292 CON("ERNl.\(J THE EFFKCT i)F (illAVITV 



In the arriclc rclVrrcJ to above, Vcgard proves from I'on- 

 f^ideiations of dynainical and therniodynamical equilibrium, 

 that the final (listril)ution of the solute will depend on whether 

 the density of the solution at that particular eimeentration 

 increases or decreases for an infinitely small inci'cnise in con- 

 centration. In the special case in which a small change in 

 concentration makes no corresponding change in density, the 

 concentration of the solution will remain unifonn throughout 

 (-\'en when ex])ose(l to gravity. 



Suppose now ihc homogeneous solution is exposed to grav- 

 ity, its concentration will begin to change, solute flowing from 

 ilic t )]) to the bottom or vice versa, according as the density at 

 that particular concentration increases oi- decreases with the 

 coiircntration. This flow will be comparatively large at first, 

 but will fall away to zero as an exponential function of the time. 

 A\'heii e(|nilibrinni is reached, there is the same concentration 

 grail icnt at cNcry height of the column. If now we consider 

 the force of gf:i\ iry removed, the solution will begin to difl^use 

 back to its initial condition of uniform concentration, and it 

 seems reasonable to supjx)se that the flow will be exactly simihir 

 to that in the oi'igiiial siolution, that is it will be cuiuparatively 

 large at first, anil w\]] fall away as an ex])oncnti;d function <^tf 

 ihe tinii". 



If this !)!■ inic. then the original difi'usion How is exactly 

 -Iniilai- to <ine in a tulx' not exjXKsed to any force such as gravity 

 and where the initial concentration gradient is ecju'd to that 

 whiidi actually exists in final efjuilibrinm in the solntii)n ex])oseil 

 to gravity. 



Xovv it is always assumed that the diUnsioii of a soliUe is 

 analagfuis to the How of heat, and obeys Foui'ier's lineai- difi'u- 

 sion laAV, and the conditions in the differential e(puition: 



d^ _ dr 



dx'^ ~ dt 



