| Two-phase flow makes up about one-half of all industrial, biological and environmental fluid mechanics. Analytical methods that are presently useful in these are still mostly ad hoc. Unlike in (single phase) fluid mechanics, there are no universal macroscopic fundamental equations existing yet, although the Navier-Stokes equations describe the microscopic details of the motion of each phase. One promising recent theoretical development in two-phase flow is the two-fluid theory. The modeling of the interfacial interaction force terms are very crucial in this theory since they govern the interfacial momentum transfer and couple the two phases together. One of the interaction forces is the inertial coupling force, or the added (virtual) mass force, which plays a significant role in deciding the well-posedness of the model, especially when dynamic interactions (relative acceleration) between phases are important (Drew, 1983).;Attention is focused on the inertial coupling aspect of two-phase modeling in this thesis, following Wallis (1989). Although the concept is classic, there is still much to be known about added mass effects in two-phase flow. The boundary (be it fluid boundary or other surfaces) effect on the added mass coefficient of a sphere is studied, resulting in several new, essentially exact solutions which are valuable contributions to the understanding of hydrodynamic interaction in potential flow. The added masses for isotropic and nonisotropic dispersions of spheres in an unbounded flow are studied. Among the new results are: (i) the "conditional" convergence experienced is physically meaningful; (ii) Geurst's conjecture (1985) is correct, contrary to Smereka & Milton's (1991) finding; (iii) predictions from the "tube model" proposed in Cai & Wallis (1992) are further validated by predictions from the image method. Some new phenomena about the added mass of dispersed flow in finite pipes with different end conditions are also studied. Experimental devices and procedures are developed to test some of the theoretical findings. The comparisons are good. |
