Understanding multiphase flow close to the electrode surface is crucial to the design of electrolyzers, such as alkaline water electrolyzers for the production of green hydrogen. Vertical electrodes develop a narrow gas plume near their surface. We apply the integral method to the mixture model. Considering both exponentially varying and step-function gas fraction profiles, we derive analytical relations for plume thickness, velocity profile, and gas fraction near the electrode as a function of height and current density. We verify these analytical relations with the numerical solutions obtained using two-dimensional mixture model simulations. We find that for low gas fractions, the plume thickness decreases with an increase in current density for an exponentially varying gas fraction profile. In contrast, the plume thickness increases with increasing current density at high gas fractions for an approximately step-function-shaped gas fraction profile, in agreement with experiments from the literature.

Membraneless parallel-plate electrolyzers use electrolyte flow to avoid product crossover. Using a mixture model neglecting inertia, and assuming an exponential gas fraction profile, we derive approximate analytical expressions for the velocity profile and pressure drop for thin plumes. We verify these expressions using numerical solutions obtained with COMSOL and validate them using experimental data from the literature. We find that the wall gas fraction increases rapidly at small heights, but becomes fairly constant at larger heights. These expressions serve as a guiding framework for designing a membraneless parallel-plate electrolyzer by quantifying the maximum possible height. We find that buoyancy driven membraneless parallel-plate electrolyzers with a 3 mm gap can be designed with a maximum height of around 7.6 cm at 1000 A/m² for operation with 98% product purity at atmospheric pressure. For a forced flow at Re=1000, the same electrolyzer can be made around 17.6 cm tall at 1000 A/m². These limits can be further improved with smaller bubbles or higher pressure.

Flow-through electrolyzers, with flow parallel to the current, are used in a wide range of industrial applications. The presence of flow avoids concentration gradients but can also be used to separate evolved gases, allowing membrane-less operation. In this work, we propose a simple multiphase flow-through electrode model. We derive and experimentally validate an analytical expression for the minimum velocity required to ensure effective gas separation. From this relation, we analytically derive design parameters that show that significant energy savings can be made using flow, compared to a physical separator.

Vibration-based energy harvesting has been investigated in this paper with the goal to utilize the ambient vibration energy to power small electronic components by converting vibration energy into electrical energy. A simply supported beam with a bonded high density piezoelectric patch to the surface is considered for the analysis. Analytical model for free vibration analysis is developed by starting with the linear constitutive relations for the beam and the patch. The equation of motion for transverse vibration of the beam is developed by considering the elastic as well as electrical properties in the generalized Hookes law and accordingly a transverse displacement function satisfying the simply supported boundary conditions is used for achieving the modal frequencies. Additionally, an analytical model is developed in order to estimate the energy generated under the action of a harmonic force applied on the surface of the patch. The results of the analytical model are validated using simulation software ANSYS and COMSOL. The developed analytical model is used to study the behavior of a simply supported harvester with various patch dimensions and locations. This paper throws light on parametric studies of eigen frequencies as well as extracted power corresponding to operating conditions.