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Review Article

Appl. Mech. Rev. 2018;70(2):020801-020801-23. doi:10.1115/1.4038699.

The design and performance of liquid metal batteries (LMBs), a new technology for grid-scale energy storage, depend on fluid mechanics because the battery electrodes and electrolytes are entirely liquid. Here, we review prior and current research on the fluid mechanics of LMBs, pointing out opportunities for future studies. Because the technology in its present form is just a few years old, only a small number of publications have so far considered LMBs specifically. We hope to encourage collaboration and conversation by referencing as many of those publications as possible here. Much can also be learned by linking to extensive prior literature considering phenomena observed or expected in LMBs, including thermal convection, magnetoconvection, Marangoni flow, interface instabilities, the Tayler instability, and electro-vortex flow. We focus on phenomena, materials, length scales, and current densities relevant to the LMB designs currently being commercialized. We try to point out breakthroughs that could lead to design improvements or make new mechanisms important.

Commentary by Dr. Valentin Fuster
Appl. Mech. Rev. 2018;70(2):020802-020802-22. doi:10.1115/1.4039144.

This work is concerned with Mathieu's equation—a classical differential equation, which has the form of a linear second-order ordinary differential equation (ODE) with Cosine-type periodic forcing of the stiffness coefficient, and its different generalizations/extensions. These extensions include: the effects of linear viscous damping, geometric nonlinearity, damping nonlinearity, fractional derivative terms, delay terms, quasiperiodic excitation, or elliptic-type excitation. The aim is to provide a systematic overview of the methods to determine the corresponding stability chart, its structure and features, and how it differs from that of the classical Mathieu's equation.

Commentary by Dr. Valentin Fuster
Appl. Mech. Rev. 2018;70(2):020803-020803-16. doi:10.1115/1.4039557.

This paper presents a comprehensive review and comparison of different theories and models for water vapor pressure under rapid heating in moisture permeable materials, such as polymers or polymer composites. Numerous studies have been conducted, predominately in microelectronics packaging community, to obtain the understanding of vapor pressure evolution during soldering reflow for encapsulated moisture. Henry's law-based models are introduced first. We have shown that various models can be unified to a general form of solution. Two key parameters are identified for determining vapor pressure: the initial relative humidity and the net heat of solution. For materials with nonlinear sorption isotherm, the analytical solutions for maximum vapor pressure are presented. The predicted vapor pressure, using either linear sorption isotherm (Henry's law) or nonlinear sorption isotherm, can be greater than the saturated water vapor pressure. Such an “unphysical” pressure solution needs to be further studied. The predicted maximum vapor pressure is proportional to the initial relative humidity, implying the history dependence. Furthermore, a micromechanics-based vapor pressure model is introduced, in which the vapor pressure depends on the state of moisture in voids. It is found that the maximum vapor pressure stays at the saturated vapor pressure provided that the moisture is in the mixed liquid/vapor phase in voids. And, the vapor pressure depends only on the current state of moisture condition. These results are contradictory to the model predictions with sorption isotherm theories. The capillary effects are taken into consideration for the vapor pressure model using micromechanics approach.

Commentary by Dr. Valentin Fuster

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