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A Laplace transform power series solution for solute transport in a convergent flow field with scale‐dependent dispersion

This study presents a novel mathematical model to describe solute transport in a radially convergent flow field with scale‐dependent dispersion. The scale‐dependent advection‐dispersion equation in cylindrical coordinates derived based on the dispersivity is assumed to increase linearly with the distance of the solute transported from its input source. The Laplace transformed power series technique is applied to solve the radially scale‐dependent advection‐dispersion equation with variable coefficients. Breakthrough curves obtained using the scale‐dependent dispersivity model are compared with those from the constant dispersivity model to illustrate the features of scale‐dependent dispersion in a radially convergent flow field. The comparison results reveal that the constant dispersivity model can produce a type curve with the same shape as that from the proposed scale‐dependent dispersivity model. This correspondence in type curves between the two models occurs when the product of the Peclet number used in the constant dispersivity model and the dispersivity/distance ratio used in the scale‐dependent dispersivity model equals 4. Finally, the scale‐dependent dispersivity model is applied to a set of previously reported field data to investigate the linearly scale‐dependent dispersion effect. The analytical results reveal that the linearly scale‐dependent dispersion model is applicable to this test site.