On the Flow of Suspensions Through Narrow Tubes

Abstract

The anomalous flow of certain suspensions through narrow tubes, known as the ``sigma'' phenomena, for which no fully satisfactory explanation has yet been given, is discussed. If it be assumed that the streamlining layers are not infinitely thin, so that a summation treatment takes the place of an integration, a series of equations can be derived depending on the relation assumed to exist between velocity gradient and shearing stress and on the nature of the friction between the layers. These equations reduce, in the limiting case of infinitely thin layers to the well-known forms of Poiseuille, Buckingham-Reiner, etc., and the general equation of Schofield-Scott Blair can also be derived. For finite thicknesses of layer, the equation derived adequately explains the sigma-phenomenon, and this is shown quantitatively by applying it to the data given in the original paper.