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-Fundamentals: Mass transfer

2.2 Fick's law

Let's consider the orange phase, as represented in the figure and let's imagine to put a physical barrier in the middle of the container in such a way to create two different volumes of the same homogenous orange phase. Finally we add only in the left part of the container some red particles.

When the physical barrier is then removed, a gradient of concentration exists between the left and the right part of the container. A disequilibrium has been created within the same phase and the red particles move from their initial position to the right part of the container following the direction of decreasing particle concentration z.

This phenomenon of the molecular diffusion stops when the concentration of the red particles is uniform all over the phase again.

The flux of components has been quantified by Fick in the following equation, known as Fick's Law:

Ni = - Di [ dci/dz ]

where
Ni = [mol/(sec. cm2)] = flux of component i
Di = [cm2/sec.] = diffusion coefficient
ci = [mol/cm3] = concentration of the component i
z  = [cm] = direction of the mass transfer

The order of magnitude for the diffusion coefficient in the three different media is:

  • In liquids: Di = 10-5 [cm2/sec.]
  • In gases: Di  = 10-1 [cm2/sec.]
  • In solids: Di  = 10-10 - 10-13 [cm2/sec.]