Non-Brownian particles

Hydrodynamic Forces Necessary To Release Non-Brownian Particles Attached to a Surface... 

The release of non-Brownian particles (diameter s 5 pm) from surfaces has been studied. The influence of several variables such as flow rate, particle size and material, surface roughness, electrolyte composition, and particle surface charge has been considered. Experiments have been performed in a physically and chemically well-characterized system in which it has been observed that for certain particle sizes there exists a critical flow rate at which the particles are released from surfaces. This critical flow rate has been found to be a function of the particle size and composition. In addition, it has been determined that the solution pH and ionic strength has an effect on the release velocity. 

For the purpose of this study, particles are classified as Brownian or non-Brownian, where Brownian particles are defined as those for which the diameter is less than five microns and non-Brownian are those with diameter greater than five microns. The major focus of this work is on the second category. The particle release process has been studied both theoretically and experimentally, and it is found that for non-Brownian particles the surface charge and the electrolyte composition of the flowing phase are less significant factors than the hydrodynamic effects. However, Van der Waals forces are found to be important and the distortion of particles by these forces is shown to be crucial. 

In this investigation we experimentally determine the factors controlling the release of non-Brownian particles. Also, we discover the initial particle release mechanism, (i.e., rolling-vs-sliding). 

A summary of the most important experimental findings of Chamoun (H), along with a description of the experimental apparatus and procedure, is presented in this chapter. In particular, the experiments have shown which factors (such as pH, ionic strength, etc.) control the release of non-Brownian particles and also have proven that the initial particle release mechanism is rolling rather than sliding. 

Adhesive force, non-Brownian particles, 549 Admicelle formation, 277 Adsorption flow rate, 514 mechanism, 646-647 on reservoir rocks, 224 patterns, on kaolinite, 231 process, kinetics, 487 reactions, nonporous surfaces, 646 surface area of sand, 251 surfactant on porous media, 510 Adsorption-desorption equilibria, dynamic, 279-239 Adsorption plateau, calcium concentration, 229... 

The previous models were developed for Brownian particles, i.e. particles that are smaller than about 1 pm. Since most times particles that are industrially codeposited are larger than this, Fransaer developed a model for the codeposition of non-Brownian particles [38, 50], This model is based on a trajectory analysis of particles, including convective mass transport, geometrical interception, and migration under specific forces, coupled to a surface immobilization reaction. The codeposition process was separated in two sub-processes the reduction of metal ions and the concurrent deposition of particles. The rate of metal deposition was obtained from the diffusion... 

The deposition of non-Brownian particles under the influence of interaction forces was treated by Spielman and FitzPatrick 1 and Spielman and Cukor.2 Theoretical predictions of the rate of deposition for Brownian particles have been made in two extreme situations. Levich 3 treated the case in which convection and diffusion control the rate of deposition. Hull and Kitchener 4 considered interaction forces and diffusion while neglecting convection. 

Fig. 4. Case 2. Single-grain capture efficiencies for the collection of non-Brownian particles by a spherical grain of a packed bed. A linear asymptote is noted by the dashed line which is valid lor 10 < M < IQ-6 7.

For particles ranging in size from 30 nm to 2 pm, the particle dissolution is influenced mainly by Brownian motion and experimentally Dr values were found to vary from 1.0 to 2.0. For bigger particles (non-Brownian) between 10 pm and 5 mm, dissolution is mainly controlled by the relative slip velocities between particles and surrounding fluid. The bigger the particles, the higher is the relative slip velocity resulting in faster dissolution rate. Therefore values of Dr for these particles (2.0 < Dr < 3.0) are higher than those affected by Brownian motion. For both the Brownian and non-Brownian particles, the dissolution is by erosion of the external surface. 

In the study to characterize the dissolution kinetics of saccharin as a sweetener excipient, it was found that as dissolution continues, cracks appeared on the surface resulting in faster dissolution. Therefore Dr of Brownian and non-Brownian particles cannot be restricted to the range of 1-3. Using Dr as a parameter to distinguish dissolution mechanism is not appropriate because Dr depends on variety of parameters and not only on the type and size of the particles. 

A colloidal system represents a multiphase (heterogeneous) system, in which at least one of the phases exists in the form of very small particles typically smaller than 1 pm but still much larger than the molecules. Such particles are related to phenomena like Brownian motion, diffusion, and osmosis. The terms microheterogeneous system and disperse system (dispersion) are more general because they also include bicontinuous systems (in which none of the phases is split into separate particles) and systems containing larger, non-Brownian, particles. The term dispersion is often used as a synonym of colloidal system. 

As illustrated by the results presented in Figure 2 and in Table 2 at high ionic strength and high Ca2 + for favorable particle-particle interactions (e.g., in the deposition of non-Brownian particles, F = F%Taviiy + Fdrag +FlVDW Fchem = 0), transport models based on physical and hydrodynamic characteristics of a system can predict the initial kinetics of aggregation and deposition processes in aquatic systems quantitatively. In the presence of repulsive chemical interactions, however, quantitative theoretical predictions of such kinetics are very inaccurate and even many qualitative predictions are not observed. The determination of Fchem in aquatic systems merits study and development,- it is necessary for the quantitative prediction of the kinetics of colloid chemical processes in these systems. 

Colloidal systems and dispersions are of great importance in many areas of human activity such as oil recovery, coating, food and beverage industry, cosmetics, medicine, pharmacy, environmental protection etc. They represent multi-component and multiphase (heterogeneous) systems, in which at least one of the phases exists in the form of small (Brownian) or large (non-Brownian) particles (Hetsroni 1982, Russel et al. 1989, Hunter 1993). One possible classification of the colloids is with respect to the type of the continuous phase (dispersions with solid continuous phase like metal alloys, rocks, porous materials, etc. will not be consider). 

The release or detachment of the fine particles from the collector surface is assumed to be induced by the hydrodynamic forces in the case of non-Brownian particles or by the colloidal forces in the case of Brownian particles [131]. For non-Brownian fine particles, the rate of hydrodynamic particle entrainment is considered to be proportional to the difference between the wall shear stress and the critical shear stress [123] ... 

One of the most beautiful results manifesting the effect of flow on diffusion is the shear-induced diffusion effect, which is the quantitative manifestation of the transition to irreversibility in a set of particles obeying the classical reversible equations of motion. Recently, this effect was studied in a series of experiments and numerical simulations were the transition from a dynamical reversible behavior to a dynamical irreversible chaotic behavior of a suspension of non-Brownian particles was directly observed (Drazer, 2002 Pine, 2005). The importance of these experiments lies in the fact that they shed light on the origin of the thermodynamic irreversibility and its relation to the chaotic dynamics of a system (Guasto Gollub, 2007 Pine, 2005). 

In Poiseuille flow, rigid, spherical, non-Brownian particles are subjected to lateral forces that result in migration to an equilibrium radial region located at approximately 60% of the distance from the tube axis to the tube wall, which... 

LaEVance, P. J. (1994) Trajectory modeling of non-Brownian particle flotation using an extended DLVO approach MS Thesis, University of Connecticut, Storrs, 55 pp. 

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