Ecological Sustainability

42 Ecological Sustainability

V C Q K C C

m m m c

g/

 

= − −

0 12

( ) minµ

(2.7a)

V C K C C K C

c c m c c

g/



= −

12 2

( ) minµ (2.7b)

Written in state form, we have

 

C C K V C K V Q V

m m m c m m

/ / / g/(Lmin)= − + + ( ) ( )

12 12 0

µ (2.8a)



C C K V C K K V

c m c c c

/ / g/(Lmin)= − + ( ) ( )

12 2 12

µ (2.8b)

Note that mass diffusion rates depend on concentrations or mass/volume, so

the diffusion rate constants, K

12

and K

2

,

must have the dimensions of liters

per minute.

From the ODEs Equations 2.8a and 2.8b, we see that the system is linear

and can be described by an SFG as shown in Figure 2.7. The SFG can easily

be reduced by Mason’s rule