Non-Brownian

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... 

An interesting aspect of Eq. (4.24) is that, even though F (t) and C (/) must represent genuine Brownian motions, / (/)may represent non-Brownian, even cyclic, motions of the antenna in the rod frame. Motion of the coordinates o>R t) and 2R(t) has been assumed to be statistically independent of the rod motions, but the nature of their trajectories has not yet been specified. 

Incorporating Magnetic Segments into Catalytic Motors. One of the short-falls with the Pt/Au nanorods was the poor directional control of the motor. Non-Brownian motion does not necessitate control over the direction of movement. A facile method to control the motion of autonomously moving Pt/Au nanorods is by... 

The second piece of evidence in distinguishing rods in a magnetic field to those out of the magnetic field was the rotational diffusion coefficient of the rod. It was the rotational diffusion coefficient that revealed the effect that an applied magnetic field had on a nanorod moving non-Brownian outside a field (2000 ° /s) and in it (70 ° /s). 

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.

Kveder, M., Lahajnar, G., Blinc, R., and Zupancic, I. (1988). Non-Brownian water selfdiffusion in lung tissue. Magn. Reson. Med. 6, 194-198. 

Note that G is time-periodic a non-Brownian axisymmetric particle rotates indefinitely in a shearing flow. This rotation is called a Jeffery orbit (Jeffery 1922). The period P required for a rotation of tt in a Jeffery orbit is ... 

The crossover from Brownian to non-Brownian behavior in a flowing suspension is controlled by a rotational Peclet number. 

Brownian rod-like objects of high aspect ratio are usually molecules, not colloidal particles. As exception is tobacco mosaic virus (TMV), which is a Brownian particle of length 300 nm and diameter 18 nm (Caspar 1963). For completeness, we shall discuss the theory of Brownian rod-like particles in this chapter, with the understanding that the theory for such particles is actually more relevant to long stiff molecules than to rod-like fibers. The behavior of non-Brownian fiber suspensions is covered in Section 6.3.2.2.------------------... 

As mentioned earlier, suspensions of particulate rods or fibers are almost always non-Brownian. Such fiber suspensions are important precursors to composite materials that use fiber inclusions as mechanical reinforcement agents or as modifiers of thermal, electrical, or dielectrical properties. A common example is that of glass-fiber-reinforced composites, in which the matrix is a thermoplastic or a thermosetting polymer (Darlington et al. 1977). Fiber suspensions are also important in the pulp and paper industry. These materials are often molded, cast, or coated in the liquid suspension state, and the flow properties of the suspension are therefore relevant to the final composite properties. Especially important is the distribution of fiber orientations, which controls transport properties in the composite. There have been many experimental and theoretical studies of the flow properties of fibrous suspensions, which have been reviewed by Ganani and Powell (1985) and by Zimsak et al. (1994). 

Figure 6.21 Steady-state values of for non-Brownian rod-like particles as a function of...

Figure 6.23 The relative viscosity at steady state of suspensions of non-Brownian rod-like particles versus dimensionless concentration vL. Simulations for p = L/d = 16.9 ( ), 31.9 (A) Bibbo s (1987) experimental results for L/d = 16.9 (O). and 31.9 (A). (Reprinted from J Non-Newt Fluid Mech 54 405, Yamane et al. (1994), with kind permission from Elsevier Science - NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

The viscous and elastic properties of orientable particles, especially of long, rod-like particles, are sensitive to particle orientation. Rods that are small enough to be Brownian are usually stiff molecules true particles or fibers are typically many microns long, and hence non-Brownian. The steady-state viscosity of a suspension of Brownian rods is very shear-rate- and concentration-dependent, much more so than non-Brownian fiber suspensions. The existence of significant normal stress differences in non-Brownian fiber suspensions is not yet well understood. 

Problem 6.6(a) How long does it take for a non-Brownian cylindrical particle of aspect ratio L/d = 10 suspended in a viscous liquid to rotate through an angle of n radians in a shearing flow at a shear rate y = 1 sec ... 

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