Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids : slender rivulets and dry patches

Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t, the rivulet and dry patch widen or narrow according to |x|3/2, and the film thickens or thins according to |x|, where x denotes distance down the plane, and that at any station x, the rivulet and dry patch widen or narrow like |t|−1, and the film thickens or thins like |t|−1, independent of N

Nanopatterning self-assembled nanoparticle superlattices by moulding microdroplets

Highly ordered arrays of nanoparticles exhibit many properties that are not found in their disordered counterparts. However, these nanoparticle superlattices usually form in a far-from-equilibrium dewetting process, which precludes the use of conventional patterning methods owing to a lack of control over the local dewetting dynamics. Here, we report a simple yet efficient approach for patterning such superlattices that involves moulding microdroplets containing the nanoparticles and spatially regulating their dewetting process. This approach can provide rational control over the local nucleation and growth of the nanoparticle superlattices. Using DNA-capped gold nanoparticles as a model system, we have patterned nanoparticle superlattices over large areas into a number of versatile structures with high degrees of internal order, including single-particle-width corrals, single-particle-thickness microdiscs and submicrometre-sized 'supra-crystals'. Remarkably, these features could be addressed by micropatterned electrode arrays, suggesting potential applications in bottom-up nanodevices