[smgrojean]

Hello,

I am working on creating a coated beadlet at work currently and I needed to calculate what size starting beadlet to work with recently in order to achieve a specific end product size.  I figured out a round about way to do it but I was wondering if anyone could think of an easier solution for the future.

So I started with 20 -25 Mesh beadlets (which I measure to average about 0.819 mm in diameter).

The beadlets are coated with a vitamin and film coating which give them an assay of about 56% assay.  At this time the beadlets are 1.450 mm in size.

I know that Volume of a sphere is = 1/6 PI D^3; so my original beadlets are 0.288mm3, and my final coated beadlets are 1.596mm3.  I know therefore that the coating comprises 1.308 mm3.

I started with 275 g of Beadlets and applied 7905.5 g of coating.  This gives me a weight ratio of (790.5 g /275 g = 2.875). 

I then calculated the volume ratio of the coating to the beadlet (1.308 mm3 / 0.288mm3 = 4.542)

I used that volume and weight ratio to get a new ratio of volume to weight 4.542 / 2.875 = 1.580.

I then calculated that if I wanted to increase the assay of the core (which I do to 65%) that I would need to apply 2028.95 g of coating onto that same starting amount of beadlets (275g). 

I used that to create a new weight ratio for the 65% coating (2028.95 g / 275 g =7.378)

I calculated a volume ratio using the volume/weight ratio from above with the weight ratio for the 65% coating (1.580 x 7.378 = 11.66)

I then calculated the volume of my desired final product size (16 - 20 mesh) Volume = PI/6 x (1.000 mm)^3 = 0.523598 mm3.

I then calculated the volume of the starting sugar I needed = (0.523598 mm3 / 11.66 = 0.0449 mm3)

0.0449 mm3 = PI/6 x (D^3)  so D = 0.4412 mm which is about half way between 35 mesh (0.500 mm and 40 mesh 0.400mm).

That to me seemed like a really complicated and convoluted way to go about solving this kind of problem is there any simpler method?

[curiouscat]

Can you restate your goal? What are the givens / constraints?

[smgrojean]

Sure,

The goal was to take a current product with 56% assay, a starting beadlet size of 20 - 25 Mesh and a final beadlet size diameter of 1.450mm, turn it into a beadlet with 65% assay, a final beadlet size of 0.450 mm and calculate what starting beadlet size should be used to obtain that goal.