The interaction of the pore scale and Darcy scale. The upper arrow indicates that the pore scale will affect Darcy scale by the pore-scale variable ϕ. As long as ϕ is changed, the pore-scale variables used in the Darcy scale are changed, which brings about the changes of the main variables u, p, and C_f in the Darcy scale. The lower arrow indicates that the Darcy scale will affect the pore scale by the Darcy-scale variables C_f and u, since the two variables will affect the value of ϕ directly. Once ϕ is changed, all the other variables in the pore scale will be changed accordingly.