Contact-line fingering and rivulet formation in the presence of surface contamination

Abstract

Many coating processes are restricted by breakup of the thin coating layer into rivulets that cause the liquid to penetrate non-uniformly into the unwetted part of the substrate. On smooth, dry, homogeneous surfaces, rivulets are known to form as a result of a fingering instability of a ridge of raised liquid that forms just behind the moving contact line, and which together with the contact line composes the layer “front”. The fingering instability can be suppressed by application of a body force normal to the substrate surface or by application of a body force tangent to the substrate surface in the opposite direction as a driving shear force. The present paper uses a finite-difference model to examine the effect of surface inhomogeneities, consisting of patches of varying contact angle, on the fingering instability and subsequent rivulet growth both with and without application of a normal body force. We find that although the front structure is relatively unchanged when the contact angle is changed uniformly by a small constant value on a homogeneous surface, the front is sensitive to small spatial inhomogeneities in contact angle. The dynamics of liquid layer front interaction with an isolated contamination spot and with arrays of many contamination spots are examined for several different conditions. The liquid front responds to passage over a single contamination spot (with small change in contact angle) in a manner consistent with linear stability theory, such that a protrusion of the front forms downstream of the spot with width and growth rate set by the fastest-growing wave of the linear stability theory. This result holds valid for a wide range of contamination spot sizes, and for perturbations in the liquid layer thickness of up to about half the ambient thickness. However, strong non-linear effects are observed during passage of the front through an array of many contamination spots, including a sub-critical instability in which rivulets form with widths corresponding to wavelengths for which the front is stable according to linear theory. Sufficiently large normal body force is able to stabilize the front in the non-linear computations on a heterogeneous surface, such that the front becomes wavy but the perturbation amplitude approaches a state where it does not grow further in time as the front passes over the contamination spots. The rivulets are observed to meander in a random array of contamination spots in such a manner as to flow in regions of small contact angle and to avoid regions of large contact angle.