Modeling of capillary-driven flows in axisymmetric geometries

•An extension of the Lucas–Washburn equation is proposed.•It describes capillary-driven flows in non-straight geometries.•The proposed model is then verified with simulations.•The simulative tool is based on the free-surface lattice Boltzmann method. We present an analytical approach, as well as computer simulations based on the free surface lattice-Boltzmann (FSLB) method, in order to model capillary-driven infiltration of liquids into porous structures. The analytical method is an extension of the Lucas-Washburn (LW) equation and applies to axisymmetric geometries with a circular cross-section. The treatment of irregular capillaries is achieved by a discretization procedure in which the original geometry is divided into small cylinders. In order to validate the derived analytical equation, we perform FSLB simulations in test geometries which show a good agreement.