Growth of spherical and cylindrical oxygen bubbles at an ice-water interface

Structural features of oxygen gas bubbles incorporated into a growing ice crystal were experimentally and theoretically investigated at various ice growth rates and ambient pressures. Four patterns of the shapes of bubbles incorporated in ice were observed within the experimental conditions used in this study: (a) egg-shaped bubbles, (b) egg-shaped bubbles and cylindrical bubbles, (c) cylindrical bubbles, and (d) bifurcated cylindrical bubbles. These four patterns were mapped out as functions of the ice growth rate and ambient pressure. When cylindrical bubbles were incorporated, the average diameter and interval of the bubbles were measured as functions of the growth rate and ambient pressure. Both the measured diameter and interval decreased with increases in either the growth rate or ambient pressure. In an analytical model developed here, a one-dimensional (1D) approximation in the diffusion boundary layer was used to derive the diameter and interval of the cylindrical bubbles. The analytical results revealed that both the diameter and interval are inversely proportional either to the growth rate or to the square root of the ambient pressure. This analytical model well reproduced the measured diameter and interval.