This study focuses on the demixing of neutrally buoyant suspensions of spheres during slow, pressure driven flows in circular conduits. Distributions of the solid fraction of particles, φ, and the suspension velocity, ν, are measured at different lengths from a static in-line mixer. Experiments were conducted over a range of volume average solids fractions, φbulk (0.10⩽φ⩽0.50), and at two different ratios of the particle radius, a, to the radius of the circular conduit, R (a/R=0.0256 and a/R=0.0625). At φbulk⩾0.20, the particles rapidly migrate to the low-shear-rate region in the center of the conduit. This migration results in a blunting of the ν profile, relative to the parabolic profile observed in homogeneous Newtonian fluids. For the flow geometry with the smaller ratio of a/R, the φ profile builds to a sharp maximum or cusp in the center. Particle structures are observed in the experiments with the higher a/R. The entrance lengths for the development of the φ and ν fields, Lφ and Lν, respectively, are strong functions of a/R and φbulk. Lφ and Lν rapidly decrease as φ and a/R increase. Over the range of our data, the ν profiles are observed to develop more rapidly than the φ profiles. The experimental results are compared with fully developed flow predictions from the shear-induced migration (SIM) model and the suspension balance (SB) model. At the smaller a/R, the SIM model more accurately predicts the experimental results. At larger a/R, some qualitative features of the experimental results are better predicted by the SB model, however, neither model provides good quantitative predictions, especially at low φbulk.

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that the efficiencies were known and that it was required to find the transient solution of the problem under consideration.It appeared that a suitable method for the determination of the transient plate efficiencies could be developed by replacing the steady state equations in the methods developed by Davis et al. and Taylor et al. by corresponding equations for the unsteady state models proposed by Waggoner et al. This approach, a logical extension of previous work, was successful, and the resulting methods are described in the first two sections that follow.A third procedure was developed for the determination of the transient plate efficiencies for the case where the compositions and plate temperatures are known functions of time. The equations needed in the application of this method are presented in a subsequent section.Also, a method was developed for separating the mixing effects of the liquid on each plate and in its downcomer which was not involved in mass transfer from the plate efficiencies of the liquid on each plate that was involved in mass transfer. This method was developed by replacing the steady state equations in the methods of Taylor et al. and Davis et al. by the unsteady state equations for the model described by Tetlow et al. (8). An example of this method is presented in which the plate efficiencies and mixing effects are determined simultaneously,In the method described in the next section, it is supposed that the product distributions (bi/di) and the tem- specifications such as the distillate rate, reflux rate, column pressure, type of condenser, number of plates, location of the feed plate, the complete definition of the feed, and the holdups are known. Information over and above this, such as any combination of product distributions (bi/di) and temperatures ( T j ) , is hereafter referred to as additional specifications. A D D I T I O N A L SPECIFICATIONS: ALL PRODUCT F U N C T I O N S OF T I M EOn the basis of these known values of the operating variables, the procedure that follows determines a set of plate efficiencies required to obtain agreement between results calculated by Waggoner's model (10) and the results of field tests.In the method developed, the transient operation period is subdivided into time increments. At the beginning of and the K values of component i (evaluated at the temperature and ressure at which the liquid leaves plate for Kjt, it is also evaluated on the basis of the temperature, pressure, and composition of the liquid leaving plate i.Since the sum of the yjls at the end of the time period (t, + A t ) under consideration has the value of unity, it follows that j ) by Kji. When t R e activity yj~ji is included as a multiplier 0 f j = 2 Eli Kji xji -1

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Measurements are reported of the pressure differences ΔP existing at large distances above and below a ball settling along the axis of a circular cylinder filled with an otherwise quiescent viscous Newtonian liquid in which identical particles, comparable in size to the settling ball, are suspended. The suspensions ranged in solids volume fraction ϕ from 0.30 to 0.50 and consisted of 0.635 cm diameter spheres density-matched to the suspending oil. The settling balls varied in diameter from 0.318 to 1.27 cm, resulting in particle Reynolds numbers always less than about 0.4 based upon ball diameter and the effective viscosity of the suspension. For the moderately concentrated suspension (ϕ=0.30), the product of ΔP with the cross-sectional area A of the containing cylinder was observed to be equal to twice the drag force D on the settling sphere, in accord with theory. In the more concentrated suspension (ϕ=0.50) this product was found to be slightly, but significantly, less than twice the drag on the settling sphere. It is speculated that this lower pressure drop may result from the presence of one or more of the following phenomena: (i) migration of the falling ball off the cylinder axis ; (ii) apparent slip of the suspension at the cylinder wall; (iii) blunting of the otherwise Poiseuillian parabolic velocity profile, the latter phenomenon being known to occur during the creeping flow of concentrated suspensions through circular tubes. Incidental to the suspension experiments, for a homogeneous fluid we verify the classical theoretical formula for the off-axis pressure drop when the sphere settles at a non-concentric position in the cylinder.