mixing tank problems
A favorite application of first order linear ODE systems is to mixing tank
problems involving multiple "mixing tanks" of solute and solvent in solution
with time evolving concentrations. Eigenvalues of the system give characteristic
times for reaching equilibrium and for any oscillations which occur in reaching
equilibrium (closed systems). This is also a special case of "compartimental
analysis" useful in pharmacokinetics (movement of drugs through the body). The
single tank starts the analysis at the beginning of the DE course.
- Edwards, Penney Calvis Edition 4 section 1.5:
33, 36, 37,
45 <<< HOMEWORK solutions
ignore the rest of this page:
- one mixing tank mixode.pdf,
mixingtanksolution.pdf [general
solution for all parameter values]
Maple template [Lake Erie example]
- 3tank.pdf, 3tank.mw
closed and open 3 tank systems [general solution for all parameter values]
- Edwards and
Penney, Differential Equations and Linear Algebra, section 7.3:
compartmental analysis: real
eigenvalues: example 2 (open
case+comparison with closed case: real/complex eigenvalues) ,
complex
eigenvalues: example 4 (closed
case);(more examples 7.3.35,36)];
do 7.3: 37 [closed 3 tank system with
oscillations (explanation,
text example4.mw), plug into Eq(22),
solve by eigenvector method] (solution
on-line: .mw,
.pdf);
choose
one problem from 7.3: 27-30 (solution
on-line: .mw).