Instability mechanisms in microfluidics and nanomaterials

Recent scientific advances in chemical engineering are leading to synthesis of micro-scale and nano-scale functional devices and materials. However, optimal design and performance of these devices and materials requires a fundamental under standing of the interfacial phenomena at micro-scale and nano-scale. Due to new physical forces unique to small scales, new phenomena appear that are unexpected at large scales. A study of new interfacial patterns that arise from various interfacial instabilities at these scales is carried out in this dissertation. Nevertheless, interfacial patterns ranging from micro to macro scale are ubiquitous in multiphase systems and material synthesis involving a surface reaction.; Fractal break up of a thin viscous oil film dewetting between two separating plates is studied experimentally. Unlike the classical patterns of pores and dendrites, it forms a fractal pattern like a branching tree with its origin at the center of the circular film. Lubrication theory is extended to such a fractal geometry, which is unlike the circular geometry of a classical dewetting problem. A power law scaling is obtained for the radial air finger length distribution to construct an idealized Cayley fractal structure. Our theory yields a result that the plate detach time decreases by half in the limit of a fully fractal pattern that is confirmed experimentally.; Nanopore formation in anodized alumina is also found to bear similarities to the interfacial pattern formation of the dewetting film between two separating plates. The oxide layer formed on the aluminum during the initial stages of anodizing is found to be unstable to perturbations on the scale of a few nanometers and hence it leads to the nanopore formation. A linear stability analysis of the dual interfacial dynamics followed by a leading mode projection produces a single evolution equation for the pores. Numerical simulations of the nonlinear model reveals the hexagonal packing and self-organization dynamics of the pores.; In microfluidic devices, electrokinetic flow produces spiral vortices and corner aggregation of particles and proteins at an inner corner of a channel turn that is unexplained by the short ranged DLVO forces. Field leakage effect due to the non perfectly insulating wall reveals a nonlinear singular and ejecting slip velocity condition at an acute angled sharp corner. The complete flow streamlines, vortices and the corner entrainment are revealed by conformal mapping, harmonic analysis and numerical simulation using Lattice-Boltzmann-Method (LBM).; The method of hodograph transform developed for the earlier projects to solve the Laplace equation is also applied to find optimum shapes of dispersion free turns for electro-osmotic microfluidic channels.