Mathematical modeling of cold cap
The ultimate goal of studies of cold cap behavior in glass melters is to increase the rate of glass processing in an energy-efficient manner. Regrettably, mathematical models, which are ideal tools for assessing the responses of melters to process parameters, have not paid adequate attention to the cold cap. In this study, we consider a cold cap resting on a pool of molten glass from which it receives a steady heat flux while temperature, velocity, and extent of conversion are functions of the position along the vertical coordinate. A one-dimensional mathematical model simulates this process by solving the differential equations for mass and energy balances with appropriate boundary conditions and constitutive relationships for material properties. The sensitivity analyses on the effects of incoming heat fluxes to the cold cap through its lower and upper boundaries show that the cold cap thickness increases as the heat flux from above increases, and decreases as the total heat flux increases. We also discuss the effects of foam, originating from batch reactions and from redox reactions in molten glass, and argue that models must represent the foam layer to achieve a reliable prediction of the melting rate as a function of feed properties and melter conditions.
Effect of bubbles and silica dissolution on melter feed rheology during conversion to glass.
Nuclear-waste melter feeds are slurry mixtures of wastes with glass-forming and glass-modifying additives (unless prefabricated frits are used), which are converted to molten glass in a continuous electrical glass-melting furnace. The feeds gradually become continuous glass-forming melts. Initially, the melts contain dissolving refractory feed constituents that are suspended together with numerous gas bubbles. Eventually, the bubbles escape, and the melts homogenize and equilibrate. Knowledge of various physicochemical properties of the reacting melter feed is crucial for understanding the feed-to-glass conversion that occurs during melting. We studied the melter feed viscosity during heating and correlated it with the volume fractions of dissolving quartz (SiO2) particles and the gas phase. The measurements were performed with a rotating spindle rheometer on the melter feed heated at 5 K/min, starting at several different temperatures. The effects of undissolved quartz particles, gas bubbles, and compositional inhomogeneity on the melter feed viscosity were determined by fitting a linear relationship between the logarithm of viscosity and the volume fractions of suspended phases.
Viscosity of many-component glasses
Abstract The effect of composition on the viscosity ( η ) of multicomponent glasses is expressed as B = ∑ i = 1 N B i x i where B = T ln ( η / η ∞ ) is the activation energy (in K), B i is the i -th component coefficient, x i is the i -th component mass fraction, T is the absolute temperature, and η ∞  ≈ 10 −5  Pa ⋅ s. The B i coefficients for three composition regions (labeled as CVS-1&2, CVS-3, and CVS-4) containing various subsets of Al 2 O 3 , B 2 O 3 , Bi 2 O 3 , CaO, Cr 2 O 3 , F, Fe 2 O 3 , K 2 O, Li 2 O, MgO, MnO, Na 2 O, NiO, P 2 O 5 , SiO 2 , UO 2 , and ZrO 2 as major components are summarized and compared. This paper presents a detailed account of the recent experimental study that generated viscosity data for the CVS-4 region of glass composition. Whereas CVS-1&2 is a well publicized dataset, CVS-3 viscosity data, though produced in 1995, are published and evaluated here for the first time. Limits of applicability of the composition models are discussed.