Most of the past experimental and analytical studies of turbulent transport have been confined to the regions of fully developed heat or mass transfer as it may occur in infinitely long transfer sections under very low flux conditions, while a limited number of studies have investigated the mass transfer entrance region. These studies have been concerned with determining the Nusselt or Stanton numbers and, to a lesser extent, the determination of the concentration profiles.Mass transfer under low flux conditions is completely analogous to heat transfer, but the studies of this process are not as numerous as those of heat transfer. A complete literature survey on heat and mass transfer studies in both the entrance region and the fully developed region is detailed elsewhere ( 7 ) . However, entrance region mass transfer studies with a fully developed velocity profile in a pipe will be discussed here.Schwarz and Hoelscher (10) have measured the concentration profiles of water vapor in a wetted-wall column with a fully developed velocity profile at the entrance. The entering Reynolds number was 25,000 and the concentration profiles were measured at aspect ratios of 5.6, 12.4, 19.6, and 25.5.Wasan and Wilke (19) and Bunch et a]. ( 2 ) have measured mass transfer from the inner surface of a tube with the entering turbulent flow being fully developed. Both of these investigators measured the concentration profiles, Wasan's measurements being in the mass transfer entrance region of a wetted porous pipe, while the measurements of Bunch were made at only one axial position 14.2 diam. from the entrance to the wetted-wall column. The work of Wasan was accomplished at low humidities where it was experimentally observed that the velocity remained unaltered by the flux of vapor leaving the surface of the porous pipe. Cairns and Roper ( 3 ) have taken data at both low and high humidities; however their Reynolds number range was limited from 2,390 to 9,095, and this study is valid for simultaneous heat and mass transfer in long wetted-wall columns.Shaw, Reiss, and Hanratty (11) and Son and Hanratty (15) have determined the entrance region mass transfer for very short aspect ratios at a Schmidt number of 2,400. By using isolated sections of the tube wall as an electrode where reduction of the ferricyanide ion occurred, Stanton numbers were reported for aspect ratios of 0.018 to 4.1 and for a Reynolds number range of 5,000 to 75,000. They (11) also obtained an equation for the Stanton number in the entrance region as a function of Reynolds number, Schmidt number, and aspect ratio. Several investigators have solved the energy and convective diffusion equations for binary equivolume diffusion in fully developed turbulent flow of gases in pipes. Most recently, Wasan and Wilke (21 1 attempted numerical solutions to the diffusion convection equations to establish the role of concentration level of the nondiffusing species in nonequivolume diffusion at ordinary mass transfer rates. Their results indicate that for a system at constant Sch...

A general treatment of entry region multicomponent mass transfer between a fully developed turbulent flow and a smooth pipe wall has been developed from a basis first derived by Toor.The coupled multicomponent equations were reduced to a n equivalent binary system by the method of undetermined constants. Numerical solutions for a forced convection, binary diffusion system involving gas-phase, nonequimolal diffusion were opplied to a ternary system. These solutions have been found to compare well with these authors entry region mass transfer data on a ternary acetone-methanol-air mixture and with the earlier analogy theories derived for the case of a n infinitely long test section. W e conclude that there is a significant interaction in some multicomponent systems, enough that the binary theory can not be satisfactorily applied in the design of multicomponent mass transfer systems. diffusion which can be described by the equation