Fick's first law

The first Fick's law suggested that the mass of fluid diffusing is proportional to the concentration gradient. As per the law,

                                                                                                               (31.1)

                                                                                                           (31.2)

Where, F is the mass flux of solute per unit area per unit time, D_d is the diffusion coefficient (L²/T), C is the solute concentration (M/L³), ∂c/∂x is the concentration gradient (M/L³/L). The negative sign indicates that the movement of solute is from higher concentration to lower concentration. This law is similar to Darcy's law where flow is take place from the higher head to lower head.

Fick's second law

Consider the control volume shown in Fig. 31.2 below

Let F be the mass flux of solute entering in to the control volume per unit area per unit time and dA is the cross sectional area of the control volume.

The mass flux in to the control volume is

                                                                                                                   (31.3)

and the flux out from the control volume is

                                                                                                (31.4)

Therefore, the net flux = flux in – flux out

                                                                                   (31.5)

                                                                                                        (31.6)

As per the law of conservation of mass

Net mass flux is equal to the rate of change in mass stored in control volume in time dt