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Small quantities of liquid water lining triple junctions in polycrystalline glacier ice form connected vein networks that enable material exchange with underlying basal environments. Diffuse debris concentrations commonly observed in ice marginal regions might be attributed to this mechanism. Following recent cryogenic ring-shear experiments, we observed emplacement along grain boundaries of loess particles several tens of microns in size. Here, we describe an idealized model of vein liquid flow to elucidate conditions favoring such particle transport. Gradients in liquid potential drive flow toward colder temperatures and lower solute concentrations, while deviations of the ice stress state from hydrostatic balance produce additional suction toward anomalously low ice pressures. Our model predicts particle entrainment following both modest warming along the basal interface resulting from anticipated natural changes in effective stress, and the interior relaxation of temperature and solute concentration imposed by our experimental protocols. Comparisons with experimental observations are encouraging, but suggest that liquid flow rates are somewhat higher and/or more effective at dragging larger particles than predicted by our idealized model with nominal parameter choices. Diffuse debris entrainment extending several meters above the glacier bed likely requires a more sophisticated treatment that incorporates effects of ice deformation or other processes. [ABSTRACT FROM AUTHOR]