Particle concentration profile

Fig. 2. (a) Particle concentration profile of liquid flowing in a pipe, where YjD = the ratio of the distance along the diameter to the diameter ( ) (b)... 

The bed was first operated at the preselected conditions at a steady state then about 455 kg of the coarse crushed-acrylic particles, similar to that used as the bed material but of sizes larger than 6-mesh, were injected into the bed as fast as possible to serve as the tracer particles. Solids samples were then continuously collected from five different sampling locations at 30-second intervals for the first 18 minutes and at 60-second intervals thereafter. The samples were then sieved and analyzed for coarse tracer particle concentration. Typical tracer particle concentration profiles vs. time at each sampling location are presented in Figs. 38-42 for set point 3. 

In Fig. 3, a particle concentration profile in a turbulent flowing fluid is shown. The concentration is virtually uniform outside the viscous sublayer, i.e., c, and the concentration at the surface is c. The transport of particles is given by... 

Sessiecq P., Mier P., Gruy F., Cournil M., Solid particles concentration profiles in an agitated vessel, Trans IChemE 77 (1999) 11, p. 741-746... 

The slip effect can be so severe that one commonly observes a plug flow of concentrated suspensions in capillary tubes. Hence, the method does not form an intrinsically suitable basis for examining the bulk rheological characteristics. There are other problems associated with this method as well, such as wall separation (a depletion zone exists in the wall region), resulting in variation of the local particle concentration profile. 

In Chapter 5 the need for a concentration gradient to drive the mass transfer process was discussed. Fig. 7.1 shows the particle concentration profile within a fluid flowing through a pipe under turbulent conditions. In terms of the rate of deposition the transport of particles to a surface can be defined by... 

Rieger, F., Ditl, P., and Havelkova, O. (1988). Suspension of Solid Particles—Concentration Profiles and Particle Layer on the Vessel Bottom, In Proceedings of the 6th European Conference on Mixing, Associane Italiana di Ingeneria Chimica, Milan. 

Rose, N. L., S. Harlock, P. G. Appleby R. W. Battarbee, 1995. The dating of recent lake sediments in the United Kingdom and Ireland using spheroidal carbonaceous particle concentration profiles. Holocene 5 328-335. 

Rieger F, DM P, Havelkova O. (1988) Suspension of solid particles—concentration profiles and particle layer on the vessel bottom. In Proceedings of Sixth European Conference on Mixing, Pavia, Italy, 24—26 May, BHRA, Cranfield, UK. p 251-258. 

The diagrams in Fig. 1 illustrate how the particle concentration profile relaxes in the FFF channel under the influence of a sedimentation force field.Initially, at time zero, particles are homogeneously distributed across the channel. Under the force field (as time progresses), the particle concentration profile is as predicted by the kinetic theory developed by Yau and Kirkland, and the particles are compacted toward the bottom wall. After 5 min relaxation, or longer (in typical operating conditions), as shown in Fig. 1, particle concentration approaches the steady-state or equilibrium condition and will no longer vary with increasing relaxation time. 

The transient particle concentration profiles for a 20 w/o and 60 w/o dolomite starting mixture are presented in Figs. 32 and 33. They are shown for 3, 5, 10, and 20 seconds of operation. When the jetsam concentration is low (e.g., 20 w/o dolomite mixture), both the... 

Xu G, Sun G, Nomura K, Li J, Kato K. Two distinctive variational regions of radial particle concentration profiles in circulating fluidized bed risers. Powder Technol 101 91-100, 1999. 

The effect of the magnetic field (intensity Hq) on the spontaneous curvature Cq is due to the modification it implies on the particles concentration profile in the vicinity of the bilayer. Qualitatively the depletion in nanoparticles is reduced near the magnetic poles because of magnetic attraction. The effect of this phenomenon on Cq can be quantitatively described by introducing an angular dependence in the expression of the decay factor of the electrostatic potential away from the bilayer ... 

Solution of the particle concentration profile in the particle concentration boundary layer from in the feed suspension liquid to the concentration on top of the cake (and equal to the concentration in the cake) requires consideration of the particle transport equation in the boundary layer. We will proceed as follows. We will first identify the basic governing differentied equations and appropriate boundary conditions (Davis and Sherwood, 1990) and then identify the required equations for an integral model and list the desired solutions from Romero and Davis (1988). However, we will first simplify the population balance equation (6.2.51c) for particles under conditions of steady state 8n rp)/dt = O), no birth and death processes (B = 0 = De), no particle growth (lf = 0) and no particle velocity due to external forces Up = 0), namely... 

Solution of equation (7.2.121) requires a knowledge of the particle concentration profile y) and the velocity profile vjy). This is achieved hy solving equations (7.2.117) and (7.2.118) for vJy) and (y) (Davis and Leighton, 1987). These profiles have heen employed hy Romero and Davis (1988) to calculate a quantity called the excess particle flux,... 

The strategy is to calculate the axial particle concentration profiles of a given particle size in the three regions 1, 2 and 4, where the efficiency is computed from ... 

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