Two-phase bubbly suspensions are encountered in flotation columns, oil wells, and bioreactors. They are also encountered in food processing and processing of polymer melts. During the ascent of magma from a magna chamber to the earth’s surface, nucleation and growth of gas bubbles occur by exsolution of volatiles that are initially dissolved in magma at high pressures. Understanding the effect of bubbles on the rheological properties of bubbly suspensions is important for the analysis and modeling of processes where such systems are encountered. As bubbles can undergo changes in volume, bubbly suspensions behave as a compressible fluid with nonzero dilational viscosity. The presence of surfactant film on the surface of bubbles can have a significant influence on the rheology of bubbly suspensions. The dilational properties of a bubbly suspension can be determined using the cell model approach.