A convection-dispersion flow of vapor water should be treated as a component of the whole gas mixture in soil, since all components are transported not only by molecular diffusion but by mechanical dispersion as a result of counter movement. Binary system can, therefore, explain the interactions between component-flow equations. One of the significant results shows the gas mixture flux is not influenced by dispersion, but directly corresponds to a convective term in heteronomous expression. The Darcian-type gas transport equation, or transport equation in autonomous expression is verified to have its content necessarily. Thus we express the gas transport equation in heteronomous form as,

                                                                                                            (1)

where is mole flux of gas mixture (mol/m²/s), , volume fraction of gas, , mole density of mixture gas (mol/m³), , flow rate (m/s). And the equation in autonomous form is also expressed as,

                                                                                   (2)

where , mole conductivity of gas (mol s/kg), , pressure gradient (Pa/m), , intrinsic gas permeability (m²), , viscosity (kg/m/s). Comparison of Eq.(1) with (2) gives the flow rate of gas mixture.

                                                                                                          (3)

Thus we can formulate the binary transport equations in terms of Eq. (3)

For vapor water                                  (4)

For other components in air                       (5)

The whole gas mixture                                    (6)

where  is the counter-dispersion coefficient, , the mole phase transition rate (mol/m³/s), , mole concentration of vapor (mol/m³), , mole concentration of other components(mol/m³). Since Eq. (6) is only the sum of Eqs. (4) and (5), either Eq. (4) or (5) is sufficient to be solved simultaneously together with Eq. (6). The whole gas flux is driven by the gradient of the square of pressure while the convective terms in components cannot say to be driven by it.

The theory is now applied to the soil evaporation problem, and solved simultaneously with Darcian liquid flow equation,

                                                                         (7)

where  is volume fraction of soil liquid, , mass density of soil liquid (kg/m³), , hydraulic conductivity (kg s/m³), , matric potential (J/kg), , gravitational acceleration (m/s²), , molar mass of liquid water (kg/mol). Assumed that the mole phase transition rate is proportional to the difference between liquid and vapor activities, numerical results show fairly well agreement with experimental data.