The onset of interfacial instability in two-fluid systems using a viscous, leaky dielectric model is studied. The instability arises as a result of resonance between the parametric frequency of an imposed electric field and the system’s natural frequency. In addition to a rigorous model that uses Floquet instability analysis, where both viscous and charge effects are considered, this study also provides convincing validating experiments. In other results, it is shown that (a) the imposition of a periodic electrostatic potential acts to counter gravity and this countering effect becomes more effective if a DC voltage is also added, (b) a critical DC voltage exists at which the interface becomes unstable such that no parametric frequency is required to completely destabilize the interface and (c) the leaky dielectric model approaches a model for a perfect dielectric/perfect conductor pair as the conductivity ratio becomes large. It is also shown via experiments that parametric resonant instability using electrostatic forcing may be reliably used to estimate interfacial tension to sufficient accuracy. 

As long-term space exploration progresses, the need for effective thermal management systems becomes increasingly important. Buoyancy-driven convection is the primary mechanism for heat transfer devices on Earth. However, in space, the absence of gravity, extreme temperatures, and limited resources present unique challenges that require new solutions. Current state-of-the-art devices used consist mainly of active and passive management systems. Active thermal management systems rely on power-input from external equipment for systems that primarily require smaller thermal variability. Shortcomings of active management are high power cost and capability of miniaturizing for smaller space crafts. Passive thermal management systems keep temperature control without power from external sources, while less expensive, they still have their drawbacks. The work proposed uses resonant instability by forcing an otherwise passive system at its natural frequency as an alternative method to circumvent issues from traditional methods. The natural frequency is the frequency a system oscillates at when perturbed in the absence of external forcing. When a fluid bilayer is subjected to a vertical parametric forcing, at a critical forcing amplitude for a given frequency, the system becomes unstable. This is known as Faraday instability. Faraday instability manifests as vigorous standing waves at the free surface, exciting flow in the bulk of the fluid. This work theorizes the use of Faraday instability from electrostatic forcing will dramatically enhance heat transfer in a system with diminished buoyance driven convection. 

An electrochemical cell is composed of two metal electrodes separated by an aqueous solution. When a voltage is applied across the cell, the anodic front starts to recede as the metal at the anode undergo oxidation and form ions. These ions travel through the solution and meet electrons, travelling via outside circuit, at the cathode-solution interface and undergo reduction, thereby forming metal again and hence the cathodic front moves forward. But this metal does not deposit uniformly on the cathode surface and form wave like and branched patterns, leading to electrodeposition instability. The project involves development of theoretical models to predict the onset of instability and conduct experiments in microfluidic channels that are fabricated using photolithography. 

In this work,  the oscillations of a pendulum are utilized to elucidate the effect of vertical oscillations on a fluid layer. When a simple pendulum is vertically oscillated at a frequency near its natural frequency, it becomes unstable, resulting in violent oscillations due to resonance. Additionally, vertical oscillations can serve to stabilize an erstwhile unstable system, such as an inverted pendulum, by constraining it to its upright equilibrium position. Stability analysis shows that the equations governing the simple pendulum are identical in structure to those describing the interface of a fluid layer. Analogous to a simple pendulum, resonance in a fluid layer destabilizes the fluid layer, giving rise to violent undulations at the interface. Moreover,  vertical oscillations can stabilize an inherently unstable fluid system under opposing gravity, by confining this inverted fluid layer with a flat interface.  These findings also extend to the suppression of thermal convective flows in liquid systems with imposed temperature gradients.