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

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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.