Symbiotic Fungi: Principles and Practice (Soil Biology)

5 Measurement of Net Ion Fluxes Using Ion-Selective Microelectrodes 69
5.3.2 Estimation of Ion Fluxes at the Root Surface
When a root is placed in a solution where ions are moving by diffusion and where
the coordinates of radial symmetry apply (Fig. 5.2), the net radial ion flux is given
by the following equation (Newman et al. 1987; Henriksen et al. 1992):
J ¼ 2pD C2 ð C1Þ
ln ðr2=r1Þ ðin mmol cm 1 s 1 Þ; ð5:6Þ
with D diffusion coefficient (cm 2 s 1 ), C1 concentration at a radial distance r1, C2
concentration at a radial distance r 2, r 1 and r 2 radial distances from the cylinder
centre.
The ion flux crossing the transversal root section of area A and with a root
density r (that we take by default equal to 1) for 1 h will be
kð2pD=ArÞðC2=C1Þ J ¼ ; ð5:7Þ
ln ðr2=r1Þ kð2D=r2ÞðC2=C1Þ J ¼ : ð5:8Þ
lnðr2=r1Þ Finally, we obtain the following equation used to calculate the ion flux occurring at
the root surface:
kð2D=r2ÞðC2=C1Þ J ¼
ln½ðd2þrÞ= ðd1þrÞŠ ðin mmol g 1 root fwt 1 h 1 Þ; ð5:9Þ
Fig. 5.2 Schematic representation of the radial symmetry of ion diffusion occurring in the
solution at the surface of the root