Micromixing in Reactive, Deformable Bubble and Droplet Swarms

Review-Mathematical Formulations of Electrochemically Gas-Evolving Systems

Electrochemically gas-evolving systems are utilized in alkaline water electrolysis, hydrogen production, and many other applications. To design and optimize these systems, high-fidelity models must account for electron-transfer, chemical reactions, thermodynamics, electrode porosity, and hydrodynamics as well as the interconnectedness of these phenomena. Further complicating these models is the production and presence of bubbles. Bubble nucleation naturally occurs due to the chemical reactions and impacts the reaction rate. Modeling bubble growth requires an accurate accounting of interfacial mass transfer. When the bubble becomes large, detachment occurs and the system is modeled as a two-phase flow where the bubbles can then impact material transport in the bulk. In this paper, we review the governing mathematical models of the physicochemical life cycle of a bubble in an electrolytic medium from a multiscale, multiphysics viewpoint. For each phase of the bubble life cycle, the prevailing mathematical formulations are reviewed and compared with particular attention paid to physicochemical processes and the impact the bubble. Through the review of a broad range of models, we provide a compilation of the current state of bubble modeling in electrochemically gas-evolving systems.

Particle segregation by Stokes number for small neutrally buoyant spheres in a fluid

It is a commonly observed phenomenon that spherical particles with inertia in an incompressible fluid do not behave as ideal tracers. Due to the inertia of the particle, the planar dynamics are described in a four-dimensional phase space and thus can differ considerably from the ideal tracer dynamics. Using finite-time Lyapunov exponents, we compute the sensitivity of the final position of a particle with respect to its initial velocity, relative to the fluid, and thus partition the relative velocity subspace at each point in configuration space. The computations are done at every point in the relative velocity subspace, thus giving a sensitivity field. The Stokes number, being a measure of the independence of the particle from the underlying fluid flow, acts as a parameter in determining the variation in these partitions. We demonstrate how this partition framework can be used to segregate particles by Stokes number in a fluid. The fluid model used for demonstration is a two-dimensional cellular flow.