Model of inertial spreading and imbibition of a liquid drop on a capillary plate

We outline a low-order Lagrangian model for the inertial dynamics of spreading and imbibition of a spherical liquid cap on a plane featuring independent cylindrical capillaries without gravity. The analysis predicts the relative roles of radial and axial kinetic energy, reveals the critical Laplace number beyond which the drop oscillates, and attributes the exponent of the initial power-law for contact patch radius vs. time to the form of capillary potential energy just after the liquid sphere touches the plate. (C) 2017 American Institute of Chemical Engineers