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necessary to evaluate the response time of the aluminum film before the measurement,
namely how long it takes for the bottom side of the aluminum film to have
the same temperature as its top side. Neglecting the contact thermal resistance, the
temperature at the top side of the aluminum film is equal to the temperature of the
bottom of the freezing lamella.
Figure 4.11.: Composition of the mechanical system in the measurement of the contact
temperature.
A quick estimation is taken with the assumption that, during the short time the
heat is conducted at a constant heat flux density ˙q = ∆T/(H alu /k alu ) in W m −2 ,
where H alu is the thickness of the aluminum film, k alu is the thermal conductivity
of aluminum. The total heat consumption per unit area is q = ρc alu ∆T H alu in
J m −2 . This leads to the response time t response = q/˙q = c p ρH 2 alu /k alu = 1.48µs.
Since the estimated value was nearly three orders of magnitude smaller than the
recording period of the infrared camera, 1.39 ms, the bottom side of the aluminum
film should faithfully follow the temperature of the ice/aluminum interface.
The temperature at the interface is neither the temperature of the lamella nor
the temperature of the germanium substrate. Rather, it is an intermediate value
determined by both the initial temperatures of the mediums and their thermal
properties, more precisely speaking, the ratio of the two thermal effusivities. The
thermal effusivity of a material is defined as
e = kρc p . (4.4)
4.2. Impact of Supercooled Drop on Superhydrophobic Surfaces 113