Thin liquid films arise in contexts ranging from tear films to coating and condensation processes. Their slender geometry enables a systematic reduction of the Navier–Stokes equations to effective low-dimensional evolution while preserving rich nonlinear wave dynamics. Classical approaches include long-wave asymptotic theory, depth-averaged (integral) models and weighted-residual formulations, centre-manifold reductions, and more recent adjustable formulations (Mukhopadhyay et al., JFM 2022). Although these models originate from distinct theoretical perspectives, they share a common objective: approximating the emergent low-dimensional dynamics associated with geometric anisotropy. Long-wave theory directly exploits this scale separation to derive asymptotic reductions, while depth-averaged models introduce closure assumptions to represent transverse structure, and centre-manifold analysis provides a systematic local reduction near the flat-film state. Despite their effectiveness, classical reductions may lose robustness at moderate inertia, exhibiting finite-time blow-up in long-wave formulations and sensitivity to the chosen transverse structure in integral models. This talk revisits thin-film modelling from this unified perspective, presents an adjustable formulation, and outlines directions for advancing reduced modelling.
Zoom link: https://icts-res-in.zoom.us/j/98040128075?pwd=b9nFbvsNBU8nHylaU2hXJpBeptf9LY.1
Meeting ID: 980 4012 8075
Passcode: 982618