Particle-wall interaction, force

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. 

There are two main approaches for the numerical simulation of the gas-solid flow 1) Eulerian framework for the gas phase and Lagrangian framework for the dispersed phase (E-L) and 2) Eulerian framework for all phases (E-E). In the E-L approach, trajectories of dispersed phase particles are calculated by solving Newton s second law of motion for each dispersed particle, and the motion of the continuous phase (gas phase) is modeled using an Eulerian framework with the coupling of the particle-gas interaction force. This approach is also referred to as the distinct element method or discrete particle method when applied to a granular system. The fluid forces acting upon particles would include the drag force, lift force, virtual mass force, and Basset history force.Moreover, particle-wall and particle-particle collision models (such as hard sphere model, soft sphere model, or Monte Carlo techniques) are commonly employed for this approach. In the E-E approach, the particle cloud is treated as a continuum. Local mean... 

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. 

The great expense in calculation time due to the inevitably large particle numbers in single-file systems calls for the application of simplified potentials. Figure 1 shows the results obtained for spherical molecules diffusing in an unstructured tube [22]. Particle-particle and particle-wall interactions have been simulated by a shifted-force Lennard-Jones potential [26] and an... 

Nonretarded van der Waals forces involving anisotropic ellipsoidal particles have been calculated by IMURA and OKANO [5.98] assuming separations much greater than characteristic particle sizes. They found that depending upon relative values of the particle s dielectric permeabilities along its different axes, preferential alignment occurred. This was of import for both particle-particle and particle-wall interactions. 

The study of the interfacial phenomena between the channel wall and the colloidal suspension under study in sedimentation field-flow fractionation (SdFFF) is of great significance in investigating the resolution of the SdFFF separation method and its accuracy in determining particles physicochemical quantities. The particle-wall interactions in SdFFF affect the exponential transversal distribution of the analyte and the parabolic flow profile, leading to deviations from the classical retention theory, thus influencing the accuracy of analyte quantities measured by SdFFF. Among the various particle-wall interactions, our discussion focuses on the van der Waals attractive and electrostatic repulsion forces, which play dominant roles in SdFFF surface phenomena. 

The retention ratio with particle-wall interaction, Rp, may be smaller or larger than that of the classical theory, depending on whether the attractive or the repulsive force... 

Thin liquid films can be formed between two coUiding emulsion droplets or between the bubbles in foam. Formation of thin films accompanies the particle-particle and particle-wall interactions in colloids. From a mathematical viewpoint, a film is thin when its thickness is much smaller than its lateral dimension. From a physical viewpoint, a liquid film formed between two macroscopic phases is thin when the energy of interaction between the two phases across the film is not negligible. The specific forces causing the interactions in a thin liquid film are called surface forces. Repulsive surface forces stabilize thin films and dispersions, whereas attractive surface forces cause film rupture and coagulation. This section is devoted to the macroscopic (hydrostatic and thermodynamic) theory of thin films, while the molecular theory of surface forces is reviewed in Section 4.4. 

Net wall interaction force acting on a single particle (N) Buoyancy force on a single particle (N)... 

In the interaction force boundary layer approach the tangential velocity of the particles in the layer is neglected. Because the center of sufficiently large particles is far from the wall (even when the minimum distance h between wall and particle is small) this velocity may be appreciable. A second goal of the paper is to account for this effect. 

In addition to the repulsive electrostatic interactions, two isolated identical particles immersed in a solvent of different index of refraction, experience an attractive interaction, namely, the van der Walls or dispersion forces, which arise from the induced dipolar interactions between the molecules constituting the two particles. This interaction depends on the geometry (the shape of the particles) and on the material of which the particles are made of. For two spherical particles, the van der Waals interparticle potential uyj(r) is given by... 

The advent of the atomic force microscope has allowed surface properties at nearly molecular length scales to be measured directly for the first time. Recently, a method has been proposed whereby a small ( 3.5 /nn) particle is attached to the cantilever tip of the commercially available, Nanoscope II AFM [67,68]. The particles are attached with an epoxy resin. When the cantilever tip is placed close to a planar surface, the AFM measures directly the interaction force between the particle and the surface. A primary difference between this technique and the surface forces apparatus (SFA) is the size of the substrates, since the SFA generally requires smooth surfaces approximately 2 cm in diameter. Other differences are discussed by Ducker et al. [68]. For our purposes, it suffices to note that the AFM method explicitly incorporates the particle-wall geometry that is the focus of this chapter. 

The other important class of solute-wall interactions are the repulsive forces which are generated when a particle is driven towards the accumulation wall equal to the particle radius. This steric exclusion effect leads to an earlier elution of the particle [67]. 

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