A new theory to predict liquid circulation was derived and compared with applicable literature data. A single dimensionless group, ε(gRd2/v2c), is shown to control mixing intensity under low-viscosity conditions, but two separate groups (ε and gRd2/v2c) are necessary for viscous systems. Closure was accomplished using the Prandtl model for Reynolds stress. Locally varying mixing length was taken to be proportional to bubble size and bubble concentration. The model was constructed based on the premise that two distinct zones exist: a mainly turbulent core joined to a thin viscous wall layer.