Many drug delivery systems suffer from undesirable interactions with the host
immune system. It has been experimentally established that covalent attachment
(irreversible adsorption) of suitable ...macromolecules to the surface of the drug
carrier can reduce such undesirable interactions. A fundamental understanding
of the adsorption process is still lacking. In this paper, the classical random
irreversible adsorption model is generalized to capture certain essential
processes involved in pharmacological applications, allowing for macromolecules
of different sizes, partial overlapping of the tails of macromolecules, and the
influence of reactions with the solvent on the adsorption process. Working in
one dimension, an integro-differential evolution equation for the adsorption
process is derived and the asymptotic behaviour of the surface area covered and
the number of molecules attached to the surface is studied. Finally,
equation-free dynamic renormalization tools are applied to study the
asymptotically self-similar behaviour of the adsorption statistics.
Many drug delivery systems suffer from undesirable interactions with the host immune system. It has been experimentally established that covalent attachment (irreversible adsorption) of suitable ...macromolecules to the surface of the drug carrier can reduce such undesirable interactions. A fundamental understanding of the adsorption process is still lacking. In this paper, the classical random irreversible adsorption model is generalized to capture certain essential processes involved in pharmacological applications, allowing for macromolecules of different sizes, partial overlapping of the tails of macromolecules, and the influence of reactions with the solvent on the adsorption process. Working in one dimension, an integro-differential evolution equation for the adsorption process is derived and the asymptotic behaviour of the surface area covered and the number of molecules attached to the surface is studied. Finally, equation-free dynamic renormalization tools are applied to study the asymptotically self-similar behaviour of the adsorption statistics.
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