Surface tension driven flow in which one fluid displaces another is of importance in microfluidic devices for diagnostics, lab on chip devices and flow in oil reservoirs. Spontaneous impregnation of a preferentially wetting phase displacing an existing non-wetting phase in a homogeneous porous medium is known to follow diffusive dynamics. However, in a heterogeneous porous medium the hydrodynamic interaction between the narrow and the wide pores significantly alters the impregnation behavior. Previous studies have shown that the imbibing fluid interface leads in the narrow pores contrary to the predictions from the diffusive dynamics of homogeneous porous medium. This is due to the higher suction pressure in the narrow pores which draw fluid from the wide pores. The effect of fluid properties and relative flow properties of the pores with respect to other pores on the non-wetting fluid displacement in the heterogeneous porous medium is still unknown. In the current work, we develop a quasi one-dimensional, lubrication approximation model, which predicts the spontaneous imbibition in a heterogeneous porous medium. We explore all the possible relative fluid properties and flow properties of the layers in the heterogeneous porous medium and show that our model is able to predict the flow behavior in all the cases. We also present the results of the spontaneous imbibition experiments, which agree with our model. The experiments show that the two phase interface progresses faster in the narrow pores as predicted by the one-dimensional model. The result is important for predicting and controlling the flow behavior in a heterogeneous porous medium.

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