Slip velocity of particulate solids in vertical tubes

Abstract

The terms involving square roots can be expressed as elliptic integrals (13) of the first ( F ) and second ( E ) kind. Thus In any system where solids are to fall through or are to be lifted by %uids a knowledge of the slip velocity of the solids is of great importance. At present there is a definite lack of experimental data in the literature for fluid-solid systems. The present work ( 2 ) in the intermediate or transition region between where the Stokes and Newton laws apply has been carried out to develop an accurate equation for slip velocity calculations for both spherical and nonspherical particles. THEORYThe slip velocity of a single body falling in a fluid is defined as the constant equilibrium velocity attained by the body when the resistance offered by the viscous medium increases to the point where it is equal to the sravitational acceleration force. If the fluid is also stationary and infinite, the slip velocity equals the terminal velocity.It has been demonstrated experimentally (4) that the resistance cp of a particle in motion involves four quantities: the surface area of the particle A,, its terminal veloc-H. Donald Allendorf is with Aerochem Research Laboratories, Inc., Princeton, New Jersey. Page 1070A.1.Ch.E.475 jb./c,u. ft.), surface to 0.31 Ib./cu. ft.) were ity ut, and the viscosity pf and density ,of of the medium through which the particle is flowing. The relationship involved may be expressed by the following equation:It should be noted that the area used here is the actual surface area of the particle rather than the area of the particle projected on a plane perpendicular to the direction of flow as used by several previous investigators. The actual area was chosen as it is much more readily detgmined experimentally.

Rheological behaviour of two-phase flow of solid particles in a gas

“…In the literature, the volume fraction of solid partitles is often regarded as the only variable influencing the rheological properties of the suspension. However, it has been shown experimentally [1] that the rheological behaviour of a system is also significantly influenced by other quantities such as density, dimension, shape and size distribution of solid particles, presence of electrostatic charge as well as the physical properties of the carrier medium [14]. Therefore, the published equations expressing the apparent viscosity or any other flow property only as a function of volume fraction of the dispersed phase are in principal incorrect.…”

Study of transition velocity from bubbling to turbulent fluidisation by recurrence plots analysis on pressure fluctuations

“…A comparison between transition velocities from bubbling to turbulent regime obtained by RQA analysis, standard deviation analysis and results of the other references (Jones et al, 1966; Bi and Grace, 1995) is given in Table 1. As can be seen, transition velocities obtained from RR and ENT are in good agreement with the values obtained from standard deviation and with the references.…”

Thermodynamics of gas‐solid flow

“…We are going to compare here the same effective work, solid effective work, and energy factor and the same calcula- tion procedure already proposed in Collado and Muiioz (1997) with experimental data for atmospheric-pressure, vertical pneumatic transport tests made by Jones et al (1966Jones et al ( , 1967 from the Pennsylvania State University. The height of the line was 5.79 m, and, until twelve different materials were tested, all of them had a very narrow size distribution.…”

“…In this article, after a brief review of this new approach based on thermodynamic fundamentals, the comparison of the energy factor against atmospheric-pressure data taken in the 5.8 m lift line of the Pennsylvania State University (Jones et al, 1966(Jones et al, , 1967 is analyzed, and a strong dependence of the energy factor on the solids reference velocity has been also verified for the atmospheric-pressure data. A brief outline of this analysis was already sketched in Collado (2000d).…”