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Water is usually the main component of ice mantles, which cover the cores ofdust grains in cold portions of dense interstellar clouds. When molecularhydrogen is adsorbed onto an icy mantle through physisorption, a commonassumption in gas-grain rate equation models is to use an adsorption energy formolecular hydrogen on a pure water substrate. However, at high density and lowtemperature, when H2 is efficiently adsorbed onto the mantle, its surfaceabundance can be strongly overestimated if this assumption is still used.Unfortunately, the more detailed microscopic Monte Carlo treatment cannot beused to study the abundance of H2 in ice mantles if a full gas-grain network isutilized. We present a numerical method adapted for rate-equation models thattakes into account the possibility that an H2 molecule can, while diffusing onthe surface, find itself bound to another hydrogen molecule, with a far weakerbond than the H2-water bond, which can lead to more efficient desorption. Welabel the ensuing desorption "encounter desorption". The method is implementedfirst in a simple system consisting only of hydrogen molecules at steady statebetween gas and dust using the rate-equation approach and comparing the resultswith the results of a microscopic Monte Carlo calculation. We then discuss theuse of the rate-equation approach with encounter desorption embedded in acomplete gas-grain chemical network. For both systems, the rate-equation modelwith encounter desorption reproduces the H2 granular coverage computed by themicroscopic Monte Carlo model. The method is especially useful for dense andcold environments, and for time-dependent physical conditions, such as occur inthe collapse of dense cores and the formation of protoplanetary disks. It isnot significantly CPU time consuming, so can be used for example with complex3D chemical-hydrodynamical simulations.

A New and Simple Approach to Determine the Abundance of Hydrogen Molecules on Interstellar Ice Mantles