In-plane mode dynamics of capillary self-alignment.

We present an experimental study of the complete in-plane dynamics of capillary self-alignment. The two translational (shift) and single rotational (twist) in-plane modes of square millimetric transparent dies bridged to shape-matching receptor sites through a liquid meniscus were selectively excited by preset initial offsets. The entire self-alignment dynamics was simultaneously monitored over the three in-plane degrees of freedom by high-speed optical tracking of the alignment trajectories. The dynamics of the twist mode is shown to qualitatively follow the sequence of dynamic regimes also observed for the shift modes, consisting of initial transient wetting, acceleration toward, and underdamped harmonic oscillations around the equilibrium position. Systematic analysis of alignment trajectories for individually as well as simultaneously excited modes shows that, in the absence of twist offset, the dynamics of the degenerate shift modes are mutually independent. In the presence of twist offset, the three modes conversely evidence coupled dynamics, which is attributed to a synchronization mechanism affected by the wetting of the bounding surfaces. The experimental results, justified by energetic, wetting, and dynamic arguments, provide substantial benchmarks for understanding the full dynamics of the process.