Experimental Investigations on the Wall-attached Bubble Growth Process in Water With Supersaturated Total Dissolved Gas

: Due to dam discharge, waterfalls, sudden increases in water temperature and oxygen production by photosynthesis, the total dissolved gas (TDG) 6 in water is often supersaturated, which may have serious effects on aquatic ecology. 7 When the atmospheric pressure is lower than the TDG pressure in water, the 8 supersaturated dissolved gas in water will slowly release into air. Wall-attached bubbles 9 were formed during the TDG release process. The generation and departure of wall- 10 attached bubbles influence the release process of TDG in water. To simulate the growth 11 period of the wall-attached bubbles under different pressures, a decompression 12 experimental device was designed to record the supersaturated TDG release process. 13 Based on experimental data and mathematical calculations, the quantitative relationship between the bubble growth rate and environmental pressure was obtained. The 15 supersaturated TDG dissipation rate increases monotonically with increasing relative 16 vacuum degree. Based on the wall-attached bubble growth rate calculation method 17 applied in this paper, a formula of the supersaturated TDG adsorption flux based on 18 wall-attached bubbles was proposed, and a prediction method of the TDG release 19 coefficient was established. The simulation results show that with increasing relative 20 vacuum degree, the TDG coefficient increases correspondingly, and the adsorption 21 mechanism of vegetation surface area can be obviously promoted under lower 22 environmental pressure. This study provides an important theoretical basis for the 23 accurate calculation of the TDG release process and provides a scientific basis for the 24 accurate prediction of the spatial and temporal distribution of supersaturated TDG 25 under different environmental conditions.

between the bubble growth rate and environmental pressure was obtained. The 15 supersaturated TDG dissipation rate increases monotonically with increasing relative 16 vacuum degree. Based on the wall-attached bubble growth rate calculation method 17 applied in this paper, a formula of the supersaturated TDG adsorption flux based on 18 wall-attached bubbles was proposed, and a prediction method of the TDG release  In the natural environment, dam discharge, waterfall, sudden rise of water 30 temperature and oxygen production by photosynthesis may lead to total dissolved gas 31 (TDG) supersaturation in water. Due to the pressure difference between water and 32 atmosphere, supersaturated TDG in water will slowly release to air. Supersaturation

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The relative vacuum degree ∅ is introduced as follows: where ∅ is the relative vacuum degree (RVD), is the vacuum degree, and B 109 denotes the standard atmospheric pressure.

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The variation in the TDG solubility at different relative vacuum degrees was 111 expressed as: where ∅=0 * represents the TDG solubility at 1 atm (mg•L -1 ) and ∅ * represents 113 the equilibrium TDG concentration at the relative vacuum degree ∅ (mg•L -1 ).
where is the TDG concentration (mg • L -1 ), * is the equilibrium TDG 116 concentration (mg•L -1 ), and is the saturation of TDG (%). Table 1 shows the pressure conditions, and Table 2 shows the TDG initial 118 saturation conditions at a temperature of 20 °C. There were 30 combined working 119 conditions. The water temperature in the experimental tanks was controlled at 20 °C 120 during the whole experimental process. involves a first-order kinetic reaction. The first-order kinetic reaction is shown as 127 follows. 128 where t represents the dissipation time (min), represents the TDG solubility of 129 t, (mg• L -1 ); 0 represents the initial TDG solubility, (mg • L -1 ); * represents the 130 equilibrium TDG concentration, (mg • L -1 ); and T represents the dissipation 131 coefficient of supersaturated TDG, (min -1 ).

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The TDG saturation level at the initial and end times was measured for each case.

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The coefficient of determination, 2 , is 0.978. The amount of supersaturated TDG released in static water can be expressed as: where G represents the release rate of supersaturated TDG, (mg• L -1 min -1 ); s 182 represents the release rate of supersaturated TDG from air-water mass transfer, (mg•L -1 min -1 ); and w represents the release rate of supersaturated TDG from wall adsorption,

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(2) The release rate of supersaturated TDG from wall adsorption: where s represents the mass transfer coefficient of the air-water interface 191 (m·min -1 ) and s represents the specific surface area of supersaturated water (m -1 ).

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The quantitative relationship between the mass transfer coefficient of the air-water where s represents the surface turbulent kinetic energy (m 2 •s -2 ).

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(3) The formula for calculating the adsorption rate of TDG by solid walls in 196 supersaturated water is as follows: where d represents the specific solid wall area of supersaturated water (m -1 ).

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The amount of TDG released from the escaped bubbles d was defined as the 214 bubble escapable adsorption flux, and the calculation formula is as follows: where d represents the wall-attached bubble departure volume, (mm 3 ); 216 represents the wall-attached bubble number density, (cell•cm -2 ), which changes with the 217 TDG concentration in water.

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The TDG release coefficient under the influence of a solid wall was simplified as According to mass conservation, the relationship between the TDG dissipation 241 process and wall-attached bubble volume growth rate can be expressed as: where B represents the wall-attached bubble volume, (mm 3 ); B represents the 243 wall-attached bubble surface area, (mm 2 ); and represents the air density in wall-244 attached bubbles, (mg•L -1 ).

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By applying the bindery condition that B =0 = 0, the differential Eq. (10) can be 246 solved as: Due to the contact angle between water, gas and solids, the shape of wall-attached 248 bubbles is not a complete sphere (Adamson, 1990 The relationship between B and ∅ is shown in Fig. 7.

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The departure frequency of wall-attached bubbles was defined as follows: where represents the departure frequency of wall-attached bubbles, (min -1 •cm -2 ) 290 and N represents the wall-attached bubble number density, (cell•cm -2 ).

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The supersaturated TDG decay process can be described by a first-order kinetic   The simulation cases of the pressure condition are shown in Table. 3. As the calculation result of Eq. (10), the mass transfer coefficient of the air-water