arXiv subjects

Asim Mukhopadhyay

Publications and source records attributed to Asim Mukhopadhyay.

4 recordsLinked to original sources

arXiv2026

Nonlinear waves and conservative transport in soluble-surfactant falling films on compliant substrates

We investigate finite-amplitude waves in a liquid film containing a soluble surfactant as it flows down an inclined compliant substrate. The coupled motion of the liquid and a spring-backed plate is described by a conservative weighted-residual model, which also accounts for surfactant transport in the bulk and at the free surface. The reduction retains viscous terms arising from wall motion, and its pressure closure recovers fluid added mass under uniform translation. Comparison with the coupled Orr-Sommerfeld problem gives a difference of approximately $1\%$ in the peak growth rate of the film mode at $Re=25$. Nonlinear computations are then used to examine travelling states and their dependence on substrate properties and surfactant coupling. Along the prescribed stiffness-damping path, substrate displacement decreases by more than four orders of magnitude, while wave speed changes by less than $1\%$. The extrema of free-surface elevation and liquid thickness vary differently, so surface height alone does not reliably indicate film thinning over a deformable support. In the cases studied, Marangoni coupling reduces surfactant localisation and weakens the wave and substrate response. Moving-frame reconstruction reveals recirculation near the wave crest and distinguishes propagation of the deformation pattern from transverse substrate motion. The load-work budget identifies capillary pressure as the principal net source of substrate work for the two compliant supports considered. A control calculation in which stiffness is varied at fixed damping shows a substantial change in damping loss but a comparatively small change in deformation.

physics.flu-dyn↗

arXiv2026

A conservative bulk-surface closure for soluble-surfactant falling films: an analytical and numerical mass-balance audit

Adsorption and desorption redistribute soluble surfactant between a liquid film and its free surface, but cannot change the total inventory in a closed periodic domain. We audit this requirement in nonlinear weighted-residual models for soluble-surfactant-laden falling films. Although a previous correction restores conservation of the nonlinear surface Marangoni flux, a separate inconsistency remains in the depth-integrated bulk diffusion. We derive the resulting mass imbalance and construct explicit positive periodic concentration fields that exhibit it. The missing contribution arises from the streamwise concentration gradient appearing in the normal diffusive flux at a sloping interface. Including this contribution restores local conservation of the coupled bulk-surface transport system while leaving the hydrodynamic equations, the leading-order adsorption-desorption closure, and the linear stability properties of the uniform equilibrium unchanged. In an independent no-slip calculation using the parameters of an earlier travelling-wave study, the reference model loses $0.0228832\%$ of its initial surfactant mass by $t=4500$, whereas the corrected run has an absolute relative mass change of $1.2\times10^{-15}$. The main hump and capillary ripples remain closely comparable at $t\approx4500$. This benchmark therefore shows that agreement with travelling-wave calculations does not, by itself, guarantee that a reduced model respects the conservation laws inherited from the underlying transport problem. Although the drift is small in this case, the corrected equations conserve the reduced total inventory for every smooth periodic solution. We also distinguish this exact conservation property from higher-order compatibility with the full curved-interface boundary conditions.

physics.flu-dyn↗

arXiv2026

A conservation-consistent boundary condition for nonlinear models of soluble-surfactant-laden falling films

A conservation-consistent boundary condition is proposed for nonlinear models of soluble-surfactant-laden falling films, ensuring exact conservation of total surfactant mass. The formulation resolves an inconsistency in widely used reduced models, Pascal et al. (PRF, 2019), D'Alessio et al. (JFM, 2020), which exhibit a gradual drift of mass during nonlinear evolution in a closed periodic domain. We show that this originates from an inconsistency in the surface transport reduction and derive a corrected boundary condition that removes this defect. As the discrepancy appears only at the nonlinear order, linear stability results remain unaffected, explaining why the issue has remained unnoticed.

math.AP↗

arXiv2026

Solutocapillary instability in slipping falling films

We present a comprehensive framework for gravity-driven, surfactant-laden thin films flowing over slippery substrates, elucidating how wall slip modifies the coupled hydrodynamics and interfacial transport. A long-wave model is formulated with a conservative bulk-surface mass balance and a Navier slip condition. The Orr-Sommerfeld eigenvalue problem governs the linear regime, while a weighted-residual model captures the nonlinear evolution over a range of equilibrium surfactant coverages, Marangoni strengths, and adsorption kinetics. The analysis predicts a non-monotonic variation of the critical Reynolds number with equilibrium coverage, exhibiting a maximum at intermediate $Γ_e$, and a slip-induced transition from single- to double-hump solitary structures with increasing Marangoni number, accompanied by attenuated capillary ripples. Under fast adsorption kinetics, the surface field homogenizes, preserving the mean film shape and flux while flattening both the surface concentration $Γ$ and the bulk inventory $χ+ hϕ$. A spurious interfacial mass growth reported by Pascal et al.(PRF, 2019) and D'Alessio et al.(JFM, 2020) is resolved through a revised surface balance ensuring strict conservation. Wall slip thus emerges as a key control parameter, reducing viscous resistance and mitigating Marangoni back-stress. The slip parameter $β$ is a useful control knob for surfactant-laden films. Slip prevents fragile multi-hump bound states, promoting a single broad crest or an almost flat, uniform sheet by carefully bonding $β$ to wave selection, ripple damping, and the bulk-surface surfactant balance.

physics.flu-dyn↗