Solidification in the Presence of Natural Convection in a Hele-Shaw Cell

The solidification of water with particles in a suspension that fills the gap in a Hele-Shaw cell has been experimentally studied by visualization and using particle image velocimetry (PIV). The upper wall of the cell is kept at a temperature lower than 0 \(^{\circ }\)C, while the lower wall is exposed to ambient temperature. Water starts solidifying near the upper wall of the cell, and a solidification front moves in the downward direction. Since the temperature gradient established is unstable in the gravity acceleration field, the liquid acquires a natural convective motion, and the solidification and convection interact with each other. The growth of the solidification region in the Hele-Shaw cell modifies the volume available to the liquid and in this way determines the convection pattern. In turn, the convective flow of the liquid is an efficient heat pump at the liquid-solid boundary, and determines the velocity and geometry of the solidification front. We present quantitative data of the velocity and shape of the solidification front and the velocity field in the liquid region as functions of time. We have found that the convective motion stops when the aspect ratio (height/width) of the liquid region is approximately 0.45 and from this time on, the motion of the solidification front follows Stefan’s law.