J.R. Philip and D.A. de Vries

J. Jpn. Soc. Soil Phys. No. +*-, p.+*/++,,**0 J.R. Philip and D.A. de Vries ** Reviewing classical studies in soil physics Moisture Movement in Porous Materials under Temperature Gradients By J.R. Philip and D.A. de Vries Transactions, American Geophysical Union, Vol. -2, No.,,,,,,-, (+3/1) Masaru SAKAI* and Nobuo TORIDE* + J. R. Philip Philip.* Philip de Vries +3/1 +3-* Darcy Richards Penman, +3.* Gurr et al., +3/, +* Philip and de Vries +3/1 Philip,, Philip +33+,*** Philip Philip, Philip Penman, +3.* - q vap aavdatm r w r v z * /+.2/*1 +/11 :

106 +*-,**0 q vap cm s + D atm cm, s + T K P D atm..., +*. T,.- P, r w gcm - v + a Penman +3.* *.00 a q r v gcm - z cm gcm, s + cm s + +33+ Miyazaki et al. +33- -,, -+ r v r hg vr vsh rr vsexp R vt r vs gcm - H r h cm g 32+ cm s, Rv.0,.+ Jkg + K + r v r vs H r r v r vs H r z Hr z rvs z r vs T H r T q r v dr vs z Hr dt T z r vs H r T T Hr z q q z T H r H rt* H r q r v dr vs z Hr dt T grv z R vt dh dq q z q Tvap q qvap, q vapq Tvapq qvap T q D Tvap z Dqvap z D Tvap, D qvap D aavdatmhrb Tvap r w D qvap aavdatm r w gr v R vt dh dq bdr vsdt +* -* b +.*/+* 0 gcm - K + -, q h liqk z + q liq cm s + K cm s + h q T hz, h h z T T h z q q z ht s h T h s ds dt gh g+sdsdt +* -* g,.*3+* - K + q Tliq q qliq, q liqq Tliqq qliqd Tliq T z Dqliq q z K D Tliq, D qliq D TliqKgh D h qliqk q. Philip

: J. R. Philip and D. A. de Vries 107 + A B Philip and de Vries +3/1, Figure, Fig. + Water flow through a liquid island. The arrow indicates the flow direction due to the temperature gradient. Vapor condenses on one side A and evaporates from the other side B. (Philip and de Vries +3/1, Figure,),.+ CS, CH -COCH - Philip + + A B a af a q Philip fa + aa K fa aa K aa K a K, Fig., a q K*., b Tz a Tz c h Philip and de Vries Cass (a) Apparent available porosity for vapor di#usion as a function of volumetric water content (q K*.,). The solid line represents the liquid island model and the dashed line is based on the conventional theory. (b) Ratio of the temperature gradient of air phase (T/z) a and the soil average temperature gradient (T/z). (c) The enhancement factor h for the thermal vapor transport. The solid line and the dashed line represent the Philip and de Vries model and the Cass model, respectively.

108 +*-,**0 - D Tvap D Tliq D qvap D qliq D Tvap Fig. - Thermal vapor (D Tvap), thermal liquid water (D Tliq), isothermal vapor (D qvap), and isothermal liquid water (D qliq) di#usivities for a loam soil as a function of volumetric water content. The dashed line indicates D Tvap based on the conventional theory. q K, a q K*., qq K aa K qq K aa K q a,., Philip Tz Tz Tz a, b Philip +.- -.-, q afaqvdatmhrb T Tvap r w za a Tz a h enhancement factor h afaq aa Tz a Tz, c h q, h - 1 T aavdatmhrbh q TvapD Tvap z r w T z h Jury and Letey +313 Tz atz /*

: J. R. Philip and D. A. de Vries 109. *.*1. *.+-. *.-+- / Philip Fig.. Volumetric water content profiles for the initial water content of *.*1., *.+-., and*.-+- for a loam soil after / days. The solid lines and dashed line represent simulated results with the Philip and de Vries model and the conventional theory, respectively, and the plots are observed data. Philip +./, h Cary +313 h Cass et al. +32. h h q h3./- q 2./exp + q. q s q s q s f c h, c Cass et al. h Noborio et al., +330 ; Scanlon et al.,,**- Philip h Philip q t T q K z DT z Dq z z D TD TvapD Tliq, D qd qvapd qliq T C s t z l T z L q z Dqvap z C s L l ll sld Tvap l s de Vries +3/2 C st t L qvap t z T ls z L qvap z q liqt q vapt C liq C vap z z C liq C vap / 0 Philip.

