Bubble removal from glass melts: Power-law model

Abstract

An attempt is presented to understand published experimental results regarding bubble removal from molten glass, such as an exponential decrease in bubble count with time at constant temperature, in terms of the behavior of individual bubbles and bubble size distribution. It is assumed that bubbles of all sizes within a given range are initially randomly distributed in space; no new bubbles form at t > 0; the bubble growth/shrinkage rate depends on bubble radius according to a simple power-law relation; and each bubble rises to the melt surface with a velocity proportional to the square of its radius. The time dependence of bubble size distribution, including the maximum and minimum sizes and the total removal time, is determined. In particular, it is shown that an exponential decrease in bubble count requires either an improbable initial bubble size distribution or an unusual bubble growth/shrinkage history. Moreover, the exponential (or similar to exponential) decrease in bubble count is incompatible with both the constant bubble growth rate as observed experimentally for a multibubble mixture and bubble growth rate proportional to the reciprocal bubble radius as predicted theoretically for an isolated bubble. It is suggested that the bubble number observed in refining experiments is, in the final stage, controlled by bubble generation on the container walls.