On the attainment of steady state in turbulent pipe flow of dilute dispersions

An apparently significant disagreement is identified between the experimentally obtained particle-size distributions (measured at relatively short times but reported to represent the steady state) and theoretical steady-state predictions using realistic breakage kernels. By employing a theoretical analysis of temporal dispersion evolution, based on the breakage equation, it is suggested that essentially all the distributions for pipe flow, reported in the open literature so far, are not the true steady states but transients. Theoretical evidence is also presented that a long period of time is required to reach the true steady state in pipe flow and thus to estimate directly from measurements the maximum stable drop/bubble size, d(max). Furthermore, it is argued that d(max) imposed by pipe turbulence alone may be of limited practical significance, since the time required to achieve it may be unrealistically long, and its influence on the evolving distribution rather unimportant. (C) 1997 Published by Elsevier Science Ltd.