ON DIFFUSION; OSMOSIS 



209 



tration changes within a volume is proportional to the rate of change of the 

 concentration gradient at the boundaries of the volume. 



One simple example will be used to illustrate the problem described by 

 Fick's second law. This will be done only qualitatively, for the detailed de- 

 scription is too complicated to be practical here. Consider the red blood cell, 

 with various components contained within, and separated from the medium 

 by a membrane, the cell wall. There are fluids on both sides of the wall in 

 osmotic equilibrium (see Chapter 2). This is a condition of no net change: 

 potassium ion, at higher concentration inside the cell is being transported in 

 both directions across the cell at equal rates; sodium ion, at higher concen- 

 tration outside the cell, is being transported in by diffusion, out by "active 

 transport," but both at the same rate so that there is no net change. Water 

 moves across the membrane freely in both directions. (Recent radioactive 

 tracer experiments using tritium have shown that complete exchange of 

 water can occur in a few milliseconds.) If for some reason the "sodium 

 pump," which provides the active transport, fails, then both K + and Na + 

 will diffuse passively, each in the direction towards lower concentration 

 (Figure 8-9). The rate of diffusion, expressed by the rate of change of con- 

 centration, dc/dt, is given by the second law as D d 2 c/dx 2 . Solution of the 

 equation for c, gives c as a function of t; or c = /(/). The form, /, can be 

 worked out explicitly, provided certain other conditions are known. The 

 result is approximately r K+ = c { + c 2 /y/T+t for the decay of the internal 

 K + concentration and r Na+ = c[ — c' 2 /y/t + t for the buildup of internal 

 Na + concentration to the concentrations of K + and Na + in the plasma in 



Time after failure (sec) 



Figure 8-9. Readjustment of Concentration of Na + and K + Inside the Erythrocyte 

 Following Failure of the Sodium Pump — A Diffusion-Controlled Process. Final values, 

 1 38 and 1 6, are those of the plasma. 



