Abstract
The imbibition of a complex fluid in porous media often exhibits anomalous behavior, which is dominated by multiple time-spatial scales. In this work, a spatiotemporal fractional imbibition model (SFIM) is proposed to capture anomalous imbibition. The anomalous exponent and the non-Newtonian index of SFIM are introduced to characterize the heterogeneity of porous media and the nonlocality of the non-Newtonian fluid. It is found that the anomalous exponent is inversely proportional to the fractal dimension of tortuosity. The non-Newtonian index unveils the radius variation due to the interaction between the non-Newtonian fluid and the interface of porous media. In addition, the proposed model is superior to the Lucas-Washburn model (LWM) with respect to the experimental data of oil and epoxy resin. This work is provided as a preliminary probe into a study on anomalous imbibition via fractional calculus.
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