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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 Cf in the Darcy scale. The lower arrow indicates that the Darcy scale will affect the pore scale by the Darcy-scale variables Cf 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.