www.VadoseZoneJournal.org Transport by Oscillatory Flow in Soils with Rate-Limited Mass Transfer: 1. Theory Oscillatory flow of fluid in a porous medium can generate a one-way transport of heat or chemicals if there is a gradient of temperature or chemical concentraƟon and a rate- limited heat or mass transfer between the moving fluid and an immobile phase. For chemical transport in soils, the immobile phase can occur in stagnant porosity, by sorpƟon, or by dissoluƟon of a vapor in the pore water. As a funcƟon of oscillaƟon frequency, the transport rate has a broad peak near the value ωτ c = 1, where ω is the angular frequency of oscillaƟon and τ c is the characterisƟc equilibraƟon Ɵme of the mobile phase. The transport rate is propor Ɵonal to the gradient and to the square of the amplitude of periodic fluid displacement. A unique di ffusivity derived from the analysis enables predicƟon of the long-term transport by a diffusion calculaƟon without fluid flow, thereby providing a tool for esƟmaƟng the removal of contaminant vapors by passive soil vapor extracƟon (PSVE). We compared predicƟons of the analyƟc theory with numerical simulaƟons of PSVE. The mobile–immobile model is also applicable to transport in other cases of oscillatory flow in porous media, including cyclic moƟon of water or gas due to Ɵdal aquifers or earth Ɵdes. AbbreviaƟons: PSVE, passive soil vapor extracƟon. This study explores isothermal one-dimensional chemical transport due to oscillatory low of gas or liquid in a porous medium, with application to the ventilation of soils by barometric pressure variations. Oscillatory low can increase the transport of heat, dissolved chemicals, or vapor species in the moving luid, in efect increasing the difusivity along the axis of low. his transport occurs whenever a mobile phase of a substance (such as a chemical dissolved in moving water) equilibrates over time with an immobile phase (such as the chemical sorbed on the soil matrix) while the mobile phase undergoes oscil- latory motion. We consider a model in which the equilibration between the mobile and immobile phases is represented by a irst-order rate constant. Although the model applies to many situations, we speci ically apply it to PSVE, in which contaminant vapors are removed from the vadose zone by barometric pumping of air at an open borehole. Earlier analyses of oscillatory transport have explicitly depended on particular mechanisms of mass transfer between the moving luid and a less-mobile phase and thereby did not result in a simple picture of the dynamics or a simple tool for estimating the eicacy of PSVE that this study ofers. 6 Review of Passive Soil Vapor ExtracƟon Ellerd et al. (1999) and Neeper (2002, 2003) reviewed PSVE and barometric pressure propagation in soils. More recently, Rossabi (2006) reviewed barometric pumping. You et al. (2010) presented a two-dimensional solution for gas low during PSVE. You et al. (2011) reviewed analytical methods for PSVE and presented an analysis of gas low when controlled by a check valve. he two studies by You et al. (2010, 2011) did not include contaminant transport. Jennings and Patil (2002) noted that application of PSVE has been hindered by the absence of procedures for estimating its efectiveness. his study ofers such a procedure, expressing the transport as a difusivity that depends on the period of motion and the rate of exchange between the mobile and immobile phases of the transported substance. We call this the exchange difusivity. When chemicals or heat in a fluid equilibrate in time with an immo- bile (dissolved or sorbed) phase, oscillatory motion of the fluid causes one-way transport similar to an enhanced diffusion. Analytic theory offers a simple understand- ing of the process and a tool for estimating the efficacy of passive soil vapor extraction. Earth and Environmental Sciences Division, Los Alamos NaƟonal Lab., P.O. Box 1663, Los Alamos, NM 87545. *Corresponding author (dneeper@earthlink.net). Vadose Zone J. doi:10.2136/vzj2011.0093 Received 21 July 2011. Original Research Donald A. Neeper* Philip H. Stauffer © Soil Science Society of America 5585 Guilford Rd., Madison, WI 53711 USA. All rights reserved. No part of this periodical may be reproduced or transmiƩed in any form or by any means, electronic or mechanical, including pho- tocopying, recording, or any informaƟon storage and retrieval system, without permission in wriƟng from the publisher.