This chapter develops the point-force Equations of Motion for a single spherical particle moving in an unbounded fluid. This includes the particle Equations of Motion, which are considered as a sum of pointwise forces. The drag force is described for solid and fluid particles for Reynolds numbers ranging from creeping flow to turbulent flow. The three acceleration forces of added-mass, fluid-stress, and history forces are explained, and all the forces are combined to provide various Equations of Motion. Finally, heat and mass transfer effects on the particle are discussed.

Nearly one-third of the energy produced in the US comes from liquid fuels derived from crude oils, natural gas plant liquids, and other condensates. Fuel atomization to produce spray(s) is necessary for practical combustion systems employing liquid fuels. This requirement stems directly from the high energy density of the liquid fuels. Despite the major changes underway in the portfolio of liquid fuels, fuel atomization and combustion systems have remained vastly unchanged. The current practice is to design drop-in liquid biofuels that can be used “as is” in existing combustion devices. However, such fuels can be energy intensive to produce and create wasteful byproducts, eroding the carbon footprint benefits of the liquid biofuels. Thus, it is imperative that the liquid fuel injection, atomization, and combustion systems of the future consider increased fuel flexibility to utilize both fossil and alternative fuels from multiple sources within the same combustor hardware. Fuel properties and fuel atomization and combustion hardware should be co-optimized to minimize the carbon footprint based on the life-cycle analysis of the fuel. This chapter discusses atomization of renewable liquid fuels, detailing the phenomenology and controlling physical processes.

Nearly one-third of the energy produced in the US comes from liquid fuels derived from crude oils, natural gas plant liquids, and other condensates. Fuel atomization to produce spray(s) is necessary for practical combustion systems employing liquid fuels. This requirement stems directly from the high energy density of the liquid fuels. Despite the major changes underway in the portfolio of liquid fuels, fuel atomization and combustion systems have remained vastly unchanged. The current practice is to design drop-in liquid biofuels that can be used “as is” in existing combustion devices. However, such fuels can be energy intensive to produce and create wasteful byproducts, eroding the carbon footprint benefits of the liquid biofuels. Thus, it is imperative that the liquid fuel injection, atomization, and combustion systems of the future consider increased fuel flexibility to utilize both fossil and alternative fuels from multiple sources within the same combustor hardware. Fuel properties and fuel atomization and combustion hardware should be co-optimized to minimize the carbon footprint based on the life-cycle analysis of the fuel. This chapter discusses atomization of renewable liquid fuels, detailing the phenomenology and controlling physical processes.