There are many options available when selecting a computational model for two-phase flows. It is important to understand all the features of the model selected, including when the model is appropriate and how using it may affect your results. This work examines how volume displacement effects in two-phase Eulerian-Lagrangian models manifest themselves. Some test cases are examined to determine what input these effects have on the flow, and if we can predict when they will become important. Bubble injection into a traveling vortex ring is studied in-depth, as it provides significant insight into the physics of these volume displacement effects. When a few bubbles are entrained into a traveling vortex ring, it has been shown that even at extremely low volume loadings, their presence can significantly affect the structure of the vortex core (Sridhar & Katz 1999). A typical Eulerian-Lagrangian point-particle model with two-way coupling for this dilute system, wherein the bubbles are assumed subgrid and momentum point-sources are used to model their effect on the flow, is shown to be unable to accurately capture the experimental trends of bubble settling location, bubble escape, and vortex distortion for a range of bubble parameters and vortex strengths. Accounting for fluid volume displacement due to bubble motion, using a model termed as volumetric coupling, experimental trends on vortex distortion and bubble settling location are well captured. The fluid displacement effects are studied by introducing the notion of a volume displacement force, the net force on the fluid due to volumetric coupling, which is found to be dominant even at the low volume loadings investigated here. A method of quantifying of these forces is derived and used to study the effects for a wide range of particle to fluid density ratios in Taylor-Green vortices. A simple modification to the standard point-particle Lagrangian approach is developed, wherein the interphase reaction source terms are consistently altered to account for the fluid displacement effects and reactions due to bubble accelerations. / Graduation date: 2013 / Access restricted to the OSU Community at author's request from Sept. 24, 2012 - Sept. 24, 2013