Sublimation Kinetics of Carbon Dioxide
Abhishek Purandare is a PhD student in the department of Energy, Materials and Systems. Promotors are prof.dr.ir. S. Vanapalli and prof.dr.ir. H.J.M. ter Brake from the faculty of Science & Technology.
The solid form of carbon dioxide (CO2), commonly known as dry ice, undergoes sublimation directly from solid to gas without passing through a liquid phase under normal atmospheric pressure. Its non-wetting behavior, high phase change enthalpy, and low sublimation temperature make it suitable for various practical applications such as spray cooling, cryopreservation, refrigeration, machining, and cleaning operations. Despite its wide use, the underlying physical mechanisms governing dry ice sublimation are not completely understood. Therefore, this thesis focuses on investigating dry ice sublimation, particularly in a controlled gas environment and on a hot solid surface.
After providing a general introduction to dry ice and related physical phenomena in Chapter 1, Chapter 2 focuses on determining the sublimation temperature of dry ice for various far-field CO2 concentrations and pressures in the surrounding gas. We demonstrate that neglecting appropriate far-field conditions leads to significant deviations from the commonly quoted temperature of dry ice, −78.5 ◦C/194.6 K, valid when dry ice is in an environment saturated with its own vapor at 1 bar pressure. Specifically, our results show that for a certain far-field pressure, the sublimation temperature of dry ice decreases as the far-field CO2 concentration reduces, due to sublimative cooling. Furthermore, variations in the far-field pressure also affect the sublimation temperature of dry ice. When the pressure decreases while keeping the far-field CO2 concentration constant, the temperature at which dry ice sublimates decreases. This effect arises from the increase in the diffusion of CO2 vapor in the gas mixture as the ambient pressure decreases, leading to enhanced sublimation from the dry ice surface and cooling to a lower sublimation temperature.
In Chapter 3, we implemented a Schlieren imaging technique to study the nature of density gradients near the surface of a sublimating dry ice sphere in a relatively hot gas stream, using the light intensity variations observed in the Schlieren images. The measured light intensity values in the Schlieren images and the density gradient predictions from a numerical model exhibit a similar overall variation along the curvature of the dry ice sphere for a given radial position from the boundary of the dry ice. Both parameters progressively increase along the curvature of the sphere, reaching a peak at the horizontal plane, before decreasing along the curvature towards the bottom of the sphere. Additionally, both parameters decrease exponentially in the radial direction for a given position on the sphere’s curvature. Lastly, unlike liquid droplets evaporating in a gas stream, which retain or tend towards a spherical shape, dry ice tends towards the shape of a streamlined body due to the absence of deformation caused by surface tension. This shape evolution persists until frost forms on the surface of the dry ice during experiments, distorting its morphology in the later stages of sublimation.
In Chapter 4, we shift our focus to the Leidenfrost dynamics of dry ice by investigating a small disc-shaped pellet sublimating on a temperature-controlled sapphire substrate. We employed the Optical Coherence Tomography (OCT) technique, utilizing a common path interferometer with the reference beam reflected at the substrate. Through this method, we revealed the spatial and temporal profiles of the vapor layer beneath the disc-shaped dry ice pellet. The vapor layer is demonstrated to be nearly flat below the pellet, within the surface roughness and resolution limits of the experimental setup. Additionally, the vapor layer thickness is shown to increase non-linearly over time until the near end of the pellet’s lifespan. These observations contrast with the Leidenfrost dynamics of liquid puddles, where the thickness of the vapor layer exhibits spatial fluctuations that decrease with time. Additionally, a theoretical model based on the lubrication approximation is employed to estimate the vapor layer thickness and the temporal evolution of the pellet’s geometry. The theoretical predictions generally agree well with the measurements throughout the majority of the pellet’s lifespan, with deviations observed towards the end of its sublimation due to the assumption of a constant pellet diameter in the model. Furthermore, the theoretical predictions reasonably represent the pellet’s lifetime and initial value of the vapor layer thickness across a wide range of substrate temperatures, validating the predictive capabilities of the theoretical model in the presented scenario.
In Chapter 5, we demonstrated the use of a non-invasive capacitive method as a relatively simpler experimental technique to investigate the Leidenfrost phenomenon. To this end, we first designed and characterized the capacitance output of a sensor featuring in-plane miniaturized electrodes forming a double-comb structure. The characterization study revealed that such a sensor exhibits an exponential decrease in capacitance as a dielectric material moves away from its surface. Additionally, we found that the sensor’s output is not highly sensitive to the geometry, particularly the height, of the sensor and the dielectric material. To validate this concept, we placed a sublimating dry ice pellet on the temperature-controlled capacitive sensor and analyzed its output. The temporal change in capacitance from the sensor was consistent with the expected variation of the vapor layer beneath a disc-shaped dry ice pellet. Furthermore, we compared the values of the initial vapor layer thickness and the pellet’s lifetime derived from the sensor’s output with benchmark data obtained from OCT for a wide range of substrate temperatures. While the pellet’s lifetime measured from both methods agreed reasonably well, notable deviations were observed when comparing the initial values of the vapor layer thicknesses. These discrepancies may be attributed to impurities resulting from condensation and freezing of water ice on or inside the dry ice, thereby altering its electrical permittivity to which the sensor is highly sensitive. Nonetheless, the capacitive sensors introduced in this work hold the potential for further exploration, refinement, and application in quantifying Leidenfrost vapor layers.
Finally, in Chapter 6, we investigated the sublimation of dry ice pellets inside an insulated container—a practical problem of direct relevance to cold-chain logistics applications. The temporal variation of dry ice mass inside insulated containers, a practical parameter of interest, depends on the rate of heat transfer from the ambient environment into the box. To estimate the sublimation rate of dry ice in such containers, we proposed a simplified iterative modeling approach in this chapter. We observed that the area of the inner wall of the container in the vicinity of the dry ice significantly contributes to the total heat transfer rate for the majority of the dry ice’s lifetime. Reducing the surface emissivity of the inner walls of the container appears to reduce the sublimation rate of dry ice. Despite its engineering relevance, the proposed approach lacks an accurate prediction of the temperature profile in the head-space between the dry ice and the container due to the unaccounted convective heat transfer relevant in that region. Considering the transport of vapor from the dry ice surface towards the exit of the container may be of relevance in accurately determining the shape of the dry ice-vapor interface inside the box, which is otherwise assumed flat. This, in turn, can assist in determining the contact area of dry ice with the walls of the container, thereby allowing more accurate predictions of the heat leak and the sublimation rate of dry ice.
