A mistake has been found while cross-checking the computer code of a mathematical model1 for the laminar flow diffusion chamber (LFDC) with a fluid dynamics software FLUENT with fine particle model. The mathematical model describes a coupled mass and heat transfer inside the LFDC, and its solution provides (at particular boundary conditions in a steady state) profiles of temperature and vapor concentration in axial and radial directions.

The mistake resided in the implementation of the heat capacity mixing rule for ideal vapor-gas mixture. The pure components’ heat capacities in the code are defined in units of J×kg1×K1 because mass fractions together with a mass flow rate are used throughout the code when mass transfer is calculated. In our erroneous implementation, the heat capacity of a mixture was calculated as a mole fraction weighted average instead of a mass fraction weighted average. This error has been fixed and the experimental results published in Lihavainen et al.2 Table 2 have been recalculated and they are presented in Table I.

The difference with the original results becomes larger as a function of nucleation temperature (Fig. 1). This is because the amount of n-pentanol in the carrier gas and vapor mixture increases as the nucleation temperature increases. At 260K the difference is only minor; in nucleation temperature 0.01%, in saturation ratio 0.8%, and in experimental nucleation rate about 1%. However, at 290K the difference is clear; in nucleation temperature 0.1%, in saturation ratio 5.2%, and in experimental nucleation rate about 9%. Compared to the original results, the major difference is in the temperature dependency compared to classical nucleation theory (see Fig. 2). The original data had no or slightly increasing temperature dependency, which was in contrast to other measurements (e.g., Lihavainen et al.2). The recalculated results have decreasing temperature dependency, which is the same as what has been observed with other experimental setups. 

FIG. 1.

The experimental nucleation rates, Jexp as a function of saturation ratio S of n-pentanol. Filled symbols: LFDC data recalculated with corrected mixing rule for heat capacity. Open symbols: Original data.

FIG. 1.

The experimental nucleation rates, Jexp as a function of saturation ratio S of n-pentanol. Filled symbols: LFDC data recalculated with corrected mixing rule for heat capacity. Open symbols: Original data.

Close modal
FIG. 2.

Ratios between experimental nucleation rate, Jexp, and theoretical nucleation rate, Jtheor, as a function of nucleation temperature. Filled symbols: LFDC data recalculated with corrected mixing rule for heat capacity. Open symbols: Original data.

FIG. 2.

Ratios between experimental nucleation rate, Jexp, and theoretical nucleation rate, Jtheor, as a function of nucleation temperature. Filled symbols: LFDC data recalculated with corrected mixing rule for heat capacity. Open symbols: Original data.

Close modal
The homogeneous nucleation rates of n-pentanol measured in the LFDC are presented. TS2 (K) is the temperature of the preheater, TC (K) is the temperature of the condenser, P (Pa) is the total pressure, Q(cm3s) is the average flow rate, Tlab (K) is the temperature of the laboratory, TS1 (K) is the temperature of the saturator, N(cm3) is the particle concentration, Tnuc (K) is the calculated temperature at the nucleation maximum, Snuc is the saturation ratio at the nucleation maximum, Jexp(cm3s1) is the experimental nucleation rate. Temperatures of the preheater, condenser, and laboratory, as well as pressure and flow rate, are averages over one measurement session of an isotherm.
n-pentanol–helium, 26-08-1998 n-pentanol–helium, 16-10-1998 
TS2=291.53K, TC=258.21K, P=98700Pa, Q=17.00cm3s, Tlab=293.79K TS2=296.60K, TC=263.36K, P=98800Pa, Q=17.01cm3s, Tlab=293.15K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
285.53 22.22 259.66 9.79 1.54E 5 289.75 1.04 264.88 8.14 8.85E 3 
285.22 5.34 259.61 9.55 3.87E 4 290.36 11.94 264.88 8.54 9.31E 4 
284.99 2.09 259.61 9.37 1.57E 4 290.98 149.02 264.88 8.98 1.07E 6 
284.75 0.67 259.61 9.18 5.21E 3 291.59 1531.71 264.90 9.42 1.01E 7 
284.31 0.14 259.61 8.85 1.16E 3          
                    
