How to calculate the area of change, e.g. ice in water

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I want to calculate the change value of a changing area in a region, say a glass of water that is freezing, and I want to get the change value of ice, the difference between ice and water can be described by a phase field parameter (0 or 1), but it is not clear to me how to get the volume (or area, a 2D model) of the ice at each moment in time, and also how to get the rate of freezing (say the volume or area of ice per second). Any help would be appreciated!


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