Mathematics – Logic
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008icar..195..131m&link_type=abstract
Icarus, Volume 195, Issue 1, p. 131-139.
Mathematics
Logic
16
Scientific paper
Microscopic liquid layers of water can evolve via adsorption on grain and mineral surfaces at and in the soil of the surface of Mars. The upper parts of these layers will start to freeze at temperatures clearly below the freezing point of bulk water (freezing point depression). A sandwich structure with layers of ice (top), liquid water (in between) and mineral surface (bottom) can evolve. The properties of the interfacial water (of adsorption water and premelted ice) on grain surfaces are described by a sandwich-model of a layer of liquid-like adsorption water between the adsorbing mineral surface layer and an upper ice layer. It is shown that the thickness or number of mono-layers of the interfacial water (of adsorption water and premelted ice) depends on temperature and atmospheric relative humidity. The derived equations for the sandwich model fit well to a known phenomenological relation between thickness of the liquid layer and relative humidity, and can be a tool to estimate or to determine for appropriate materials Hamaker's constant for van der Waals interactions on grains and in porous media. The curvature of grain surfaces is shown to have no remarkable effects for particles in the μm-range and larger. The application of these equations to thermo-physical conditions on Mars shows that the thickness of frost-layers, which can evolve over several hours on cooling surface parts of Mars, is typically of the order or a few tenths of one millimeter or less. This is in agreement with observations. Furthermore, an equation is derived, which relates the freezing point depression for van der Waals force governed interfacial water to the value of the Hamaker constant, to the latent heat of solidification, to the mass density of water ice, and to the thickness of the liquid-like layer. Again, this equation fits well to a known phenomenological relation between freezing point depression and thickness of the liquid-like layer. The derived equation shows that the lower limiting temperature of the liquid phase can reach about 180 K under martian conditions having an atmospheric water content of around 10 pr μm. An “Equilibrium Moisture Content” (EMC)/“Equilibrium Relative Humidity” (ERH) relation for the water content of martian soil has been derived, which relates, for equilibrium conditions, soil water content and atmospheric relative humidity. This relation indicates that the content of liquid interfacial water in the upper surface of Mars can reach up to 10% by weight and more in course of saturation during night hours, and it can be of about 2% by weight during the dry daytime hours.
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