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5.3. Results and discussion 65Table 5.1: Transverse relaxation time T 2 of deuterium in methanol (CH 3 OH) - D 2 O mixtures.x M is the molar fraction of methanol, and T is the temperature.x MT 2 [s]T = 25 ◦ C T = 50 ◦ C0.000 0.389 0.6470.047 0.315 0.5450.101 0.267 0.4920.161 0.230 0.4310.230 0.207 0.3940.309 0.194 0.3640.402 0.188 0.3510.511 0.186 0.3340.642 0.195 0.3195.3 Results and discussion5.3.1 Experimental observationsSome results of the experimental work on the two-phase bulk systems using NMR techniques(see Chapter 4) are briefly reviewed below. This is done for two reasons. First,the profiles of n o versus time are considered in order to derive a set of coefficients forthe mass transfer rate α T (defined by Eq. 5.3), which are based on the experimentalsystems. Secondly, the obtained T 2 profiles are considered, since the population balancemodel described above is used to predict (qualitatively) the reduction of T 2 due to thesol-gel reaction.Transverse relaxation in calibration fluids and gelsThe effect of methanol in solution on the bulk relaxation time of D 2 O was determined bypreparing calibration mixtures containing pure methanol and pure D 2 O. The transverserelaxation time T 2 was measured for deuterium at a temperature of 25 ◦ C and 50 ◦ C,respectively. The results are given in Table 5.1.Calibration gels were prepared from gelling solutions of TMOS in heavy water with orwithout buffer. The initial concentration of TMOS, φ g T, was varied between 0.10 and 0.40.The gels were aged for 20 days. The transverse relaxation time T 2 , which was measuredat 25 ◦ C and 50 ◦ C, were found to decrease with increasing φ g T .It was found that the relaxation times could adequately be described by Eq. 5.30. Thebulk relaxation time T 2,b of the water/methanol mixture in the pores, which is a functionof φ g T, was derived from the calibration results of the water/methanol mixtures togetherwith the calculation of the final water/methanol ratio in the gels. The fraction f s wasapproximated by Eq. 5.31.
66 5. Cross-linking of silica with a time-dependent monomer source3.53.0no bufferpH = 2.95pH = 9.482.5n O[mmol]2.01.51.00.50.00 2 4 6 8 10 12 14 16 18 20time [h]Fig. 5.4: Number of TMOS molecules in oleic phase as a function of time derived from the T 1measurement of the oleic phase (with φ T (0) = 0.20). The measurements were doneat 25 ◦ C using buffered and normal D 2 O. The solid curves indicate the fit using Eq.5.3 modified with an additional offset.Two-phase bulk experimentsThe number of TMOS molecules n o in the oleic phase versus time for three bulk experiments,done at 25 ◦ C with varying pH of the aqueous phase, are shown in Figure 5.4. Allconcentration profiles were fitted with Eq. 5.3, modified to include an additional offset(to account for noise present in the profiles), yielding an excellent description of the data.From the fits the mass transfer rate coefficients α T were derived, which are listed in Table5.2.The transverse relaxation time (T 2 ) profiles of 2 H in the aqueous phase are shown inFigures 5.5 and 5.6 for T = 25 ◦ C and T = 50 ◦ C. At T = 25 ◦ C, T 2 is initially about350 ms (similar to the bulk value of D 2 O) and decreases gradually to values below 100ms within several hours. However, the profiles show a significant difference. In the pH =9.48 system T 2 decreases relatively quickly to 100 ms within the first 5 hours, after whichit decreases slowly and monotonically to 30 ms during the remainder of the experiment(up to t = 47 hours). In the pH = 2.95 system T 2 decreases quickly from 335 ms to 250ms in the first hour, after which it decreases more slowly to 34 ms in the remainder ofthe experiment (up to t = 47 hours). In the unbuffered system T 2 starts at 360 ms anddecays to 73 ms in the first 10 hours of the experiment. In the systems at T = 50 ◦ C, T 2is initially about 630 ms in the unbuffered system and drops to 58 ms within two hours.In the buffered systems T 2 is initially shorter, around 540 ms, which is due to the alreadysignificant degree of hydrolysis in the initial minutes of the experiment. In the lower pHsystem T 2 drops to 20 ms within 5 hours. Both in the unbuffered system as in the pH= 2.95 system the decay of T 2 is faster with respect to the same systems at T = 25 ◦ C,
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TWO-PHASE REACTIVE TRANSPORTOF AN O
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2 1. Introductionproducerbarrierlow
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4 1. IntroductionTwo inter-European
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Part ITwo-phase bulk systems7
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148 Appendix B
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150 Appendix CwhereΩ A (θ) = −2
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152 Appendix C
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154 Appendix D
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156 Appendix Eand equal to zero in
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158 Appendix EAs the saturations, d
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160 Bibliography[12] B. Vinot, R. S
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162 Bibliography[40] M. D. Mantle a
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164 Bibliography[70] F. J. M. van d
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166 Bibliography[97] K. Yoshida, A.
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168 Bibliography[127] G. W. Scherer
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170 Bibliography
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172 Summaryand gelation rates. The
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174 Samenvattingwaterfase. De T 1 v
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176 List of publications
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178 Dankwoordimmer opgewekte stemmi
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