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Analytical solution and simplified analysis of coupled parent-daughter steady-state transport with multirate mass transfer

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  • In this technical note, a steady-state analytical solution of concentrations of a parent solute reacting to a daughter solute, both of which are undergoing transport and multirate mass transfer, is presented. Although the governing equations are complicated, the resulting solution can be expressed in simple terms. A function of the ratio of concentrations, In (daughter/parent + P), can be used as a metric of mass transfer and reaction if the reactions are mostly confined to the immobile domain, where P is the ratio of production of daughter to decay of parent. This metric is applied with the resazurin-resorufin (Raz-Rru) tracer system in a stream to obtain an integrated measure of respiration that occurs on or in a stream bed. The slope of the graph of In (Rru/Raz + P) versus advective travel time is a function of the strength of surface-bed interaction and respiration. This graph can be used for rapid comparison of different experiments and streams. Citation: Haggerty, R. (2013), Analytical solution and simplified analysis of coupled parent-daughter steady-state transport with multirate mass transfer, Water Resour. Res. 49, doi: 10.1029/2012WR012821.
  • Keywords: Nitrification, Soil, Behavior, Reactive transport
  • Keywords: Nitrification, Soil, Behavior, Reactive transport
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  • Haggerty, R. (2013), Analytical solution and simplified analysis of coupled parent-daughter steady-state transport with multirate mass transfer, Water Resources Research 49, doi:10.1029/2012WR012821.
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  • 49
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  • Financial support for this work was provided by the National Science Foundation (EAR 08-38338). Data and facilities were provided by the H.J. Andrews Experimental Forest research program funded by the National Science Foundation’s Long-Term Ecological Research Program (DEB 08-23380), U.S. Forest Service Pacific Northwest Research Station, Oregon State University, and the Hollis Dole Fund in Environmental Geology.
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