Freezing time for 1mL of water

[Usjes]

Hi,

Does anyone have a formula for the freezing time (ie time taken for it to freeze) of a fixed volume of water (1mL) at a given temperature (Ts) and pressure (1 Atmosphere) when the surrounding temperature is set to below 0 Celsius (Ta < 0C) ?

ie. I'm looking for Time to freeze if you place a sample with initial temperature (Ts) in a freezer whose internal temp is Ta.

Thanks,

Usjes

 

[xts]

There are no such formulae, and the time do not scale with the volume nor even with freezer temperature. It depends on multiple factors, especially shape of the vessel containing water, thermal properties of the vessel, and shape of the interior of the freezer, as it in turn determines the airflow of cold air around your sample.
In practice there is no better way than to determine it experimentally for your particular shapes, or estimate it by first order approximations, if you have experimental data for similar setup.

You may check importance of these factors with your kitchen freezer and icecube forms: the time needed to freeze them may vary by factor of three or more depending on which shelf of the freezer you put them.

For bigger vessels of simple shape (eg. a spherical one of the radius of several cm)it might be a bit easier to predict freezing time, as the most limiting factor in such case is thermal conductivity of the already formed ice, which may be modeled.