Research Projects

Rationale and Scientific Objective: This research addresses the theoretical dynamics of resonance-driven waves, specifically Faraday waves, on a bilayer of fluids confined by flexible walls. Understanding how these waves evolve is essential for improving thermal management in microgravity settings and micro heat exchangers that utilize channels with flexible walls. In this study, Faraday waves are generated when a bilayer confined between flexible walls is exposed to oscillatory motion at a frequency matching its natural frequency, which is defined as the oscillation rate of the interface in response to a brief pulse disturbance. By aligning the oscillation frequency with the bilayer's natural frequency, resonance occurs, producing waves on the fluid’s surface. Hypothesis: To improve thermal management in microgravity and micro heat exchangers, this work aims to understand the evolution of Faraday waves at the interface of a bilayer confined by flexible walls. The study proposes any wave theory, reduced-order model and weak nonlinear analysis incorporating interactions between the flexible walls and fluids. In microgravity, where buoyancy-driven flow is absent, resonance-induced flows from Faraday waves provide essential mixing. The flexible walls are key factors in genration of Faraday waves. The flexible walls elasticity plays a role in amplifying this resonance-driven flow, as their elasticity can be tuned to optimize wave formation at the interface, enhancing fluid mixing and, subsequently, heat transfer. Theoretical Model: The model includes three components. First, a general wave model addresses the full governing equations to estimate the critical conditions needed for the onset of Faraday waves, derived through linear stability analysis of the fluid-wall system. Second, a reduced-order model is introduced to track the nonlinear evolution of the fluid interface, using a long-wave approximation to retain the fundamental physics behind the evolution of Faraday waves while simplifying the equations. Third, a weakly nonlinear analysis is applied near the stability threshold to explore branching behavior in the interface’s evolution, assessing whether deformation results in saturation (supercritical branching) or rupture (subcritical branching). Significance and Broader Technological Impacts: This project will lead to a flexible-walled channel design that enhances fluid mixing and thermal management, both on Earth and in microgravity. Additionally, the reduced-order model developed from this research will offer a valuable theoretical framework for studying Faraday waves in fluid systems with flexible boundaries. This model has broad applications, especially in areas of interest to the Indian Space Research Organization (ISRO) and the materials science community, such as phase change processes in materials processing, crystal growth, and thin-film deposition, where controlled convective flows are required to optimize material characteristics.