Transient growth in driven contact lines

The problem of transient growth in the distortion of driven contact lines has recently sparked a controversy as to whether this mechanism can provide an alternative route to pattern formation in the absence of linear instability. To resolve the disagreement between previous studies we conduct a generalized linear stability analysis of different lubrication models of gravity-driven spreading and compare our results with those based on direct numerical simulations. We find that linear and non-linear theory are in reasonable qualitative agreement and show that the quantitative discrepancies in the predicted transient growth are caused by the differences in: (1) the choice of initial disturbances and (2) the definition of the maximal transient amplification used in different studies. We further show by comparing the predictions of the precursor and the slip model that the latter substantially underestimates transient growth by neglecting the disturbances in the slip parameter.