Abstract
Marangoni contraction describes the apparent dewetting behavior of certain volatile mixtures from high-energy surfaces due to Marangoni flows. These flows also lead to strong mixing in the droplets. Here we demonstrate that this process is fully captured in the lubrication approximation if one accounts for Taylor dispersion. We derive the dimensionally reduced form of the advection-diffusion problem of bulk mixtures in thin films, showing that Taylor dispersion is required to establish consistent orders in the long-wave expansion.
Highlights
Published by the American Physical SocietyReduction, unless taking the limit of infinitely fast diffusion along the short axis
Wetting and dewetting of volatile liquid mixtures on solid surfaces is abundant in natural phenomena and technological applications [1,2,3,4,5]
The timescale of diffusion is finite and, in combination with shear flow, leads to strong dispersion. This so-called Taylor-Aris dispersion [43,44] has important consequences in many natural [45] and technological scenarios [46]. To date it remains unclear whether shear dispersion is consistent with a long-wave expansion, so no expression for the effective dispersion in general thin-film flows is available in the literature
Summary
Reduction, unless taking the limit of infinitely fast diffusion along the short axis. It is commonly accepted that vertical compositional gradients are beyond the limit of the lubrication expansion [37,38,56,60,61,62,63,64] We challenge this paradigm, identifying three regimes, depending on the aspect ratio and Péclet number: (i) a regime of faint vertical compositional gradients where previous long-wave models hold [56]; (ii) an intermediate regime of small but not negligible vertical gradients for which we derive an evolution equation for φ including Taylor-Aris dispersion; and (iii) a regime of large vertical gradients where the full advection-diffusion problem has to be solved [56].
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