Motion of spherical particles in a Bingham plastic

Abstract

There i s current interest in the utilization of homogeneous suspensions of fine sized solids in the fluid transport of heterogeneous mixtures of coarse solid particles. It has been established that the introduction of the fines beneficially affects the transport of coarse solids (1, 2 ) . Although the homogeneous suspensions have been identified as non-Newtonians, there have not as yet been satisfactory solids pipelining design criteria for the transport of coarse particles based on the rheological properties of fines suspensions. A recent investigation (3) has shown that the use of existing design formulas, all of which include the coarse solids settling characteristics a s parameters, can result in significantly erroneous design unless these parameters are determined in the fluid actually used to transport these solids. This conclusion, based on limited experimental evidence, prompted a more detailed study of settling in nowNewtonian suspensions, particularly in the Stokes and intermediate settling regimes. EXPERIMENTAL PROCEDUREConsiderable preliminary work was necessary to find a fluid with stable Bingham properties, suitable for the settling tests. Although there have been numerous investigations of homogeneous suspensions in both pipelines and viscometers in which it has been suggested that the rheological behavior of these suspensions can be approximated by the idealized Bingham model (4 to6), most suspensions develop a density gradient after standing in a column and exhibit a nonlinear relation between shear stress and rate of shear at rates of shear approaching zero. Furthermore, to extend the range of variables, it was desirable to choose a plastic material with properties distinctly different from those used by others ( 3 , 7). Tomato sauce (catsup), which had been suggested (8) a s a Bingham plastic, was investigated; it was found suitable and used in the tests. The rheological properties of a Bingham plastic fluid are defined byThe Bingham plastic properties of the tomato sauce were substantiated by a series of flow t e s t s in tubes. Testing with a rotary viscometer was discontinued when the sauce showed a tendency to bleed after continuous shear of the material in contact with the viscometer. The tube viscometer offered much greater similarity to the subsequent settling tests in which the spheres continuously encountered material which had not recently undergone shear. Flow rates of the material under gravitational acceleration and under applied pressures were measured in stainless steel tubes ranging in internal diameter from 0.366 to 1.709 cm. to provide a similar scale to the subsequent drop tests. For the settling tests, silver balls were cast in various sizes and then neutron-irradiated to give a gamma activity of about 1 mC. of Ag 110 per sphere. The tests were made in a 6 in. x 6 in. x 54 in. high acrylic column. Spheres were dropped by hand a t the surface of the fluid in the column and were recovered from the conical bottom by permitting them to flow out with some fluid via a 3/4-in. dis...

An Approach to Understanding Cohesive Slurry Settling, Mobilization, and Hydrogen Gas Retention in Pulsed Jet Mixed Vessels

“…First, arguing against the analytical and tethered sphere results, Ansley and Smith (1967) note that, once motion ceases, the stress distributions are not known. Further, the pressure may not be hydrostatic so that the buoyant force on the sphere may not be relevant.…”

Sedimentation in Coal-Water Slurry Pipelining

“…However, in many cases of practical interest, both (3) and (4) are not in agreement with measured values. On the base of experimental evidence, a variety of "ad hoc"formulas for the terminal velocity of the particle have been suggested; a relatively recent state of art can be found in [13] and [14].…”

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