A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media

In the past decades, there was considerable controversy over the Lucas-Washburn (LW) equation widely applied in capillary imbibition kinetics. Many experimental results showed that the time exponent of the LW equation is less than 0.5. Based on the tortuous capillary model and fractal geometry, the effect of tortuosity on the capillary imbibition in wetting porous media is discussed in this article. The average height growth of wetting liquid in porous media driven by capillary force following the (L) over bar (s) (t) similar to t(T)(1/2D) law is obtained (here D (T) is the fractal dimension for tortuosity, which represents the heterogeneity of flow in porous media). The LW law turns out to be the special case when the straight capillary tube (D (T) = 1) is assumed. The predictions by the present model for the time exponent for capillary imbibition in porous media are compared with available experimental data, and the present model can reproduce approximately the global trend of variation of the time exponent with porosity changing.