Particle-wall interactions

Either a liquid or a gas can be used as the carrier fluid, depending on the size and properties of the particles, but there are important differences between hydraulic (liquid) and pneumatic (gas) transport. For example, in liquid (hydraulic) transport the fluid-particle and particle-particle interactions dominate over the particle-wall interactions, whereas in gas (pneumatic) transport the particle-particle and particle-wall interactions tend to dominate over the fluid-particle interactions. A typical practical approach, which gives reasonable results for a wide variety of flow conditions in both cases, is to determine the fluid only pressure drop and then apply a correction to account for the effect of the particles from the fluid-particle, particle-particle, and/or particle-wall interactions. A great number of publications have been devoted to this subject, and summaries of much of this work are given by Darby (1986), Govier and Aziz (1972), Klinzing et al. (1997), Molerus (1993), and Wasp et al. (1977). This approach will be addressed shortly. 

One major difference between pneumatic transport and hydraulic transport is that the gas-solid interaction for pneumatic transport is generally much smaller than the particle-particle and particle-wall interaction. There are two primary modes of pneumatic transport dense phase and dilute phase. In the former, the transport occurs below the saltation velocity (which is roughly equivalent to the minimum deposit velocity) in plug flow, dune flow, or sliding bed flow. Dilute phase transport occurs above the saltation velocity in suspended flow. The saltation velocity is not the same as the entrainment or pickup velocity, however, which is approximately 50% greater than the saltation velocity. The pressure gradient-velocity relationship is similar to the one for hydraulic transport, as shown in... 

It is noted that the particle-wall interaction in the boundary layer and the electrostatic effect due to the electrostatic charge carried by the particles may strongly affect particle collection and reentrainment in the cyclone and, consequently, affect the collection efficiency. In the presence of electrostatic charges of particles and an external electric field, the collection efficiency of a tangential inlet cyclone with a steep cone is given by [Soo, 1989]... 

For dilute suspensions, particle-particle interactions can be neglected. The extent of transfer of particles by the gradient in the particle phase density or volume fraction of particles is proportional to the diffusivity of particles Dp. Here Dp accounts for the random motion of particles in the flow field induced by various factors, including the diffusivity of the fluid whether laminar or turbulent, the wake of the particles in their relative motion to the fluid, the Brownian motion of particles, the particle-wall interaction, and the perturbation of the flow field by the particles. 

We see that all optimization goals depend strongly on reducing . Experimentally, values down to 1 fitn and less have been realized. Such thin solute layers yield high-speed separations, often requiring only a few minutes for completion. However with small l, particle-wall interactions increase and in some cases lead to departures from theory [25]. 

Retention Perturbations Due to Particle-Wall Interactions in Sedimentation Field-Flow Fractionation, M. E. Hansen and J. C. Giddings, Anal. Chem., 61, 811 (1989). 

Even with these useful results from statistical mechanics, it is difficult to specify straightforward criteria delineating when the Poisson-Boltzmann or linear Poisson-Boltzmann equations can be expected to yield quantitatively accurate results for particle-wall interactions. As we have seen, such criteria vary greatly with different types of boundary conditions, what type of electrolyte is present, the electrolyte concentration and the surface-to-surface gap and double layer dimensions. However, most of the evidence supports the notion that the nonlinear Poisson-Boltzmann equation is accurate for surface potentials less than 100 mV and salt concentrations less than 0.1 M, as stated in the Introduction. Of course, such a statement might not hold when, for example, the surface-to-surface separation is only a few ion diameters. We have also seen that the linear Poisson-Boltzmann equation can yield results virtually identical with the nonlinear equation, particularly for constant potential boundary conditions and with surface potentials less than about 50 mV. Even for constant surface charge density conditions the linear equation can be useful, particularly when Ka < 1 or Kh > 1, or when the particle and wall surfaces have comparable charge densities with opposite signs. 

NonNewtonian suspending fluids their influence on the motion of an isolated particle and on particle-particle and particle-wall interactions. 

Particle-particle and particle-wall interactions inertial effects unsteadiness. 

On the other hand, retention in lift-hyperlayer FFF only depends on the particle size and is independent of density which makes the calibration easier. Lift-hyperlayer FFF is a very fast technique applicable to a particle size range from 0.5-50 pm if cross-flow forces are applied [226,303]. A further advantage of lift-hyperlayer FFF is that the particles are held well away from the wall during separation and thus particle-wall interactions are omitted. 

Du, Q. and Schimpf, M.E., Correction for particle-wall interactions in the separation of colloids by flow field-flow fractionation, Anal. Chem., 74, 2478, 2002. 

In the different cases, RUM is not so strong an3rway because the small droplets tend to align with the gas flow and the light load avoids particle-particle and particle-wall interactions, that are the main sources of RUM. 

Theologos and Markatos (1992) used the PHOENICS program to model the flow and heat transfer in fluidized catalytic cracking (FCC) riser-type reactors. They did not account for collisional particle-particle and particle-wall interactions and therefore it seems unlikely that this type of simulation will produce the correct flow structure in the riser reactor. Nevertheless it is one of the first attempts to integrate multiphase hydrodynamics and heat transfer. 

Accurate description of particle-particle and particle-wall interactions including effects due to surface roughness and deviations from spherical particle shape... 

Huid-solid Reasonable Turbulence modeling + refined models for particle-particle and particle-wall interaction -L prediction of flow regime transition + interaction of hydrodynamics with chemical transformation processes... 

Trickle bed reactors Slurry reactors Three-phase fluidized beds No Little Little Modeling on basis of unit cell approach + development of correspondence rules for macroscopic system behavior Modeling of the effect of the solids phase on interfacial transport phenomena Modeling of the effect of the solids phase on interfacial transport phenomena -I- development of refined models for particle-particle and particle-wall interaction... 

Case II refers to situations where the particle-wall interactions are purely repulsive. The particles are separated from the wall by a thin layer of solvent, even in the absence of any motion. Slip is thus possible for very slow flows, indicating that the sticking yield stress is vanishingly small. The residual film thickness for weak flows corresponds to a balance between the osmotic forces and the short-range repulsive forces, independently of any elastohydrodynamic contribution. This is clearly reflected in Fig. 16c, d, where we observe that the particle facet is nearly flat and symmetric. Since tire pressure in the leading and rear regions of the facet are equal and opposite, the lift force is very small. The film thickness, which is set by the balance of the short-range forces, is constant so that the stress/velocity relationship is linear. 

In conclusion, it is possible to rationalize wall slip in soft glasses as a consequence of the interplay of osmotic pressure and the various specific particle-wall interactions across the film of solvent that lubricates the contact between the particles and the wall. These results open up pathways for manipulating the flow of soft concentrated suspensions by making slight changes to the surface chemistry. 

The overlap of the meniscus around a floating particle with the meniscus on a vertical wall gives rise to a particle-wall interaction, which can be both repulsive and attractive. An example for a... 

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