The first objective is to develop an equation to characterize the mass transport of water in an unsaturated porous material. Richards  was among the first authors to study the mechanisms of water transport in unsaturated porous solids. In 1931, he proposed the following equation to describe the flow of water under capillary suction:
where θ is the water content, K is the permeability of the porous material, and Γ is the capillary potential.
This relationship, known as Richards' equation, was later modified to express the transport of mass solely as a function of the gradient in water content. This modification is based on the assumption that the capillary potential Γ is a differentiable function of the moisture content θ:
Substituting Eq. (3) into Eq. (1),
where Dθ=K(dΓ/dθ) is the nonlinear water diffusivity coefficient. Eq. (4) is widely used to model the evolution of water content in a porous material kept in isothermal conditions. Eq. (4) is also known as Richards' equation.
While Richards' equation is commonly accepted among scientists, its use over the past decades has contributed to some confusion on how to describe moisture transport mechanisms in unsaturated porous materials. Richards originally wrote the equation with the water content expressed in cubic centimeters of water per gram of dry material. Over the years, some authors have preferred to define water content in kilograms of moisture per kilogram of dry material  or in kilograms of water per cubic meter of material  and . However, most authors have traditionally chosen to express the variable in cubic meter of water per cubic meter of material ,  and . To add to the confusion, many authors tend to define the moisture content as the sum of liquid water and vapor, while some others only consider the liquid phase.