A bubble curtain model applied in chlorate electrolysis

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The current density is taken as 2000 A/m 2 . The Sherwood number (Sh) is used to find the mass transfer coefficient. It can be expressed as a function of the Schmidt number (Sc) and Reynolds number (Re h ) as in Equation (4.20) [40]. Sh = k ms D = s ∆z (4.19) Sh = A Re B Sc C (4.20) Once this Sherwood number is found, both the boundary layer thickness and the mass transfer coefficient can be found. The constants A, B and C depend on the flow that could either be laminar or turbulent. The relative importance of the Reynolds number value in calculating the Sherwood number increases when the flow switches from laminar to turbulent. The Reynolds number for the flow between parallel plates is calculated to find out the flow type (Eq.(4.21)). The hydraulic diameter (d h ) is twice the width of the electrode gap. The values for viscosity, density and liquid velocity can be found in chapter 4.1. Re h = ρd h v liquid μ = 4257 (4.21) For this Reynolds number Equation (4.22) can be found in the diagram in Figure 16 which can be found in the addendum. [42] Sh ∙ Sc −1/3 = 17 (4.22) This value accounts for a 0,003 m wide and 0,5 m long electrode gap. The Schmidt number in Equation (4.23) is calculated with values for viscosity, density and diffusivity coefficient found in chapter 4.1. Sc = μ = 0,001 ρD 1419∙6,73∙10−9 = 105 (4.23) Combining Equation (4.22) and Equation (4.23) gives: Sh = 17 ∙ 105 1/3 = 80 (4.24) Rearranging Equation (4.19) gives the equations below. ∆z = d h Sh = 0,006 80 = 7,5 ∙ 10−5 m (4.25) k m = Sh D d h = 80∙6,73∙10−9 0,006 = 9,0 ∙ 10 −5 m s (4.26) The thickness of the boundary layer( ∆z = 7,5 ∙ 10 −5 m) is two orders of magnitude smaller than the distance between the two electrodes (s = 3 ∙ 10 −3 m) It is of the same order of magnitude than a typical bubble diameter in the bulk which is 0,1 mm. If an average bubble diameter in the bulk is known, it is possible to recalculate this diameter to an internal pressure which can in turn be recalculated to a saturation concentration. This saturation concentration will 12
then be used as c H2 ,bulk. The average bubble diameter in the bulk is found in Bollens´ thesis [1]. For an electrolyte of 100 and 500 g/L of NaCl and NaClO 3 at 70°C the average bubble size halfway the length of the electrode is 0,1 mm. In Table 3 it is found that a 0,1 mm bubble corresponds to a concentration of dissolved hydrogen of 0,12 mole/m 3 . If no bubbles are formed at the cathode surface ( f G = 0 ) Equation (4.18) will give the following result. c H2 ,cathode = 2000(1−0) 2∙ 96 485∙9,0∙10 −5 + 0,12 = 115 mole/m3 (4.27) Since this is the highest possible hydrogen concentration at the cathode, the diameter of the smallest possible bubble and its internal pressure can be calculated below. Equation (4.28) is made by combining equations (4.6) and (4.12). Equation (4.29) is nothing but the rearrangement of equation (4.10). P in = c H2,cathode + P S water = d = 115 mole/m 3 0,14 mole/(m 3 ,barH 2 ) + 0,25 bar = 824 bar (4.28) 4σ (P inside −P outside ) = 3,2 ∙ 10−9 m (4.29) The concentration at the cathode can be lowered by making the cathode surface rougher. In reality bubbles are formed at the surface which makes the transport of dissolved hydrogen far less and this leads to a lower surface concentration of hydrogen. In addition, the bubbles may accelerate the mass transport i.e. increase k m which also lowers the surface concentration. If 90% of the bubbles are formed at the surface (f G = 0,9) equation (4.27) will give a lower concentration at the cathode and the theoretical minimum distance will become about 3,2 ∙ 10 −8 m. In Table 4 an efficiency of gas evolution of 0,2 can be found for a current density of 2000 A/m 2 . The theoretical minimum bubble diameter then becomes 4,02 ∙ 10 −9 m . Higher values of f G correspond with larger minimum bubble diameters. This is obvious since a higher amount of bubbles formed will result in a lower surrounding concentration of hydrogen which in turn results in a larger minimum bubble diameter. The disadvantage of these small bubbles is that extra energy is needed to create bubbles with such a high Laplace pressure. The Nernst equation is used here to find the extra energy needed to form these small bubbles. ∆U = RTln(P/P 0) zF = 8,31∙343∙ln (824 ⁄ 1) 2∙96 485 ≅ 0,10 V (4.30) 13
Page 1 and 2: A bubble curtain model applied in c
Page 3 and 4: Acknowledgements Thank you Johan fo
Page 5 and 6: mR equivalent mR hydraulic Nomencla
Page 7 and 8: List of Figures FIGURE 1: THE SOLUB
Page 9 and 10: Chapter 1. Introduction Eka Chemica
Page 11 and 12: Chapter 3. Goal In chlorate electro
Page 13 and 14: Solubility diagram of sodium chlora
Page 15 and 16: Figure 2: Hydrogen solubility in a
Page 17 and 18: Equation (4.12) explains how the la
Page 19: transformation into the gaseous pha
Page 23 and 24: 2) The next step is the drainage of
Page 25 and 26: Table 5: Reynolds and Eötvös numb
Page 27 and 28: 4.7 Gas voidage In this chapter, th
Page 29 and 30: 4.8 Conductivity and mass transfer
Page 31 and 32: T α z F absolute temperature charg
Page 33 and 34: The wall voidage is connected to th
Page 35 and 36: voltages are given for the model wi
Page 37 and 38: n H2 = PV 4 = 3 πd 1 2 3 4σ d1 +
Page 39 and 40: 4.11 Hydrogen Transport Newly produ
Page 41 and 42: Chapter 5. Experimental In the work
Page 43 and 44: Above the electrolyte in the vessel
Page 45 and 46: 5.3 Results and discussion Table 10
Page 47 and 48: The cause of the early coalescence
Page 49 and 50: The experiments were made with elec
Page 51 and 52: Figure 15: This diagram divides bub
Page 53 and 54: Chapter 9. References [1] W. Bollen
Page 55: [30] L. Nylén, Influence of the el

A bubble curtain model applied in chlorate electrolysis

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