A simplified flowchart of a continuous process for the microencapsulation of beta cells is shown

below. There are two inputs to the microencapsulation system: the aqueous cell solution and

aqueous alginate solution. The outputs are the solid alginate hydrogel microcapsules $($containing

beta cells, alginate, and water$)$ and a supernatant solution $($also with beta cells, alginate, and

water$)$ The process is at steady$-$state and there are no chemical reactions occurring.

The aqueous cell solution input $($the Feed$)$ has $12\mathrm{.}48mg$ beta cells $\frac{?}{mL}$ dissolved in water $($no

alginate$)$ and its specific gravity is $1\mathrm{.}04.$ The aqueous alginate solution input contains $7\mathrm{.}0$ mass $\%$

alginate dissolved in water $($no beta cells$).$ The mass flow rates of the input cell solution and

input alginate solution are equal.

The microcapsules contain $11\mathrm{.}0mg$ beta cells $\frac{?}{g},5\mathrm{.}0$ mass $\%$ alginate and the rest water. The

mass flow rate of the output supernatant is $1\mathrm{.}6$ times that of the mass flowrate of the

microcapsules.

It is desired to produce $B\frac{g}{m}in$ of the microcapsules, where $B$ is

$\frac{g}{m}in.$

a$.$ Draw and label a flowchart for the process. $($The one given above is not completely

labeled$).$ Note: Please redraw the flowchart by hand$|$

b$.$ From the General Balance Equation, derive the Balance Equation applicable to the

problem $($e$.$g$.$ Steady$-$state, so Accumulation $=0).$ Write all the possible Material

Balances.

c$.$ Carry out a degree$-$of$-$freedom analysis for the system in $($a$).($Hint: The cells can be

considered as one chemical species$).$ Please identify the unknowns $($based on your

flowchart labels$)$ and the equations $($e$.$g$.$ from Material Balances, from given, etc.$)$ d$.$

Solve for all the unknowns. e$.$ Determine what percent of the beta cells in the feed is

recovered in the microcapsules. $f.$ The laboratory process is to be commercialized to

produce $4k\frac{g}{h}$ of product microcapsules. What is the scaling factor? g$.$ For $($f$),$ determine

the required mass flow rate of the feed cell solution in $k\frac{g}{h}.$