I've been struggling with the lognormal function in excel for the past week now.
There's a particle analysis that I've been trying to replicate in excel, using formulas, instead of probability graph paper, and so far it has been challenging.
The data stated the following :
Dvs (mean volume-surface diameter) = 231 um
Dvs transformed to D50 using Hatch-Choate transformation
log d50 = log dvs + 1.151 log2(S)
D50 (mean drop size diameter ) = 264um
Standard deviation (S) = 1.7
The d50 diameter was then transformed to d16 diameter by using d16 = d50/S
d16 = 155 mm
This represents the drop size diameter equivalent to 0.1587 wt fraction of the dispersion.
Based on the above definition I believe S = geometric standard deviation, and d50 = geometric mean
For the excel lognorm.dist formula - the inputs are (x , mean, SD), where the mean = standard deviation of ln (x), and SD = standard deviation of ln (x)
This is the part where I'm confused as I'm not too sure what inputs should I put in to replicate the above data. Originally, d50 and d16 were plotted on the probability graph paper, and the entire range of droplet size could be predicted.
I did some experimenting and found that if I substitute mean = ln (264) and SD = ln (1.7), the plot of the data (droplet size vs cumulative weight %) matches what the graph paper shows. But I'm not sure if I am even doing this correctly or it was just luck. substituting mean = ln(264) makes sense to me, but I'm unsure of ln (1.7).
Appreciate if someone can enlighten me.