Let's suppose an electrochemical system with given coordinates:(adsbygoogle = window.adsbygoogle || []).push({});

We are interested in diffusion motion of ion ##i## in the direction of ##y## axis.

Concentration ##c_i## is a function of both ##x## and ##y##. Concentration ##c_i## at ##y=0## is zero.

The system is steady thus ##\frac{\partial c_i}{\partial y}(x)## is not a function of ##y## (##\frac{\partial c_i}{\partial y}(x)## is constant with ##y##).

The first Fick's law for ion ##i## is (for simplicity I don't write ##i## subscript anymore):

$$J_{y}^{dif}(x,y=d) = - D \cdot \frac{\partial c}{\partial y}(x,y=d) = - D \frac{c(x,y=d)}{d}$$

The diffusion molar flux is:

$$J_{y}^{dif}(x,y=d) = c(x,y=d)\cdot v_{y}^{dif}(x,y=d)$$

where ##v^{dif}## is the diffusion linear velocity of ion ##i##:

$$v_{y}^{dif} = -D \cdot \frac{1}{c}\cdot \frac{\partial c}{\partial y}$$

The diffusion velocity clearly changes because concentration changes with ##y##.

Now I can put the diffusion velocity into the first equation and express ##D##:

$$D = \frac{-c(x,y=d)\cdot v_{y}^{dif}(x,y=d)\cdot d}{c(x,y=d)}=-v_{y}^{dif}(x,y=d)\cdot d$$

This seems strange to me. Since both diffusion coefficient ##D## and length ##d## are considered constant, the diffusion velocity ##v_{y}^{dif}(x,y=d)## seems to be constant along ##x## independently of the functions ##c(x) \ at \ y=d## and ##\frac{\partial c}{\partial y}(x) \ at \ y=d##. Is it true?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Diffusion velocity

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**