Precursor film ($h\to h_{\ast }>0$)

A thin liquid layer extending ahead of a thicker drop can replace a sharp zero-height contact line in a continuum film model. Keeping the height positive avoids the zero-mobility singularity of a purely no-slip $h^3$ lubrication law at the apparent contact edge. Additional microscopic surface interactions usually determine its thickness and matching to the macroscopic apparent contact angle. It is one possible contact-line regularization, rather than a universal assumption for every substrate.