208 



SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 



P in 



Figure 8-8. Illustration of Direction of 

 Diffusion of P in a Mixture of P in Q. 



therefore, it is the rate of change of concentration, c, with distance, x, which 

 determines the rate of diffusion. 



These intuitions were first set down and experimentally proven by the in- 

 genious German anatomist, Adolf Fick, in 1855: 



j = DA 



dc_ 

 dx 



(Fick's first law) 



where dcjdx is the instantaneous rate of change of concentration with dis- 

 tance, called the concentration gradient, in moles per liter per cm; "j" is the 

 flux (i.e., the flow rate, v) — the number of moles passing through a particu- 

 lar area, A cm 2 , in 1 sec; and D is the proportionality constant, which con- 

 tains all the other factors — some of them still unknown — upon which the 

 rate of diffusion depends. Self-diffusion of water across an erthythrocyte 

 membrane is an example. Absorption of gaseous 2 by the blood capillaries 

 in the lung is another example: both the partial pressure of 2 and the con- 

 centration in the circulating blood plasma are constant in time. Fick's first 

 law is limited to the case in which concentrations do not change — the 

 steady-state condition — and the source and the sink are infinite. 



However, there are many specific cases, particularly in the gastrointestinal 

 tract and associated with assimilation of the degraded products of foods, in 

 which the concentration gradient is not constant, the state is not steady. 

 Any periodic or sporadic phenomenon which makes a sudden change in the 

 rate of supply of reactants to a certain part of the living thing, will cause a 

 deviation from the steady state. Thus in the volume in which the change 

 occurs, the rate of change of concentration, dc/dt, is given by 



dc/dt = D d 2 c/dx 



(Fick's second law) 



Since d 2 c/dx 2 can be written — ( — , and since dcjdx is the concentration 



dx \dx) 



gradient, we see that the second law states that the rate at which the concen- 



