7. Question: Diffusive Mass Transfer

QUESTION: Consider a packet of tablets that is comprised of a formed sheet that includes troughs to hold each tablet and a flat aluminium foil sheet for the lid. The formed sheet is a polymer L=50

m thick with each trough of diameter D=5mm and depth h=3mm and a binary diffusion coefficient

 =6E-14 m^2/s . The aluminium is assumed to be impermeable. The molar concentration of water on the outside of the polymer is

=4.5E-03

and on the inside is =0.5E-03. Determine the rate at which water vapour is transferred through the trough wall to the tablet.

Sketch:

Assumptions:

• Steady-state, 1D conditions

• Stationary medium

• Polymer sheet is much thinner that the trough so diffusion can be analysed as if it occurs through a plane wall

Method:

From the assumption that we are working with a stationary medium we can start with the following equation for absolute molar flux:

Then from the assumption that we can analyse the polymer sheet as a plane wall of width L that has the boundary surface conditions

and

:

We have values for and , in addition to knowing that x=CA/C we can say the following. And after multiplying by area:

From this we can sub in the calculation for area: 

Now we have an equation for the vapour transfer rate through the polymer plane wall in terms of values we already have so we can move on to calculating the final value..... 

** Thoughts as to how this is useful for a pharmaceutical company to know**

The shelf life of the medicine can be figures out by the rate at which water vapour is transferred through the polymer sheet. The faster it does, the more water transferred to the tablet in a shorter time and hence the shorter the tablets shelf life. Therefore, the thickness of the polymer sheet should be altered to increase the shelf life of the tablets. However this is more expensive so the companies will have to reach a compromise between shelf life and cost.