- #1
davidgrant23
- 22
- 0
Hi all,
I am currently operating a piece of equipment that essentially collects particles and separates them based on their size. Essentially you have 8 stages, and each stage has a differing size of particles it collects. For example:
Stage----Size of Particles (D) (um)-----Mass Collected (M) (mg)
1-------------0.1 - 0.2------------------------------1
2-------------0.2-0.5------------------------------0.1
3-------------0.5 - 1--------------------------------1
4-------------1 - 2----------------------------------0.5
5-------------2 - 4-----------------------------------1
6-------------4 - 5----------------------------------0.5
7-------------5 - 9------------------------------------3
8-------------9 - 10----------------------------------2
Now, as you can see each stage has a different range of sizes collected. Stage 1 has a "width" of 0.1 um, while stage 7 has a width of 4 um. Because of these different stage widths it is common to normalise the plot to make the results indepedent of stage width, like so:
dM/dlogDp = dM/log(Du)-log(Dl)
where Du is the upper stage width and Dl is the lower stage width (ex, for stage one Du is 0.2 and Dl is 0.1). If you then plot this data:
Stage----------dM/dlogDp
1----------------3.321928
2----------------0.251294
3----------------3.321928
4----------------1.660964
5----------------3.321928
6----------------5.159426
7----------------11.75215
8----------------43.70869
Now, my question is, what exactly is the physical meaning of these new results. The initial results show me the mass of particles between 0.1 and 10 um collected after a certain time of experiment or some other factor. The total mass is 9.1 mg. But, these normalised results have much higher numbers. Do they have any inherent meaning other than being independent of stage width. Am I missing some fundamental calculus principle that imparts meaning to dM/dlogDp?
Thanks.
I am currently operating a piece of equipment that essentially collects particles and separates them based on their size. Essentially you have 8 stages, and each stage has a differing size of particles it collects. For example:
Stage----Size of Particles (D) (um)-----Mass Collected (M) (mg)
1-------------0.1 - 0.2------------------------------1
2-------------0.2-0.5------------------------------0.1
3-------------0.5 - 1--------------------------------1
4-------------1 - 2----------------------------------0.5
5-------------2 - 4-----------------------------------1
6-------------4 - 5----------------------------------0.5
7-------------5 - 9------------------------------------3
8-------------9 - 10----------------------------------2
Now, as you can see each stage has a different range of sizes collected. Stage 1 has a "width" of 0.1 um, while stage 7 has a width of 4 um. Because of these different stage widths it is common to normalise the plot to make the results indepedent of stage width, like so:
dM/dlogDp = dM/log(Du)-log(Dl)
where Du is the upper stage width and Dl is the lower stage width (ex, for stage one Du is 0.2 and Dl is 0.1). If you then plot this data:
Stage----------dM/dlogDp
1----------------3.321928
2----------------0.251294
3----------------3.321928
4----------------1.660964
5----------------3.321928
6----------------5.159426
7----------------11.75215
8----------------43.70869
Now, my question is, what exactly is the physical meaning of these new results. The initial results show me the mass of particles between 0.1 and 10 um collected after a certain time of experiment or some other factor. The total mass is 9.1 mg. But, these normalised results have much higher numbers. Do they have any inherent meaning other than being independent of stage width. Am I missing some fundamental calculus principle that imparts meaning to dM/dlogDp?
Thanks.