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The temperature effect of TDR soil water content values for clay soils needs more detailed considerations due to complex physical processes connected to the presence of bound water. Also the effect of soil electrical conductivity may play important role. 7.5. Temperature effect of soil bound water The discussion of the release of bound water from the solids with the temperature is presented in [72] and [105], where the authors applied Debye model [24] for polar liquids and liquid viscosity dependence on temperature, T, for bound water molecules at the distance x from the solid surface to present their relaxation frequency (Fig. 26): f rel ⎛ 1 ⎛ a ⎞⎞ kT exp⎜− ⎜ + d ⎟⎟ ⎝ T ⎝ x ⎠ = ⎠ (52) 2 3 8π r c ( x, T ) [Hz] where k =1.38·10 -23 [JK - 1 ] is the Boltzman constant, T [K] is the temperature, a=1621 [ÅK], d=2.047·10 3 [K] and c=9.5·10 -7 [Pa s] are constants used for the model simplification, r=2.5 [Å] is the radius of water molecule. Fig. 26. Relaxation frequency of water molecules in relation to the distance from the solid surface and temperature according to (52) on the base of Debye model [24] The water molecules that are close to the solid surface are less mobile in the imposed EM field as the ones far away from it, which is expressed in Fig. 26 by lower relaxation frequency. For a given temperature the more distant the water molecules are from the solids, the higher relaxation frequency they have. The 63
increase of temperature increases their kinetic energy that raises the relaxation frequency and they become more mobile in the imposed EM field. The bound water molecules released from the solid surface become now free water molecules with higher value of the real part of the complex dielectric permittivity. It can be added here that the release of water from the solids results in the increase of ε' and decrease of ε" in (37) describing the loss tangent of dielectric material. This phenomenon leads to a new equilibrium with more free water in expense to bound water. Following Boyarskii et al. [12], Or and Wraith [72] and Wraith and Or [105], only a few layers of water covering soil particle are subjected to the change of relaxation time in relation to relaxation time of free water. Boyarskii et al. [12] report the analysis of nuclear resonance spectra of bound water films in clay showing the approximated relation between relaxation time of bound water, and thickness of the film covering soil particles. The relaxation time of bound water drops rapidly with the number of layers covering soil particle and it seems that only one or two layers have significantly longer relaxation times than that of free water. The average rise time, t r , of TDR pulses is about 0.3⋅10 -9 s (Heimovaara [39], Malicki and Skierucha [59]). This time relates to the frequency bandwidth, bw, of TDR soil water content meters with the following formula given in Strickland [87]: 0.35 bw = ≈ 1.2 [GHz] (53) [ns] t r The authors of [72,105] recognized this frequency limit as the cut-off frequency, f * , that distinguishes water molecules between free and bound. Water layers having dielectric relaxation frequencies lower than the cut-off frequency were considered as bound water having lower dielectric permittivity than for free water. Rearrangement of (52) for a given TDR cut-off frequency, f * , and temperature, T, leads to the simplified relation for the calculation of the thickness, x(T ), of bound water layer: x ( T ) a = ⎛ kT − d + T ln⎜ 2 3 ⎝ 8π r cf ∗ ⎞ ⎟ ⎠ (54) 64
Page 2 and 3:
TDR METHOD FOR THE MEASUREMENT OF W
Page 4 and 5:
PREFACE The importance of water for
Page 6 and 7:
CONTENTS 1. Status of water as an s
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12.2. New prototype version of FOM/
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that stimulate the phenomena and pr
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The solution to the problem of elec
Page 14 and 15: 3. ELECTRICAL MEASUREMENTS METHODS
Page 16 and 17: v = c 1 2L = = ( θ ) n ∆t ε (2)
Page 18 and 19: The TDR probe consists of two waveg
Page 20 and 21: ε a =1 and φ=0.5 the Eq. (10) has
Page 22 and 23: The experiment description is given
Page 24 and 25: Results obtained with the discussed
Page 26 and 27: Notice that at C s = 0, ie when dis
Page 28 and 29: water orientation polarization [s],
Page 30 and 31: Fig. 8. Frequency dispersion of the
Page 32 and 33: The measurements were performed in
Page 34 and 35: 5. EVALUATION OF DIELECTRIC MIXING
Page 36 and 37: ε α = ∑V α iε i (29) i where
Page 38 and 39: where SAND and CLAY are percents of
Page 40 and 41: Below the transition value, the soi
Page 42 and 43: To verify the observations concerni
Page 44 and 45: 6. TEMPERATURE EFFECT ON SOIL DIELE
Page 46 and 47: chamber and the freezer, only one w
Page 48 and 49: The user interface on the main comp
Page 50 and 51: soil sample volumetric water conten
Page 52 and 53: close vicinity of the analyzed obje
Page 54 and 55: process of measurement is non-destr
Page 56 and 57: dielectric permittivity change caus
Page 58 and 59: The values of the refractive index
Page 60 and 61: The relative, ∆n/∆T, and absolu
Page 62 and 63: Fig. 25. The temperature effect on
Page 66 and 67: The purpose of the above discussion
Page 68 and 69: ( ,25 + T )( 45 + T ) 49 9 f rel =
Page 70 and 71: 8. THE ACCURACY OF SOIL WATER CONTE
Page 72 and 73: gravimetric method and the soil ref
Page 74 and 75: where: a 0 ÷ a 6 are coefficients
Page 76 and 77: values of p F calculated for the re
Page 78 and 79: eason of this is the fact that wate
Page 80 and 81: 9 ∆θ = 0,2 ⋅10 ⋅ ∆t = 0.00
Page 82 and 83: values of θ rel for lower values o
Page 84 and 85: 9. COMPARISON OF OPEN-ENDED COAX AN
Page 86 and 87: ε" = EC ε d " + (82) 2π fε wher
Page 88 and 89: dielectric permittivity, the dielec
Page 90 and 91: The applied lumped capacitance mode
Page 92 and 93: stainless steel wires soldered to t
Page 94 and 95: ε’ Open Coax and ε b-TDR , exce
Page 96 and 97: − − The difference of the imagi
Page 98 and 99: Integrated Circuit) recently introd
Page 100 and 101: 10.2. Electromechanical microwave s
Page 102 and 103: RF1. Two PIN diodes in series in ea
Page 104 and 105: The significant aspect of the proto
Page 106 and 107: visible for lower values of soil el
Page 108 and 109: In the TDR method the signal propag
Page 110 and 111: description of functional and techn
Page 112 and 113: MASTER modules are wireless transce
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time the Real Time Clock module wak
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ase station distinguishes A SLAVE d
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sensor, format the data received fr
Page 120 and 121:
12. SOIL WATER STATUS MONITORING DE
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D-LOG/mpts is a moisture/pressure/t
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For compatibility reasons it uses t
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D-LOG/mts (Fig. 59) is a TDR (Time-
Page 128 and 129:
12.4. FP/m, FP/mts - Field Probe fo
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inside of a separate polyethylene b
Page 132 and 133:
differential water capacity and the
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− maximum number of LP/p probes t
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12.7. LP/t - Laboratory Probe for s
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From the collected data set, after
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25. de Loor G.P.: Dielectric proper
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TDR. Symposium on Time Domain Refle
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100. Whalley W.R.: Considerations o
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Fig. 14. Fig. 15. Fig. 16. Fig. 17.
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Fig. 38. The three-rod TDR probe -
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Fig. 67. A set of LP/ms and LP/p LO
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Table 17. An example of the executa
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