n-pentanol–helium, 28-08-1998 n-pentanol–helium, 19-10-1998 
TS2=291.45K, TC=258.21K, P=99800Pa, Q=16.67cm3s, Tlab=294.74K TS2=296.60K, TC=263.36K, P=99800Pa, Q=16.67cm3s, Tlab=293.15K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
286.12 121.24 259.70 10.28 7.70E 5 289.46 0.24 264.84 7.96 2.10E 3 
286.48 629.59 259.70 10.59 3.81E 6 290.05 3.08 264.85 8.34 2.48E 4 
286.75 1841.99 259.70 10.83 1.07E 7 290.65 39.30 264.87 8.75 2.91E 5 
          291.25 455.27 264.89 9.17 3.10E 6 
n-pentanol–helium, 27-10-1998 n-pentanol–helium, 28-10-1998 
TS2=291.50K, TC=258.42K, P=99200Pa, Q=16.50cm3s, Tlab=293.80K TS2=296.60K, TC=263.34K, P=99500Pa, Q=16.67cm3s, Tlab=293.80K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
284.49 0.18 259.84 8.80 1.48E 3 289.56 0.44 264.82 8.04 3.87E 3 
284.99 1.05 259.86 9.17 8.07E 3 289.88 2.66 264.83 8.25 2.20E 4 
285.48 8.81 259.87 9.55 6.31E 4 290.49 22.45 264.85 8.65 1.71E 5 
285.99 77.44 259.89 9.96 5.17E 5 291.00 179.45 264.86 9.01 1.27E 6 
286.48 532.67 259.90 10.37 3.32E 6 291.00 191.54 264.86 9.01 1.36E 6 
          291.47 1108.96 264.88 9.35 7.36E 6 
                    
n-pentanol–helium, 08-10-1998 n-pentanol–helium, 29-10-1998 
TS2=301.59K, TC=268.31K, P=102200Pa, Q=17.02cm3s, Tlab=293.15K TS2=306.49K, TC=273.06K, P=96600Pa, Q=16.67cm3s, Tlab=292.79K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
294.66 1.03 269.82 7.37 9.15E 3 299.47 1.14 274.67 6.74 1.14E 4 
295.26 14.75 269.82 7.72 1.20E 5 300.08 16.96 274.69 7.05 1.56E 5 
295.86 172.35 269.89 8.06 1.29E 6 300.65 156.23 274.71 7.34 1.33E 6 
296.43 1521.63 269.90 8.42 1.05E 7 301.28 1504.43 274.73 7.68 1.17E 7 
                    
n-pentanol–helium, 09-10-1998 n-pentanol–helium, 02-11-1998 
TS2=301.59K, TC=268.33K, P=100900Pa, Q=16.80cm3s, Tlab=293.15K TS2=306.5K, TC=273.08K, P=99100Pa, Q=16.80cm3s, Tlab=293.55K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
294.38 0.33 269.85 7.19 3.11E 3 299.18 0.30 274.67 6.60 3.02E 3 
294.97 4.07 269.88 7.52 3.51E 4 299.84 3.99 274.70 6.92 3.72E 4 
          300.37 40.75 274.72 7.19 3.52E 5 
          300.93 373.78 274.73 7.48 2.99E 6 
                    
n-pentanol–helium, 12-10-1998 n-pentanol–helium, 15-11-1998 
TS2=301.59K, TC=268.35K, P=98500Pa, Q=17.15cm3s, Tlab=293.15K TS2=306.53K, TC=273.10K, P=101700Pa, Q=16.68cm3s, Tlab=293.15K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
294.97 5.28 269.89 7.51 4.68E 4 299.45 0.51 274.70 6.72 4.86E 3 
295.55 58.65 269.92 7.84 4.79E 5 299.91 3.39 274.71 6.95 3.04E 4 
296.15 547.90 269.94 8.21 4.12E 6 300.45 32.11 274.73 7.22 2.68E 5 
          300.96 241.17 274.75 7.49 1.87E 6 
          301.46 1506.12 274.77 7.76 1.10E 7 
                    
n-pentanol–helium, 28-10-1998 n-pentanol–helium, 03-11-1998 
TS2=301.59K, TC=268.33K, P=99400Pa, Q=16.65cm3s, Tlab=293.20K TS2=311.65K, TC=278.26K, P=99220Pa, Q=16.86cm3s, Tlab=293.65K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
294.54 0.60 269.86 7.28 5.57E 3 304.41 0.43 279.90 6.07 4.47E 3 
294.98 3.86 269.88 7.53 3.38E 4 305.06 6.46 279.95 6.31 6.32E 4 
295.46 33.77 269.90 7.80 2.76E 5 305.69 83.55 279.98 6.59 7.49E 5 
296.03 312.27 269.92 8.15 2.36E 6 306.23 682.21 280.00 6.83 5.69E 6 
296.47 1586.16 269.93 8.42 1.13E 7          
                    
