Droplet observation

The cold stage is mounted to the z-stage of an Olympus BX51 optical microscope with 10× magnification and a trinocular observation tube. This tube allows simultaneous observation using the eyepiece and an attached digital camera (Hitachi KP-M1AP). In the centre of the stage there is a hole which allows observation of the droplets by transmission microscopy. As the droplets are positioned over this hole, there is a temperature difference between the droplets and the aluminium stage. At 0.22 mm thick, the glass cover slips are too thin to sufficiently conduct heat away from the droplets at the desired rate. Therefore, the hole is spanned by thermally conductive window (thermal management grade polycrystalline diamond: TM180, ~1800 W m-1 K-1, 0.25 mm thick, supplied by Element Six, UK) to minimise the temperature difference between the droplets and stage, while still allowing transmission microscopy. The diamond is smoothed (to 50 nm) on one side and rough (250 nm) on the other. The smooth side is used to support the cover slip assembly and the rough side is in contact with the stage. The window is attached to the stage using a heat transfer paste (Omegatherm 201, ~2.3 W m-1 K-1), taking care not to get the paste in the hole in the stage. As this paste is a less efficient heat conductor than the other materials used to construct the stage as thin a layer as possible is used.

Figure 3.8. Comparative images of A): liquid and B): frozen droplets. The droplets are isolated from the environment by oil (see section 3.1.2). In droplets larger than about 10 µm the droplet outline is visibly distorted by freezing, whereas in smaller droplets a subtle contrast change is all that occurs.

Video recordings are stored on a large networked hard drive in .avi format. This format ensures that any potential loss of detail from compressed formats such as .mpg does not impact the analysis of smaller droplets. To keep the amount of data collected to a manageable size, recordings are made at ~5 frames per second; at this frame rate, a typical 1 K min-1 homogeneous experiment creates a video file 3 GB in size. To facilitate the video recording and simultaneously record the time of each frame to millisecond resolution, a program with a simple GUI was written in the National Instruments LabVIEW environment (see appendix). The videos are then analysed to produce nucleation statistics (Chapter 4). In droplets larger than about 10 µm diameter, freezing is clearly noticeable as a change in the outline of the droplet. For smaller droplets generally the only visible change is a darkening of the droplet outline (Figure 3.8). The size of the droplet is measured prior to freezing and the time of freezing retrieved via the frame time.

The shape distortions observed occurring in larger droplets in Figure 3.8 are an interesting feature. They are probably a side effect of performing these experiments in oil, as they are seen infrequently in experiments in air. After nucleation, the growth rate of the solid phase depends upon the rate of dissipation of the heat of crystallisation[57]. If nucleation does not occur in the very centre of the droplet, cooling by conduction to the surrounding oil will encourage the growth of the crystal phase towards, and then across, the surface of the droplet (e.g. refs [132-134]). The result is a core of supercooled water surrounded by a shell of ice[135]. As the ice grows into the liquid core, its expansion increases the pressure on the core until a fracture in the shell occurs, and a jet of liquid is ejected from the fracture. This jet rapidly freezes, resulting in a protrusion of ice, as has been seen by many in the past[135-

137]

, and can be seen in some of the larger droplets in Figure 3.8B. 3.1.5.1. Droplet size measurements

Droplet sizes are measured shortly before freezing directly upon a monitor using a ruler with 1 mm divisions. The on-screen image sizes are then converted to actual droplet sizes in µm, using the mm to µm ratio from the measurement of an image of a micrometre (Figure 3.9). As the lines of the micrometre are approximately 2 µm thick an error in the size conversion can occur; to minimise this a long section of the micrometre (700 µm) was used to calculate this ratio. By assuming that any slight lack in focus caused by droplet sizes and/or contraction of the stage does not result in a significant error, the uncertainty in the droplet size is due to the ±0.5 mm accuracy of the on-screen measurement. The conversion

ratio on the screen used for the majority of analysis is ~2:5 mm:µm, resulting in a droplet size uncertainty of ±1.25 µm.

3.1.5.2. Freezing time accuracy

The time of droplet freezing is taken from the frame time records created by the computer. These records are at millisecond resolution and each frame is approximately 200 ms apart. Assuming that ice nucleation occurs and becomes visible during the same frame, the uncertainty in the time of freezing is ±100 ms. In a 1 K min-1 experiment this corresponds to a temperature error of ±1.67 × 10-3 K. However, the stage temperature is measured by a hand held temperature logger which does not have the capability to record directly to the computer, and it is necessary to synchronise the timing of the temperature logger to that of the stage. This synchronisation is performed shortly after beginning the video recording by sharply adjusting the light on the microscope in conjunction with starting the temperature logger, giving a frame time for the start of the temperature logger record. It is estimated that the error introduced by this synchronisation is about ±1 s, equivalent to ±0.02 K when cooling at 1 K min-1. In comparison with the temperature uncertainty due to the stage (see section 3.1.7.1) the temperature error due to timing in a 1 K min-1 experiment is small and is considered insignificant.

Figure 3.9. A) Image of a section of the micrometre and B) an example of droplets with an overlaid 10 µm scale. The micrometre in A) provides 100 ticks, each 10 µm apart, for a total length of 1 mm. The image shown in B) has been magnified and contrast adjusted for clarity, and shows the largest droplet visible in Figure 3.8.