Dynamics of low capillary number interfaces moving through sharp features

The success of any nanoimprint process depends upon its ability to exactly reproduce the template pattern. Thus, complete filling of recessed features in the template is an important issue that is controlled by the dynamics of the flow through these sharp structures. At these small scales, capillary forces are large and must be included in the fluid flow model. The mechanism of interface advancement at low capillary number through sharp rectangular features is useful for understanding how and why features fill or trap air. In this study we present a two-dimensional simulation of this feature filling to capture the details of the process, including the viscous and capillary effects. Fluid is injected into the channel between the template and substrate, where the fluid-air interface soon encounters a rectangular feature with some height greater than the channel gap. As the fluid advances through the channel, the shape of the interface is a circular arc due to the strong capillary forces. The interface maintains this circular arc as it negotiates the first sharp corner of the feature; the upper contact line effectively pins to the initial corner of the feature as it moves around this corner, during which time the lower contact line continues to advance forward along the substrate surface, causing the interface to stretch. For sufficiently wide or shallow features, once the upper contact line has negotiated the first corner and has moved vertically up the inner wall of the feature, it must move through the top corner of the feature. At this point the interface undergoes a rapid reconfiguration from a high surface area circular arc to a lower surface area circular arc inside the feature. Alternatively, for narrow or high features, the stretched interface can catch on the far, final corner of the feature, trapping air inside the feature and preventing filling. The conditions for filling are studied parametrically for a variety of wetting contact angles and feature dimensions with both the simulation and a simpler, successful geometric model. The dynamics of the feature filling suggest an effective boundary condition for a macroscopic lubrication model of the imprint lithography process in which a critical pressure is required to move fluid through a feature.