thin-film stability problems.