30 MINERAL SALTS ABSORPTION IN PLANTS 



This equation indicates the minimum amount of energy which 

 must be supplied in transferring m molecules of solute from the 

 lower to the higher concentration under the same conditions. 



In biological systems, one is often concerned with diffusion of 

 substances across lipid membranes which have low permeability. 

 In these circumstances, Pick's law does not apply, even approx- 

 imately. The diffusing particle has to acquire sufficient kinetic 

 energy to overcome an appreciable potential energy barrier {fi^ in 

 passing from solvent into membrane, and a series of smaller potential 

 energy barriers (//J in the bulk of the membrane, before it passes into 

 solution on the other side via the final energy barrier (jx^ (Fig. 6a). 

 The particle can be thought of as alternately vibrating about a mean 

 position, and moving to a new position when it acquires sufficient 

 energy {activation energy) by collisions with neighbouring particles. 

 Such diff"usion has a high Q-^q (often 2-3) because at higher tem- 

 peratures more particles acquire sufficient energy to diffuse in a 

 given time. Diffusion may be assisted by the presence in the 

 membrane of substances with which the penetrating particle can 

 combine reversibly to form more soluble complexes {facilitated 

 diffusion, Danielli, 1954). Facilitated diffusion resembles active 

 transport (see below) in exhibiting saturation effects, competition 

 between particles, and specificity, but differs in that movement is 

 always along a concentration gradient, and metabolic energy is not 

 directly involved. 



C. Mass Flow 



A familiar example of mass flow is the discharge of liquid from 

 a burette under the influence of gravity. Rates of mass flow can be 

 calculated from Poiseuille's law as follows: 



dm=— (rV8^)-(d/7/dx)-d/ 

 where dm = the quantity of liquid passing a given plane in a tube ; 

 r = radius of tube ; 

 d/7/djc = the pressure gradient; 

 dt =time; 

 7] = coefficient of viscosity of the liquid. 



Because mass flow varies with the square of the area (r*), whereas 

 diffusion is proportional to area, mass flow is reduced relative to 



