Question

You purchase an expensive O2 microelectrode and use it to measure the dissolved O2 profile in a sediment core that you obtained from Long Island Sound. You find that the O2 concentration on the water-sediment interface is 240 mol/L, and it sharply drops to 40 mol/L at 0.2 cm deep in the sediment. If the corresponding dissolved O2 diffusion coefficient (Ds) in porewater seawater is 1.0 × 10-5 cm2 /s. The porosity () of sediment is approximately constant over the sampled interval with  = 0.9. Calculate the diffusive flux of O2 across the sediment – water interface assuming Fick’s First Law of diffusion for porous media in 1-dimension. Make sure that you indicate the sign of the flux (into or out of the sediment).

Answer 1

According to Ficks first low: The diffusion flux to the conc. Under steady state.The flux goes from region of high concentration to region of low concentration,with magnetude that is praportional to the conc. Gradient . i.e. J = -D (dC/dx)..............1

-ve sign indicate that J is positive when momentum is down the concentration gradient i.e . Negative sign cancel negative gradient along the direction positive flux .

Where J = diffusion flux

D= diffusion coefficient

C= concentration

X = position

In given problem diffusion coefficient (D) is 1×10^-5 cm2/sec

I.e 1×10^-9 m2/sec

dc = (40-240)×10^-3 mol/m3 =-200 ×10^-3 mol/m3

dx = (0.2)cm = 2×10^-3 m

Putting all value in equation 1

J= -((10^-9)×(200×10^-3))/(2×10^-3)

J = 10^-7 mol/m2 sec

Hence diffusion flux having positive sign.