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Freezing processes of water and peanut oil droplets on a cold surface are investigated in this paper. We observed during our experiments that the base surface of a water droplet that is in direct contact with the cold surface keeps its original shape, but the other part of the droplet shows an obvious growth along the direction normal to the base surface. One small protrusion appears on the top of the water droplet at the end of the freezing process. The experimental observations also show that no obvious shape change happens during the freezing of peanut oil droplets. It is postulated that the effects of surface tension and volume dilatation resulted from liquid-to-solid phase change cause the shape change and protrusions formation. Based on this postulation, a physical and mathematical model is developed. The results of the model of a water droplets freezing process correspond with our experimental observations. The observed phenomenon that frost-growth speed on the protrusion is higher than that on the other part of the water droplet is also analyzed.