110 +*-,**0 0, q h K h van Genuchten- Mualem van Genuchten, +32* q r*.*+ q s*..1, a*.*1. cm + n+.-3 K s--.1 cm day + l+ h Philip q K*.,Tz atz+.1 - D Tvap, D Tliq, D qvap, D qliq + q*.,/ D Tvap q*.,/ / Fig. / *.*1. *.+-. *.-+- / q Tvap q Tliq q qvap q qliq Thermal vapor (q Tvap), thermal liquid water (q Tliq), isothermal vapor (q qvap), and isothermal liquid water (q qliq) flux profiles for the initial water content of *.*1., *.+-., and *.-+- for a loam soil after / days. Gurr et al. +3/, 0+ Gurr +* cm +*,/ q i*.*1. *.+-. *.-+- / q i*.*1. *.+-. q i*.-+- D Tliq Philip D Tvap D Tvap D qliq q*.*/ D qvap Kz* q i,* +*,/ * HYDRUS-+D Simunek et al., +332. x* / q i*.*1. q i*.+-. q i*.-+- q i*.*1. *.+-. h Philip Philip D Tvap. -. / /. q i*.*1. q Tvap q Tliq D Tliq x0 cm q*.*/ q qliq x0 cm

: J. R. Philip and D. A. de Vries 111 q qvap x0 cm D qliq x0 cm D qvap x0 cm, q Tvap q qvap q i*.+-. q i*.*1. q Tvap q qliq q i*.-+- q i*.*1. *.+-. q Tvap q Tliq q qliq 0 q i*.*1. *.+-. *.-+- q i*.*/ *.*2 / q i*.+-. *.-+- *.0+0 day + *.13+ day + *.023 day + *./,0 day + q i*.*/ *.*1. *.*2 q i *.+-. *.-+-. / 0. Philip 1 Philip. Nassar and Horton +323 Milly +32, Jury and Letey, +313 ; Cary, +313 ; Cass et al.,+32. Philip Philip /* Fig. 0 0 *.*/ *.*1. *.*2 *.+-. *.-+- / Evaporation rate profiles for the initial water content of *.*/, *.*1., *.*2, *.+-., and*.-+- for a loam soil after / days.

112 +*-,**0 Philip Philip Cary, J.W. (+313) : Soil heat transducers and water vapor flow. Soil Sci. Soc. Am. J.,.- : 2-/2-3. Cass, A., Campbell, G.S. and Jones, T.L. (+32.) : Enhancement of thermal water vapor di#usion in soil. Soil Sci. Soc. Am. J.,.2 :,/-,. de Vries, D.A. (+3/2) : Simultaneous transfer of heat and moisture in porous media. Trans. Am. Geophys. Union, -3 : 3*33+0. Gurr, C.G., Marshall, T. J. and Hutton, J.T. (+3/,) : Movement of water in soil due to a temperature gradient. Soil Sci., 1. : --/-./. Jury, W.A., and Letey, J. (+313) : Water vapor movement in soil : reconciliation of theory and experiment. Soil Sci. Soc. Am. J.,.- : 2,-2,1. Milly, P.C.D. (+32,) : Moisture and heat transport in hysteretic, inhomogeneous porous media : a matric head-based formulation and a numerical model. Water Resour. Res., +2 :.23.32. Miyazaki, T., Hasegawa, S. and Kasubuchi, T. (+33-) : Water flow in soils. pp.+10+12, Marcel Dekker Inc., New York.,*** : pp. 203, +33+ : pp. 2330 Nassar, I.N. and Horton, R. (+323) : Water transport in unsaturated nonisothermal salty soil : II. theoretical development. Soil Sci. Soc. Am. J., /- : +--* +--1. Noborio, K., McInnes, K. J. and Heilman, J.L. (+330) : Two-dimensional model for water, heat, and solute transport in furrow-irrigated soil : II. field evaluation. Soil Sci. Soc. Am. J., 0* : +*+*+*,+. Penman, H.L. (+3.*) : Gas and vapor movement in soil : I. The di#usion of vapors through porous solids. J. Agric. Sci., -* :.-1.0,. Scanlon, B., Keese, K., Reedy, R.C., Simunek, J. and Andraski, B. J. (,**-) : Variations in flow and transport in thick desert vadose zones in response to paleoclimatic forcing (*3* kyr) : Field measurements, modeling, and uncertainties. Water Resour. Res., No. 1, ++13, doi : +*.+*,3/,**, WR**+0*.. -.+-.1. Simunek, J., Sejna, M. and van Genuchten, M.Th. (+332) : The HYDRUS-+D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variablysaturated media. Version,.*. IGWMC-TPS-1*. International Ground Water Modeling Center, Colorado School of Mines, Golden, CO. van Genuchten, M.Th. (+32*) : A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J.,.. : 23, 232. Philip and de Vries +3/1 Philip. :,**0. +, :,**0 / +2