High-speed propulsion is a challenging and critical area of research. A major challenge with high-speed propulsion is the limited time scales available to mix
and combust the flow within the residence time. When exploring practical propulsion systems, the requirement to utilize liquid fuels adds a further challenge,
as the liquid needs to breakup, evaporate, mix, and burn within the same residence time. One promising method to deal with this challenge is to utilize
detonations or shock waves to accelerate the breakup, evaporation, and combustion. The details of a shock or detonation-driven breakup of liquid droplets is
receiving significant attention. However, a physical understanding and modeling of such multiphase detonations are hampered by a lack of models for the
evolution and breakup of a single droplet after a shock or detonation. Experimental studies of this problem are available but can only measure macroscopic
properties and cannot resolve the quantitative details at small scales. High-fidelity interface-resolving numerical studies are needed to understand the
break-up process better and the similarities and differences between detonation and shock-driven breakup.

The goals of this thesis are: 1) to gain insights into the stages of breakup and secondary droplet distribution throughout the breakup, 2) to leverage the stages
of breakup and the droplet distribution to understand the impact of evaporation and how that may impact liquid fueled detonations. The breakup was found
to follow five stages. Two of the key stages are the droplet flattening due to the pressure difference, while instabilities form on the droplet surface. That is
followed by the rapid recurrent piercing of the droplet by these surface instabilities, resulting in the sudden catastrophic shattering of the droplet. The fraction
of mass contained in secondary droplets was found to be minimal until this recurrent piercing. During the recurrent piercing, the secondary droplets followed
a log-normal distribution, with a few larger droplets not well represented by the log-normal distribution. However, these large droplets were short-lived and
rapidly decayed to the log-normal distribution. This allows for the breakup to be approximated as an induction time until the breakup begins, followed by a
breakup where droplets are shed at the final log-normal distribution. For detonation-driven breakup, a similar process occurs, and the breakup time scale is
significantly faster than the evaporation time scale for the primary droplet, resulting in minimal evaporation prior to breakup. Thus, the evaporation is
controlled by the resulting change in the effective area due to the breakup and secondary droplet distribution. This allows for an extension of the mass
stripping model to account for the induction time prior to breakup beginning and accounting for the secondary droplet distribution. Further work exploring
liquid-fueled detonations is needed as the current work predicts the breakup and resulting distribution will control the evaporation time scales, but the mixing
and ignition delay times scales have not yet been explored. This work represents the first interface-resolving study of detonation-driven breakup that captures
heat transfer, phase change, and the secondary droplets; it is also the first study to capture the secondary droplet distribution during a shock-driven breakup.