Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

Abstract

A long-wave lubrication analysis is used to study the influence of topographical features on the linear stability of noninertial coating flows over a locally heated surface. Thin liquid films flowing over surfaces with localized heating develop a pronounced ridge at the upstream edge of the heater. This ridge becomes unstable to transverse perturbations above a critical Marangoni number and evolves into an array of rivulets even in the limit of noninertial flow. Similar fluid ridges form near topographical variations on isothermal surfaces, but these ridges are stable to perturbations. The influence of basic topographical features on the stability of the locally heated film is analyzed. In contrast to its destabilizing influence on liquid films resting on heated, horizontal walls, even such nonoptimized topography is found to be effective at stabilizing the flowing film with respect to rivulet formation and subsequent rupture. Optimal topographical features that suppress variations in the free-surface shape are also determined. The critical Marangoni number at the instability threshold increases substantially with appropriate topography even for nonzero Biot numbers. An energy analysis is used to provide insight into the mechanism by which the topography stabilizes the flow. Because the stabilizing effect of the topographical features is only weakly sensitive to the governing parameters and particular temperature profile, the use of such features could be a simple alternative in applications to more complicated methods of stabilization.

Stability of a volatile liquid film spreading along a heterogeneously-heated substrate

“…The heater was sufficiently narrow and evaporation sufficiently weak that the film did not rupture to form a contact line. It has been shown that this rivulet instability can be suppressed for a range of values of the Marangoni parameter and Biot number by modifications to the substrate temperature profile via feedback control [24] or by the introduction of suitable topographical features on the substrate [25]. Klentzman and Ajaev [26] recently studied the two-dimensional evolution of spreading, volatile films by numerically integrating the governing evolution equation in a rectangular domain.…”

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

“…The figure shows that for small values of κ, the relative deformations y of the thin-liquid film are periodic ripples with harmonic profiles. As we increase κ (κ = 0.95) the ripples gain in anharmonicity, a feature noticeable in their typical fingering shapes 33 reminiscent of rivulet structures [34][35][36] . As κ → 1 the ripples are more and more broad (graphs for κ = 0.98 and κ = 0.99).…”

Stability of Thin Liquid Films Falling Down Isothermal and Nonisothermal Walls

“…They found a Hopf bifurcation increasing the Marangoni number from criticality, which in the linear case destabilizes into a transverse perturbation. Tiwari and Davis (2010) introduce the effect of wall deformations in the problem of local heating. It is of interest because in isothermal flow a film passing through a small step forms a stable ridge above the highest part of the step, in contrast to the unstable one in the heated finite plate.…”