A water droplet that impacts on a cold surface will start to freeze and in time ice will accumulate. To exemplify, effects of ice accretion is important in areas such as power generation e.g. wind power and vehicles located in a cold climate e.g. aircraft, cars, and boats. The common denominator for these examples is that ice accumulation can lead to a loss of efficiency and in some cases danger.

Most studies have so far focused on investigating freezing water droplets visually in experiments or numerically in regards to how the freezing process behaves in terms of shape or freezing time for either a sessile or impacting droplet. It has been observed that the surface material and structures of the substrate is of importance. One part of the freezing process that has been less investigated is the internal flow and how it affects the freezing process.

In this thesis, the internal flow in a freezing water droplet has been investigated experimentally. The internal flow inside a droplet is calculated by using Particle Image Velocimetry. A metal plate with a groove filled with ice was used to generate an area for the nucleation to start and to be able to control the shape of the droplet. 

Previous work indicate that the substrate is of importance for the freezing process. The influence of the substrate material on the internal flow for similar shaped droplets is therefore investigated in Paper A, for a substrate temperature of -8°C. The results show that the substrate material, here in terms of metals such as aluminum, copper and steel, affect the magnitude of the internal velocity. In paper B it is investigated how the contact angle influence the internal flow. The vector field is examined at 9% of the total freezing time for water droplets at five different contact angles. A droplet with a higher contact angle will have a higher internal velocity in the center. A lower contact angle will barely show any movement in the center, however a higher velocity magnitude is observed close to the free surface compared to a droplet with a higher contact angle. Paper C studies the time until the directional change of the internal flow in a water droplet. Experiments at -8°C as in Paper B are used as well as experiments at -12°C for the five different contact angles. The time until the directional change is similar in time for both -8°C and -12°C while the total freezing time and also the time of the directional change varies with contact angles. A droplet with a lower contact angle will have a shorter time until the directional change occure while an increase in contact angle prolongs both freezing time and the time until the directional change.

Freezing water is a common occurrence in Arctic climates and can pose hazards, for instance when water droplets impact surfaces. This is of specific interest in for example de-icing and anti-icing applications for wind turbine blades, aircraft, and roads. When a droplet hits a cold surface and begins to freeze, an internal flow is initiated. This thesis aims to study this internal flow, to determine the driving factors, and explore if it can be controlled for de-icing or anti-icing purposes. Such motions are also of generic interest and may be of importance for mixing on the micro-scale for medical purposes as one example. Since there are two possible driving mechanisms for the flow, temperature induced gradients in density and in surface tension, the flow direction within the droplet may change during the freezing process.

Experimental work was carried out using Particle Image Velocimetry (PIV) to investigate droplets initially having room temperature being placed on metal surfaces cooled below 0 ^oC. Grooves were etched into the plates and filled with ice to control the contact area of the droplet and the material in contact (e.g., aluminium, or a combination of ice with aluminium, steel, or copper). The results show that the groove enabled consistent droplet shapes, with a deviation of around 0.85% in normalized contact radius. Among different substrate materials, copper (with the highest thermal conductivity) exhibited the highest velocity along the centerline of the droplet, while steel and aluminium showed similar magnitudes.

For droplets on aluminium and ice, droplets with contact angle between 65^o and 94^o were compared and it was observed that smaller contact angles resulted in higher velocity magnitude along the free surface of the droplet and a lower velocity magnitude in the center as compared larger contact angles. The contact angle also affected freezing time and the time until directional change, meaning the time when the internal velocity changes direction before coming to a complete stop. The experimental observation is that the internal flow moves down along the surface and up in the center to start with, and switches to down in the center and up along the surface after a while. Along the centerline, the increase of contact angle presented an increase in velocity magnitude, freezing time, and time until directional change. Interestingly, substrate temperature (at -8 ^oC and -12 ^oC) had little impact on the time of the directional change, in comparison to the influence from the contact angle.

When the ice was removed from the contact area and only aluminium was in contact with the droplet, heat transfer naturally increased, reducing freezing time and slightly shortening the time until directional change. In experiments where solidification was prevented, i.e. causing the droplet to become supercooled, a similar flow pattern was observed, though the directional change occurred much later. This indicates that while phase change affects velocity magnitude and time of the directional change, it is not the main driver of internal flow.

Complementing the experiments, numerical methods using Computational Fluid Dynamics (CFD) to further analyse the effect of heat transfer on internal flow were used. Specifically, the effects of external heat transfer (i.e conduction, natural convection and evaporation) on the internal flow and temperature was examined. Although comparison with experiments show an underestimation of the internal velocities, natural convection as the driving force of the internal flow give comparable results in terms of time of the directional change.  For this set-up, simulations show that the directional change is closely related to the density inversion of water. 

In summary, the time from droplet impact until the internal flow is approaching zero, a phenomenon closely related to the time of the directional velocity change, is strongly influenced by both phase change and the contact angle of the droplet. The two variables are dependent on the substrate, suggesting the flow can be controlled by manipulating the substrate material and possible used for anti-icing purposes. The magnitude and direction of the internal flow may in its turn be further controlled by heat fluxes and surface tension effects, i.e. of importance for mixing, deposition or orientation of particles in a droplet. Future research should focus on clarifying heat transfer effects, the temperature field, and the impact of surrounding air with forced convection.