2 results
The interface dynamics of a surfactant drop on a thin viscous film†
- MARINA CHUGUNOVA, JOHN R. KING, ROMAN M. TARANETS
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- Journal:
- European Journal of Applied Mathematics / Volume 28 / Issue 4 / August 2017
- Published online by Cambridge University Press:
- 08 November 2016, pp. 656-686
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We study a system of two coupled parabolic equations that models the spreading of a drop of an insoluble surfactant on a thin liquid film. Unlike the previously known results, the surface diffusion coefficient is not assumed constant and depends on the surfactant concentration. We obtain sufficient conditions for finite speed of support propagation and for waiting-time phenomenon by application of an extension of Stampacchia's lemma for a system of functional equations.
Adsorbed water and thin liquid films on Mars
- C. S. Boxe, K. P. Hand, K. H. Nealson, Y. L. Yung, A. S. Yen, A. Saiz-Lopez
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- Journal:
- International Journal of Astrobiology / Volume 11 / Issue 3 / July 2012
- Published online by Cambridge University Press:
- 24 February 2012, pp. 169-175
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At present, bulk liquid water on the surface and near-subsurface of Mars does not exist due to the scarcity of condensed- and gas-phase water, pressure and temperature constraints. Given that the nuclei of soil and ice, that is, the soil solid and ice lattice, respectively, are coated with adsorbed and/or thin liquid films of water well below 273 K and the availability of water limits biological activity, we quantify lower and upper limits for the thickness of such adsorbed/water films on the surface of the Martian regolith and for subsurface ice. These limits were calculated based on experimental and theoretical data for pure water ice and water ice containing impurities, where water ice containing impurities exhibit thin liquid film enhancements, ranging from 3 to 90. Close to the cold limit of water stability (i.e. 273 K), thin liquid film thicknesses at the surface of the Martian regolith is 0.06 nm (pure water ice) and ranges from 0.2 to 5 nm (water ice with impurities). An adsorbed water layer of 0.06 nm implies a dessicated surface as the thickness of one monolayer of water is 0.3 nm but represents 0.001–0.02% of the Martian atmospheric water vapour inventory. Taking into account the specific surface area (SSA) of surface-soil (i.e. top 1 mm of regolith and 0.06 nm adsorbed water layer), shows Martian surface-soil may contain interfacial water that represents 6–66% of the upper- and lower-limit atmospheric water vapour inventory and almost four times and 33%, the lower- and upper-limit Martian atmospheric water vapour inventory. Similarly, taking the SSA of Martian soil, the top 1 mm or regolith at 5 nm thin liquid water thickness, yields 1.10×1013 and 6.50×1013 litres of waters, respectively, 55–325 times larger than Mars’ atmospheric water vapour inventory. Film thicknesses of 0.2 and 5 nm represent 2.3×104–1.5×106 litres of water, which is 6.0×10−7–4.0×10−4%, respectively, of a 10 pr μm water vapour column, and 3.0×10−6–4.0×10−4% and 6.0×10−6–8.0×10−4%, respectively, of the Martian atmospheric water vapour inventory. Thin liquid film thicknesses on/in subsurface ice were investigated via two scenarios: (i) under the idealistic case where it is assumed that the diurnal thermal wave is equal to the temperature of ice tens of centimetres below the surface, allowing for such ice to experience temperatures close to 273 K and (ii) under the, likely, realistic scenario where the diurnal thermal wave allows for the maximum subsurface ice temperature of 235 K at 1 m depth between 30°N and 30°S. Scenario 1 yields thin liquid film thicknesses ranging from 11 to 90 nm; these amounts represent 4×106–3.0×107 litres of water. For pure water ice, Scenario 2 reveals that the thickness of thin liquid films contained on/within Martian subsurface is less than 1.2 nm, several molecular layers thick. Conversely, via the effect of impurities at 235 K allows for a thin liquid film thickness on/within subsurface ice of 0.5 nm, corresponding to 6.0×104 litres of water. The existence of thin films on Mars is supported by data from the Mars Exploration Rovers (MERs) Spirit and Opportunity's Alpha Proton X-ray Spectrometer instrumentation, which have detected increased levels of bromine beneath the immediate surface, suggestive of the mobilization of soluble salts by thin films of liquid water towards local cold traps. These findings show that biological activity on the Martian surface and subsurface is not limited by nanometre dimensions of available water.