The dissipation theorem is applied to turbulent pipe flow. The eddy-viscosity profiles can be made to agree with some in the literature in the sense that the eddy viscosity starts at zero on the solid pipe wall, rises to a maximum, and declines again toward the center line. A relationship between the volumetric dissipation and the eddy viscosity is derived by means of an energy balance on a core of fluid of radius r. The question of what exponent to use on the radius in another governing equation is clarified, thereby giving better agreement with experimental data than other values tried. Negative values of the eddy viscosity can be obtained in some regions of the flow field, such as near the center line, and it is suggested that these can be eliminated by slight modification of the decay term. Better agreement with the shapes of friction-factor and mass-transfer curves could be achieved by further (empirical) modification of the stress dependence of parameters in the model.

A fully integrated model of a photoelectrochemical cell for water electrolysis is applied to the case of light-absorbing particles embedded in a membrane separator. Composition of the product gases is shown to be one critical measure of device performance. Not only must the composition be kept outside the explosive window for mixtures of H2 and O2, but also product purity is a concern. For the absorber-in-membrane geometry and the model assumptions used here, results show purely water-saturated H2 on the cathode side and water-saturated O2 on the anode side. Since it is possible to design devices that violate these assumptions, it should not be assumed that a polymer separator or an absorber-in-membrane geometry will be effective in preventing explosive mixtures in all cases. Net H2 collected, iH2,net, is the second essential performance metric, and it is shown to differ significantly from the more commonly reported total H2 produced and operating current density. Schemes which co-evolve H2 and O2 violate the first metric and do not provide the second. A composite of triple-junction silicon absorbers in a Nafion membrane is shown to have an optimum thickness of 30 μm, dependent on the properties of the light absorber. Varying membrane properties reveals a tradeoff between conductivity, κm, and gas permeabilities, ψH2 and ψO2, that can potentially be exploited differently than in a fuel cell. Modulating the relative humidity (RH) is insufficient. The maximum iH2,net is calculated to be 6.97 mA cm−2 at RH = 30% relative to a value of 6.92 mA cm−2 at RH = 100%. The model identifies target material properties for new polymers. If ψ is dropped one order of magnitude below that of Nafion (ψ/ψNafion = 0.1), the optimum value for iH2,net increases by 63.5%. For ψ/ψNafion = 0.01, the optimum iH2,net increases by 73.5%, which compares favorably to the 74.5% improvement that would result if Nafion were made impermeable (ψ/ψNafion = 0). Meanwhile, κm can drop to a value of 1.2 × 10−3 S cm−1 (two orders of magnitude below liquid-equilibrated Nafion) with less than a 5% decline in iH2,net.

This work compares the performance of lithium batteries with polymer electrolytes with unity (“ionomer”) and nonunity (“polymer electrolyte”) transference numbers. The study is performed with respect to a particular cell chemistry, Li metal∣polymer∣LiV6O13-composite electrode, which is currently a top candidate for use in electric vehicles. Cell performance was modeled to determine the best possible performance of cells containing four different electrolytes: “ideal” polymer membrane and ionomer with properties defined by USABC goals, and the presently best available polymer electrolyte and ionomer. Positive electrode thickness, porosity, and current density were varied to find the cell geometry with the highest combined energy density and peak power performance for cells with each electrolyte, and concentration and potential profiles are examined to determine the limitations of the electrolytes. The results show that at 40°C, the “ideal” polymer electrolyte can provide 104 W h/kg and 99 Wp/kg, the “ideal” ionomer can provide 94 W h/kg and 58 Wp/kg, and the currently available electrolytes can provide about one-fifth of these values.