From the definition of Sauter mean diameter in the below link:
http://www.thermopedia.com/content/1108/
Can we assume the variance to be in the following form?:
variance = (d_64)^2 - (d_32)^2
OR, if you are not too familiarized with the notation, see gif file below.
THANKS IN ADVANCE!
Can you please provide more information about the intended meaning/interpretation of your variance? Did you measured the sizes of several particles (expressed by their Sauter diameters), calculated the mean value and now you want to express the magnitude of deviations between the replicates? Or do you have a particle distribution and you want to express the width of your distribution? In both cases, the given formula doesn't make much sense to me (besides that you use an exponent of 2 over both, d_64 and d_32, in your text but only one over the brackets in the gif file).
Dear Stephan,
Perhaps you are not too familiarized with the particle size notation. The d_64 would be the square root of the ratio of two sums. See image below and the algebraic power of d_pq. Does it make sense now? As to my interpretation for variance would be the classic one i.e. + ^2, where is an average of x_i samples
If there is no way to calculate the variance of a sauter diameter measurement, how can we assess the goodness of fit for experimental data with a sauter diameter model? For instance, from the literature we can find expressions for correlating the Sauter diameter, such as the one shown below. Is an R^2 assessment good enough for these purposes?
When comparing your measurements with a literature model, the R^2 should be at least a good starting point to assess the goodness of the fitting. If you compare the model predictions with the measurements in a parity plot (i.e. measured values vs. predictions), the plot should give you also some idea about systematic deviations - for example, if your Sauter diameter is well-predicted for one surface tension, but the prediction fails for a second surface tension. Furthermore, I recommend to look at the deviations between replicate measurements, if you have some, (e.g. expressed by the standard deviation) and to compare it with the deviations from the model predictions (i.e. is the deviation/agreement statistically significant related to the measurement reproducibilty?).
Good luck.
Regards,
Stephan
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