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. Figure 3. Interface potential energy G † vs. h for h e 5p=3. Inset: dimensionless contact patch radius r à c vs. h.Solid, dashed and dotted lines represent, respectively, expressions for a spherical cap, 11 and corrections consistent with a51=2 and 1/3, respectively.Dashed and solid lines are integrations of Eqs. 28 and 35 for, respectively, equilibrium angles h e 536 and h CB e in Eq. 37. At h CB e , the critical Laplace number is La c ' 2, while it is ' 17; 000 at h e . Inset: predictions of effective drop radius R i 5½3V=ð4pÞ 1=3 relative to its initial value R 0 .
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