A quasi‐liquid mediated continuum model of faceted ice dynamics

Abstract

We present a quasi‐liquid mediated continuum model for ice growth consisting of partial differential equations informed by molecular dynamics simulations. The main insight from molecular dynamics is the appearance of periodic variations in the equilibrium vapor pressure and quasi‐liquid thickness of the ice/vapor interface. These variations are incorporated in the continuum model as subgrid scale microsurfaces. We show that persistent faceted ice growth in the presence of inhomogeneities in the ambient vapor field is due to a spontaneous narrowing of terraces at facet corners, which compensates for higher ambient water vapor density via feedback between surface supersaturation and quasi‐liquid thickness. We argue that this emergent behavior has the mathematical structure of a stable limit cycle and characterize its robustness in terms of ranges of parameters that support it. Because the model is relevant in the high‐surface‐coverage regime, it serves as a useful complement to the Burton‐Cabrera‐Frank framework. Quantitative aspects and limitations of the model are also discussed.

Structure and water attachment rates of ice in the atmosphere: role of nitrogen

“…The results for attachment coefficients at zero pressure are in full agreement with previous trajectory studies from molecular simulation, which have consistently observed that the fate of vapor water molecules directed towards the ice surface is to stick onto the ice surface, [94,99,100] irrespective of the rate of impingement. [13,14] Our study of trajectories in the presence of nitrogen gas seem to indicate that a similar fate awaits water molecules unless an unfavorable collision with free nitrogen gas molecules occurs. Our results thus clearly favor (microscopic) attachment coefficients of unity, with little evidence of a significant temperature dependence.…”

“…[97] We believe the literature does not always clarify which is the actual coefficient that is measured, and this likely is one reason for the great scatter of experimental results. [98] Additional support for a (microscopic) attachment coefficient of unity is given by the study of water gas water is that the water/vapor interface here is much simpler in structure, so that one does not have to account for the complicated premelting mediated crystal growth mechanisms (c.f., [13,93,101]), and only the evaporation flux and diffusion processes needs to be considered. Despite of this somewhat simpler situation, attachment coefficients on liquid water are also difficult to measure and experiments exhibit a large scatter.…”

Lateral facet growth of ice and snow – Part 1: Observations and applications to secondary habits

“…A wall of steps builds up here, at the step-clumping region (SCR), forming the edge of the hollow. (Neshyba et al, 2016, proposed a more detailed model of step dynamics for ice with a thick surface-disordered region, but it is not yet clear how a hollow would develop in that model.) However, after the hollow forms, the local supersaturations may change.…”

How ice grows from premelting films and water droplets

“…Results from different experimental techniques 15 – 18 , as well as computer simulations, confirm that the surface disorder of ice grows steadily as the triple point is approached, and what is sometimes referred to as a “quasi-liquid layer” of premelted ice is formed on its surface 19 – 23 . Unfortunately, classical growth models based on the terrace-ledge scenario do not account for the impact of premelting films at all, and attempts to incorporate this effect have met only limited success 24 – 26 .…”