n-pentanol–helium, 04-11-1998 n-pentanol–helium, 05-11-1998 
TS2=311.39K, TC=278.26K, P=99550Pa, Q=16.73cm3s, Tlab=294.15K TS2=316.38K, TC=283.17K, P=99230Pa, Q=16.82cm3s, Tlab=295.15K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
304.13 0.09 279.93 5.93 1.04E 3 309.23 0.20 284.96 5.48 2.34E 3 
304.70 1.36 279.94 6.17 1.42E 4 309.55 0.69 284.94 5.61 8.04E 3 
305.35 18.53 279.98 6.45 1.77E 5 309.81 2.18 284.94 5.70 2.43E 4 
305.93 188.89 279.99 6.71 1.67E 6 310.21 11.56 284.96 5.85 1.22E 5 
          310.41 29.63 284.98 5.93 3.05E 5 
          310.77 138.19 284.99 6.07 1.36E 6 
          311.05 379.39 285.00 6.18 3.59E 6 
          311.33 997.57 285.02 6.29 9.09E 6 
n-pentanol–helium, 06-11-1998           
TS2=320.52K, TC=288.29K, P=99500Pa, Q=16.56cm3s, Tlab=294.15K           
TS1 N Tnuc Snuc Jexp           
314.40 0.16 290.13 5.06 2.06E 3           
314.68 0.50 290.16 5.14 6.26E 3           
315.01 1.87 290.17 5.25 2.24E 4           
315.32 7.15 290.19 5.35 8.21E 4           
315.98 74.01 290.23 5.57 7.79E 5           
315.98 186.26 290.25 5.66 1.89E 6          
The homogeneous nucleation rates of n-pentanol measured in the LFDC are presented. TS2 (K) is the temperature of the preheater, TC (K) is the temperature of the condenser, P (Pa) is the total pressure, Q(cm3s) is the average flow rate, Tlab (K) is the temperature of the laboratory, TS1 (K) is the temperature of the saturator, N(cm3) is the particle concentration, Tnuc (K) is the calculated temperature at the nucleation maximum, Snuc is the saturation ratio at the nucleation maximum, Jexp(cm3s1) is the experimental nucleation rate. Temperatures of the preheater, condenser, and laboratory, as well as pressure and flow rate, are averages over one measurement session of an isotherm.
n-pentanol–helium, 26-08-1998 n-pentanol–helium, 16-10-1998 
TS2=291.53K, TC=258.21K, P=98700Pa, Q=17.00cm3s, Tlab=293.79K TS2=296.60K, TC=263.36K, P=98800Pa, Q=17.01cm3s, Tlab=293.15K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
285.53 22.22 259.66 9.79 1.54E 5 289.75 1.04 264.88 8.14 8.85E 3 
285.22 5.34 259.61 9.55 3.87E 4 290.36 11.94 264.88 8.54 9.31E 4 
284.99 2.09 259.61 9.37 1.57E 4 290.98 149.02 264.88 8.98 1.07E 6 
284.75 0.67 259.61 9.18 5.21E 3 291.59 1531.71 264.90 9.42 1.01E 7 
284.31 0.14 259.61 8.85 1.16E 3          
                    
n-pentanol–helium, 28-08-1998 n-pentanol–helium, 19-10-1998 
TS2=291.45K, TC=258.21K, P=99800Pa, Q=16.67cm3s, Tlab=294.74K TS2=296.60K, TC=263.36K, P=99800Pa, Q=16.67cm3s, Tlab=293.15K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
286.12 121.24 259.70 10.28 7.70E 5 289.46 0.24 264.84 7.96 2.10E 3 
286.48 629.59 259.70 10.59 3.81E 6 290.05 3.08 264.85 8.34 2.48E 4 
286.75 1841.99 259.70 10.83 1.07E 7 290.65 39.30 264.87 8.75 2.91E 5 
          291.25 455.27 264.89 9.17 3.10E 6 
n-pentanol–helium, 27-10-1998 n-pentanol–helium, 28-10-1998 
TS2=291.50K, TC=258.42K, P=99200Pa, Q=16.50cm3s, Tlab=293.80K TS2=296.60K, TC=263.34K, P=99500Pa, Q=16.67cm3s, Tlab=293.80K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
284.49 0.18 259.84 8.80 1.48E 3 289.56 0.44 264.82 8.04 3.87E 3 
284.99 1.05 259.86 9.17 8.07E 3 289.88 2.66 264.83 8.25 2.20E 4 
285.48 8.81 259.87 9.55 6.31E 4 290.49 22.45 264.85 8.65 1.71E 5 
285.99 77.44 259.89 9.96 5.17E 5 291.00 179.45 264.86 9.01 1.27E 6 
286.48 532.67 259.90 10.37 3.32E 6 291.00 191.54 264.86 9.01 1.36E 6 
          291.47 1108.96 264.88 9.35 7.36E 6 
                    
