Formulate mixing matrixes for the following problems and solve the evolution of the system until equilibrium

Formulate mixing matrixes for the following problems and solve the evolution of the system until equilibrium. In task 1-3 deliver at least the mixing matrix, initial conditions, particular solutions for each cell and graphs showing convergence to equilibrium. In task 4 first formulate a matrix representing the actual surface, for instance A =

and then the mixing matrix

 (coupling of cells)

1. 4 Tanks, T1, T2, T3 and T4, T1=100L, T2=3000L, T3=900 and T4=6000L. All tanks are series connected, double direction pumping from T1 to T2 to T3 to T4. The pumps operate at 100 L/min. All tanks have initial concentration C_i(0) = 0 only T1 has however C₁(0) = 400g/m³ desinfectant.

2. All same as problem 1, mixing single direction, T4 is connected to T1. Else all the same.

3. All same as problem 1 but star configuration, flow is in both directions. T1 is star center.

4. A medical research wishes to study how an active ingredient spreads inside some tissue after injection. How does the matrix look like if we consider 2D and 25 cells making a 5x5 set of fields? Injection point is central, position 3,3.