Similitude Analysis for Gas-Liquid-Fiber Flows in Cocurrent Bubble Columns

Gas-liquid-fiber systems are different from conventional gas-liquid-solid systems in that the solid material (i.e., fiber) is flexible, has a large aspect ratio, and forms flocs or networks when its mass fraction is above a critical value. With its wide application to the pulp and paper industry, it is important to investigate the hydrodynamics of gas-liquid-fiber systems. In this paper, 19 parameters that influence gas holdup in gas-liquid-fiber bubble columns are critically examined and then a dimensional analysis based on the Buckingham Pi Theorem is used to derive the dimensionless parameters governing gas-liquid-fiber bubble column hydrodynamics. Seven dimensionless parameters that are related to the fiber effects on gas holdup are further analyzed, and a single dimensionless parameter combining these dimensionless parameters is derived based on a force analysis and experimental results. This dimensionless parameter is shown to be sufficient to quantify the influence of fiber on gas holdup in gas-liquid-fiber cocurrent bubble columns. It also reduces the number of parameters needed in correlating experimental gas holdup data in gas-liquid-fiber bubble columns.