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Force-balance-based one-dimensional algebraic formulations that are often used in characterizing the capillarity of a multi-component system (e.g., predicting capillary height rise in porous media) are discussed. It is shown that such formulations fail to provide accurate predictions when the distribution of wetting (or non-wetting) surfaces is not homogeneous. A more general mathematical formulation is suggested and used to demonstrate that for media with heterogeneous wettability, hydrophilic (or hydrophobic) surfaces clustered in groups will have less contribution to the overall capillarity of the system.

On applications and limitations of one-dimensional capillarity formulations for media with heterogeneous wettability