Lab on a chip devices utilizing microfluidics and nanofluidics have the capability of bringing a paradigm shift in medical and analytical technologies. Given the large surface to volume ratio in these devices, as well as the small length scales involved, the basic fluid manipulating mechanisms in these systems, including electrokinetics, electrohydrodynamics, capillary phenomena, etc. are quite different from the bulk pressure gradient systems found in almost all engineering devices at large length scales. These surface phenomena have traditionally received widespread attention, and there are specific theories explaining their behavior under standard conditions. However when the experimental system is modified to include non-standard forcing, the conventional theories fail. For example, using an AC electric field instead of a DC electric field for electrospraying produces dramatically different results, which can not be explained from DC electrospraying theories. In this work four such anomalous microfluidic behaviors are examined in detail. We focus on systematically studying and classifying our observations and on providing a mechanistic explanation behind the departure from conventional theories. In the first part of this work, we focused on AC electrospraying, which was broadly classified into a low and a high frequency regime. At low frequencies a resonance effect was dominant, which produced specific polyhedral shapes and enhanced the flow rate. At high frequencies, significant departure from DC spraying occurred, and new spraying modes were seen. A combination of the applied frequency and sample conductivity along with the applied voltage determined the exact spraying mode. The difference from conventional spraying behavior was explained. In the second part, the use of AC electrospraying was extended to entirely different areas. We demonstrate the use of an AC electric field for electrospinning in Chapter 3, and report the generation of novel multi-stranded threads. It was found that the use of an AC field, lead to the localization of the whipping instability, and formation of the threads. In Chapter 4, drops generated by electrospraying were studied, and a unique multi-ring phenomenon was observed. It was found that this behavior was independent of the applied field. Instead precipitation dynamics were responsible for the slip-stick behavior seen. In chapter 5, the AC electrospraying set-up was used for generating a non-contact converging flow in a small volume of a liquid suspension. This converging flow acted as a particle trap and increased the local concentration at the stagnation point. Suitable modifications were used to generalize the particle trap under different flow conditions, and in conjunction with Raman Scattering, the particle trap was used for bacteria detection.