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Ice Adhesion


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      Where ρi is the density of ice and Hm is the enthalpy of ice formation. Also, using heat conduction equation, c03_Inline_11_15.jpg is obtained as:

Schematic illustration of ice growth on a sub-zero substrate when the droplet is in an environment without airflow.

      Figure 3.6 Ice growth on a sub-zero substrate when the droplet is in an environment without airflow. In this case, ice growth is controlled mainly by heat transfer through the substrate [5].

      The important assumption in the aforementioned analysis is quasi-steady heat transfer. In quasi-steady heat transfer it is assumedthat time-scale for ice growth, c03_Inline_12_13.jpg is more than thermal diffusion, c03_Inline_12_14.jpg in which Di is thermal diffusivity of the ice. This assumption is correct in the case of a water droplet. For example, for a water droplet with 1mm diameter, the time-scale for growth is around 10 s and time-scale for diffusion is around 1 s.

Schematic illustration of the experimental data for ice growth rate are compared to theoretical model that shows that experimental data for ice growth match theoretical model well.

      Figure 3.7 The experimental data for ice growth rate are compared to theoretical model obtained from Eq. (3.26) and Eq. (3.27) which shows that experimental data for ice growth match theoretical model well. l and l0 are height of liquid at the top of the ice and total height of the droplet, respectively [5].

      As shown in Figure 3.7, the predicted model obtained by heat transfer analysis matches experimental data well [5]. As an example, freezing times of a water droplet on stainless-steel at -20°C and -30°C are 9.6 and 7 s, respectively, which are obtained from the experiment [23]. The freezing times obtained from predicted model are 10 and 6 s for -20°C and -30°C, respectively, which are in a great harmony with the experimental data. In order to obtain isotherms in the ice, the heat equation should be solved in the ice domain (∇2T = 0). The boundary conditions in this case are that ice-water interface temperature is constant and ice-icephobic substrate interface temperature is prescribed.

      3.2.2 Scenario II: Droplet in an Environment with External Airflow

      Second scenario occurs when there is airflow around the water droplet in which convective heat transfer becomes significant (Figure 3.8). In this case, instead of solid-liquid interface, ice nucleation occurs at liquid-vapor interface, as convective heat transfer reduces temperature at the surface [24]. Figure 3.8 shows ice growth pattern for the droplet exposed to an environment with airflow.

Schematic illustration of ice growth on a sub-zero substrate when the droplet is in an environment with external airflow.

      Figure 3.8 Ice growth on a sub-zero substrate when the droplet is in an environment with external airflow. In this case, ice growth is controlled mainly by convective heat transfer through airflow [5].

      Similarly to Scenario I, one can use energy balance at phase-changing interface to obtain ice growth rate. The enthalpy released from freezing makes a heat flux at ice-water interface which is carried out with airflow. Thus,

      (3.28)c03_Inline_14_9.jpg