n-pentanol–helium, 08-10-1998 n-pentanol–helium, 29-10-1998 
TS2=301.59K, TC=268.31K, P=102200Pa, Q=17.02cm3s, Tlab=293.15K TS2=306.49K, TC=273.06K, P=96600Pa, Q=16.67cm3s, Tlab=292.79K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
294.66 1.03 269.82 7.37 9.15E 3 299.47 1.14 274.67 6.74 1.14E 4 
295.26 14.75 269.82 7.72 1.20E 5 300.08 16.96 274.69 7.05 1.56E 5 
295.86 172.35 269.89 8.06 1.29E 6 300.65 156.23 274.71 7.34 1.33E 6 
296.43 1521.63 269.90 8.42 1.05E 7 301.28 1504.43 274.73 7.68 1.17E 7 
                    
n-pentanol–helium, 09-10-1998 n-pentanol–helium, 02-11-1998 
TS2=301.59K, TC=268.33K, P=100900Pa, Q=16.80cm3s, Tlab=293.15K TS2=306.5K, TC=273.08K, P=99100Pa, Q=16.80cm3s, Tlab=293.55K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
294.38 0.33 269.85 7.19 3.11E 3 299.18 0.30 274.67 6.60 3.02E 3 
294.97 4.07 269.88 7.52 3.51E 4 299.84 3.99 274.70 6.92 3.72E 4 
          300.37 40.75 274.72 7.19 3.52E 5 
          300.93 373.78 274.73 7.48 2.99E 6 
                    
n-pentanol–helium, 12-10-1998 n-pentanol–helium, 15-11-1998 
TS2=301.59K, TC=268.35K, P=98500Pa, Q=17.15cm3s, Tlab=293.15K TS2=306.53K, TC=273.10K, P=101700Pa, Q=16.68cm3s, Tlab=293.15K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
294.97 5.28 269.89 7.51 4.68E 4 299.45 0.51 274.70 6.72 4.86E 3 
295.55 58.65 269.92 7.84 4.79E 5 299.91 3.39 274.71 6.95 3.04E 4 
296.15 547.90 269.94 8.21 4.12E 6 300.45 32.11 274.73 7.22 2.68E 5 
          300.96 241.17 274.75 7.49 1.87E 6 
          301.46 1506.12 274.77 7.76 1.10E 7 
                    
n-pentanol–helium, 28-10-1998 n-pentanol–helium, 03-11-1998 
TS2=301.59K, TC=268.33K, P=99400Pa, Q=16.65cm3s, Tlab=293.20K TS2=311.65K, TC=278.26K, P=99220Pa, Q=16.86cm3s, Tlab=293.65K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
294.54 0.60 269.86 7.28 5.57E 3 304.41 0.43 279.90 6.07 4.47E 3 
294.98 3.86 269.88 7.53 3.38E 4 305.06 6.46 279.95 6.31 6.32E 4 
295.46 33.77 269.90 7.80 2.76E 5 305.69 83.55 279.98 6.59 7.49E 5 
296.03 312.27 269.92 8.15 2.36E 6 306.23 682.21 280.00 6.83 5.69E 6 
296.47 1586.16 269.93 8.42 1.13E 7          
                    
n-pentanol–helium, 04-11-1998 n-pentanol–helium, 05-11-1998 
TS2=311.39K, TC=278.26K, P=99550Pa, Q=16.73cm3s, Tlab=294.15K TS2=316.38K, TC=283.17K, P=99230Pa, Q=16.82cm3s, Tlab=295.15K 
TS1 N Tnuc Snuc Jexp TS1 N Tnuc Snuc Jexp 
304.13 0.09 279.93 5.93 1.04E 3 309.23 0.20 284.96 5.48 2.34E 3 
304.70 1.36 279.94 6.17 1.42E 4 309.55 0.69 284.94 5.61 8.04E 3 
305.35 18.53 279.98 6.45 1.77E 5 309.81 2.18 284.94 5.70 2.43E 4 
305.93 188.89 279.99 6.71 1.67E 6 310.21 11.56 284.96 5.85 1.22E 5 
          310.41 29.63 284.98 5.93 3.05E 5 
          310.77 138.19 284.99 6.07 1.36E 6 
          311.05 379.39 285.00 6.18 3.59E 6 
          311.33 997.57 285.02 6.29 9.09E 6 
n-pentanol–helium, 06-11-1998           
TS2=320.52K, TC=288.29K, P=99500Pa, Q=16.56cm3s, Tlab=294.15K           
TS1 N Tnuc Snuc Jexp           
314.40 0.16 290.13 5.06 2.06E 3           
314.68 0.50 290.16 5.14 6.26E 3           
315.01 1.87 290.17 5.25 2.24E 4           
315.32 7.15 290.19 5.35 8.21E 4           
315.98 74.01 290.23 5.57 7.79E 5           
315.98 186.26 290.25 5.66 1.89E 6          
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