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Notes 1773 0.022 30 0.020 i b 0.019 c - 5 0.016 E - 0.017 2 0.016 I 0.015 25 I 2 20 0 c g 15 8 2 10 5 Corrected Velocity _ 0.014 u 5 10 15 20 25 30 35 40 Salinity, 20 0 A 0 30 40 50 60 Rodius. cm Fig. 5. Calculated concentration difference of CaSO, between the solid-liquid interface and bulk solution of clod cards in natural seawater sources based on Eq. 7. Curve A was calculated based on literature values of seawater chemical content at 32%1 and assuming that seawater was diluted with distilled water to achieve the lower salinities; curve B was calculated based on chemical analyses of Puerto Peiiasco seawater at 40?&0 and Tucson tapwater used as the diluent in our study. Ac = 1( _ [Ca2+lb + W42% 2 + K Oo5 2 1 SP I Ka2+lb + W42- lb 2 ) . (7) [Ca2+]i, [Ca2+lb, [S042-]i, and [S042-]b are calcium and sulfate ion concentrations at the interface and in the bulk solution. Ksp is the solubility product, which can be computed by the expressions given by Marshall and Slusher (1968), who allow for the presence of ion pairs such as MgS040 in their correlations. The values of [Ca2+16 and [S042-]b used in Eq. 7 are based on the total calcium and sulfate measured in solution; we have made no attempt to correct these concentrations for the presence of ion pairs containing calcium or sulfate. Increasing the ionic strength (or salinity) increases the CaSO, solubility product, thereby increasing the gradient between the interface and the bulk solution and accelerating the dissolution rate of a clod card. However, this effect is counteracted if the concentration of CaSO, in the bulk solution increases with salinity, which is the case with seawater; the seawater used in our experiments contained CaSO, at concentrations more than eight times that of the freshwater supply. The brackish supply, prepared by dilution, was intermediate. Figure 5 contains salinity correction curves Fig. 6. Correction for the induced-water-motion effect of the rotating arm in the tank. Top line is the velocity of the clod card in the tank at each position on the arm; bottom line is the velocity of the water in the tank estimated by the movement of suspended particles in the water; middle line is the corrected velocity used to correlate the card dissolution rates with water motion. based on Puerto Peiiasco seawater and Tucson tapwater used in our study (curve B) and on literature values of normal seawater constituents (Hansson 1973) assumed to be diluted with distilled water (curve A). Curve B falls below curve A because Tucson tapwater and Puerto Pefiasco seawater contain proportionally more CaSO, than distilled water and standard seawater. The water motion tank was used to obtain data for velocity-weight loss correlations. The velocity of the clod card through the water was easily calculated from the rotation rate of the arm and the distance of the card from the center of rotation. However, it was necessary to correct for the rotary movement imparted to the water in the tank by the moving arm. This movement was determined at each of the five positions by measuring the movement of small suspended particles in the water. A drag model was correlated to the data and used to correct the velocities of the cards into estimates of their velocities relative to the water at each position (Fig. 6). The correction was more significant at low than at high velocities. Forced convection tests were run at temperatures from 13 to 35°C in three different salinities on the rotating arm (Fig. 7). Plots in the form of Eq. 5 were subjected to regression analyses (Table 2). In all runs, clod card weight loss at the lowest test velocity was increased by free convection, and the points fell - 15% above the curve of best fit to the other points;
1774 Notes 0.6 A 25.5’ A 30.5. 0 33.5. Table 2. Regression analyses of clod card runs at various salinities and temperatures. The model equation was in the form [ 1 - (WI W,)]” = a I/‘“; both sides of the equation were converted to natural logarithms to reduce the equation to a linear function for analysis. a 0 2 4 6 6 Velocity. cm a-l 14 16 20 0 13.0 8 0.0146 0.653 0.992 3.16 0 19.5 8 0.0126 0.749 0.992 3.67 0 25.5 8 0.0157 0.772 0.997 2.49 0 30.5 8 0.0178 0.750 0.984 5.33 0 33.5 8 0.0187 0.799 0.996 2.81 20 12.0 8 0.0141 0.765 0.988 4.73 20 19.0 8 0.0136 0.823 0.991 4.43 20 25.5 8 0.0164 0.867 0.990 4.75 20 30.7 8 0.0180 0.868 0.997 2.95 40 13.0 8 0.0130 0.768 0.994 3.24 40 24.5 8 0.0183 0.793 0.998 2.53 40 28.3 8 0.0307 0.757 0.987 4.84 Temperature compensated 0 40 0.0162 20 32 0.0176 40 24 0.0204 0.745 0.965 6.94 0.83 1 0.976 6.41 0.773 0.984 4.93 0.6 V.” 0 2 4 6 6 10 12 14 16 16 20 Velocity, cm *-l 0 13% (4O.h.) C 0 2 4 6 6 10 12 14 16 16 20 Velocity, cm se1 Fig. 7. Temperature curves for clod cards run at different velocities in tapwater (A), brackish water (B), and seawater (C). Lines were fit to data points using Eq. 5. hence, data for the lowest velocity were omitted from curve fitting. The model equation can be used to calculate V as long as the velocity is >2 cm s-l. Coefficients of determination (r2) were 0.98 or higher, and percent error of estimates of y were in the range 2.5-6.0%. Although m varied somewhat, the mean value was -0.8, the value expected for mass transfer from a flat surface in a turbulent flow (Skelland 1974). As expected, increased temperatures accelerated the dissolution rates of clod cards at all test salinities. For the temperature-compensated sequence of Table 2, [ 1 - ( Wr/ Wi)“] was divided by (T/T,,,) (P,&). Note that temperature-corrected data fell onto a response surface of the shape predicted by calculations of AC (Fig. 8). The effects of both temperature and salinity variations are included in the experimental data correlation (Eq. 8). Dissolution rates were lower in tapwater than in brackish water or seawater at a given temperature, but over the range 20-40?& salinity had a minor effect on dissolution rates. Hence, salinity does not appear to be a major factor controlling dissolution rates in marine systems. The dimensional equation fitting our data is %=I -[I -0.71(~)($-Jy) (8) with Y = 0.985. The concemration difference, AC,, (mol liter-‘), is computed at 25°C by means of Eq. 7 or Fig. 4; 8 is expressed in days and V in cm s-l. The average ratio of Ai : Wi for our clod cards was 1.38 cm2 g- l. The results of mass transfer experiments are commonly reported in terms of the appropriate dimensionless groups, although most readers will likely find equations such as Eq. 8 more
Page 1 and 2: 1768 Notes coming tide over a broad
Page 3 and 4: 1770 Notes r=0.15 (typ.) ‘F q- El
Page 5: 1772 Notes J 1.0 2 E 0.9 L 2 0.6 P
Page 9 and 10: 1776 Notes 1000 500 < 200 p 100 7 f
Page 11 and 12: 1778 Notes Sample Points Along cent

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