(a) Thin liquid film flowing over a heater. The Marangoni stress at the upstream edge of the heater opposes the gravitational flow, which leads to the formation of a fluid ridge. (b) Isothermal liquid film flowing over step-down topography. The fluid ridge forms in response to the capillary pressure gradient induced by the topography.
Representative step-down and mound topographies with , , , , and .
(a) Effect of the amplitude of the step-down topography with and on the steady base profile for , , and . The ordinate is the film thickness plus the height of the topographical feature. The substrate temperature is superimposed. (b) Corresponding dispersion curves. The computational domain is
(a) Effect of the steepness of the step-down topography with and on the steady base profile for , , and . (b) Corresponding dispersion curves. The computational domain is
(a) Effect of the amplitude of the mound topography with and on the steady base profile for , , and . (b) Corresponding dispersion curves. The computational domain is
(a) Effect of the steepness of the mound topography with and on the base profile for , and , and . (b) Corresponding dispersion curves. The computational domain is
Effect of Bi on for flow over (a) and (b) with varying and . (c) Effect of steeper topography with and on a film flowing over a substrate with a sharper temperature increase with .
(a) Film profile and interfacial temperature for flow over a flat substrate with . (b) Optimal topographical feature that produces a uniform free-surface even with localized heating.
(a) Dispersion curves for , , , and topography with and for (unstable), (unstable), and (linearly stable). There is a band of stable discrete modes corresponding to for . (b) Eigenfunctions corresponding to the leading (least stable) eigenvalue for for different feature heights to illustrate the slow decay as . The computational domain is .
Energy production rate of the individual terms of the governing linear operator listed in Table I for the film with , , , , and (a) , (b) , and (c) .
Energy production rate relative to that for the neutrally stable, transversely invariant mode with and normalized by the magnitude of the rate for term 7 (dominant Marangoni term): . (a) . (b) . (c) .
Change in the normalized energy production rate of each term in Fig. 11 from to : .
Terms comprising the governing linear operator from the stability problem along with the physical interpretation of each term.
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