  We consider the classical problem of droplet impact and droplet spread on a
smooth surface in the case of an ideal inviscid fluid. We revisit the
rim-lamella model of Roisman et al. [\textit{Proceedings of the Royal Society
of London. Series A: Mathematical, Physical and Engineering Sciences},
458(2022), pp.1411-1430.]. This model comprises a system of ordinary
differential equations (ODEs); we present a rigorous theoretical analysis of
these ODEs, and derive upper and lower bounds for the maximum spreading radius.
Both bounds possess a $\mathrm{We}^{1/2}$ scaling behaviour, and by a sandwich
result, the spreading radius itself also possesses this scaling. We demonstrate
rigorously that the rim-lamella model is self-consistent: once a rim forms, its
height will invariably exceed that of the lamella. We introduce a rational
procedure to obtain initial conditions for the rim-lamella model. Our approach
to solving the rim-lamella model gives predictions for the maximum droplet
spread that are in close agreement with existing experimental studies and
direct numerical simulations.
