## Abstract

When a bed of dense solid particles in a horizontal tube is subject to an oscillatory liquid flow, five different 'flow regimes' can be identified, ranging from a stationary bed regime to a complete suspension of the particles in the liquid. In the present investigation, the transitions between these regimes have been measured as a function of the following variables: angular frequency $\omega $ (2.5 to 9 rad/s), amplitude A (up to 41 cm), particle diameter d (100 to 1100 $\mu $m), the ratio $\gamma $ of the density difference between particles and liquid to the density of the liquid (0.26 to 4.1) and the kinematic viscosity of the liquid $\nu $ (0.89 to 80.6 cSt). Two further conditions were dept constant, namely the volume concentration of solids (2%) and the diameter of the tube (5.08 cm). The amplitude-frequency threshold at which general surface motion of the particles for part of the oscillation cycle was first observed could be correlated as follows: $\frac{A\omega ^{1.5}}{(\gamma g)^{0.75}d^{0.25}}$ = 0.37. (i) The left-hand side of the correlating equation can be obtained from a modified form of a theory (Taylor 1946) based on an oscillating laminar boundary layer near the surface of the particle bed. Once general surface motion of particles has been established, the beds tends to form regularly spaced dunes. The dune wavelength can be correlated approximately as follows: $\lambda =18[(A-A_{23})\ d]^{\frac{1}{2}}$, (ii) where $A_{23}$ is the transition amplitude calculated from equation (i). Deviations from this correlation occur when the crest height of the dunes becomes very high, owing to an effect of the tube diameter. The transition from a dune-forming bed to a bed in which the surface particles were in motion through the oscillation cycle was found to occur when $\frac{A\omega ^{1.2}}{(\gamma g)^{0.5}d^{0.1}\nu ^{0.2}}$ = 6.6. (iii) The data for large sand particles in viscous liquids deviated from this correlation, owing possibly to a rolling effect. At a sufficiently high amplitude $(A_{45})$ it was possible to suspend all the particles. It was found that $A_{45}$ was 1.55 times the amplitude calculated from equation (iii). The conditions found in this work for the threshold of general surface motion and for particle suspension have been compared with available correlations for steady flows. When the comparison is based on oscillation velocity $(A\omega)$, it was found that oscillatory flow was generally more effective than steady flow in bringing about the threshold of particle motion. However, oscillatory flow was somewhat less effective in bringing about suspension. This is consistent with the well-known tendency for purely oscillatory flows to remain laminar at velocities which, in steady, flow, would correspond to turbulent conditions.