Chain of particles

When electron microscope studies first showed clearly the anisotropy of carbon black particles the appearance was of a chain of particles fused together, to which the term reticulate chain structure was given, later abbreviated simply to structure . The degree of structure has an influence on the level of reinforcement conferred by the carbon black. 

We did not differentiate between the various modes of vibration (longitudinal, transversal, acoustical, optical) for the sake of simplicity. The vibrational states in a crystal are called phonons. Figure 5-2 illustrates the collective, correlated transversal vibrational motion of a linear elastic chain of particles. 

A final assumption made in the derivation of Stokes law was that the particles of interest were spheres. In many cases this is not true. Particles may have irregular shapes, depending on how they were formed and the amount of agglomeration which may have taken place. Liquid aerosols are always spherical, so that for liquid aerosols the assumption of sphericity holds. For isometric particles this assumption can also be used with little error. For long chains of particles or flocculated particles, large deviations from Stokes law are possible. 

First (Sections II-V), we shall tackle the problem of translation. The simplest way of doing this is to study one-dimensional chains of particles. Bishop et al. have shown via computer simulation that one-dimensional Lennard-Jones systems exhibit the same dynamic properties as real three-dimensional liquids. This makes our investigations less academic than they seem at a purely intuitive level, as physical intuition would refuse to take as a Uquid sample a chain of particles which cannot bypass each other. 

Section II is devoted to reviewing the basic ideas of the RMT, having in mind a linear chain of particles coupled with each other via linear interactions. Section III is devoted to illustrating the results of computer experiments that we did to supplement those of the interesting paper of Bishop et al. with additional information as to whether or not the non-Gaussian features of the velocity variable are the same as those of the real three-dimensional fluids. We shall show that these are qualitatively similar, although in the one-dimensional case the non-Gaussian character is more intense and much more persistent. 

An inhnite one-dimensional regular chain of particles (atoms, electrons, or molecules), separated by equal distances d, is thermodynamically unstable entropy requires that it cannot exist as two or more phases, or have a phase transition at hnite temperatures [157]. 

The Mason number is related to the parameter k defined in Eq. (8-7) and the Peclet number Pe, defined in Chapter 6 [Eq. (6-12)] by Ma k — (n/4) Pe. For the typical values T s 0.02Pa s, E 1000 V/mm, 3 (and hence = 0.4), and Sg 3, we obtain 1 msec, Ma ss 10 " for y = 0.1, and Ma 1 for y = 1000. The time scale ts is very roughly the time required for a particle to move a distance equal to its own diameter, under a polarization interaction with a nearby particle. Thus, the Mason number is near unity when the shearing is rapid enough to pull particle parrs apart as fast as they can form. Even at Mason numbers much smaller than this, chains of particles can be broken, although particle... 

Experimentally, while G" is small, il is still much larger than the viscous contribution to G" from the solvent. Hence, relaxation processes do occur in ER fluids, even when they have been solidified by a strong electric field. Proposed sources of relaxation in ER fluids include (a) relaxation of free chains of particles that are attached to only one or no electrodes (McLeish et al. 1991) and (b) competition between hydrodynamic and electrostatic forces on particles in columns (Klingenberg 1993). 

RBCs, circulate more easily in the capillary beds than RBCs. They will be present in large numbers in the plasma gaps that exist between red cells in the micro-circulation, thereby increasing O2 content. These plasma gaps are particularly large when the patient suffers from acute anemia or when hemodilution is practiced. It is likely that PFC particles not only transport O2, but also facilitate its diffusion from RBCs to the tissues by providing numerous stepping stones or dynamic chains of particles for O2 to travel The... 

Shih et al. (1) proposed that this expression could be used to represent the force constant of an entire fractal floe. The assumption made is that the elastic properties of the floe are given by an effective backbone of stress transduction—a tortuous long chain of particles within the floe. Shih et al. (1) thus modified Kantor... 

Figure 24 illustrates possible flocculation and chaining of particles in flow conditions. Larger particles close to the walls of the vessels experience greater shearing forces because of the nature of the flow patterns shown. Particles that adhere to er5dhrocytes move with them until detachment, often prolonging their own circulation times. Adhesion, seen as a prerequisite to cellular uptake from blood and interstitial fluids is not a foregone conclusion. The probability of adhesion, Padheaon can be written phenomenologically as in Figure 24. The factors include particle diameter, flow rate, the density of receptors, and the force of attraction between particle and receptor.

Ti-5.5A1-1.9B alloy. In as-cast state, as-dendritic structure is well visible. Structure of matrix is martensite. Borides of eutectic are located between dendrites. Borides have rod- and strip-like, and plate-like morphologies. Plates are splitting well. In as-forged state, martensite structure of matrix is not visible. Crashed borides form chains of particles of rod and strip morphologies. Thickness of strips is less 1 pm. 

In as-forged state, structure of matrix is close to polygonal (Fig. 5a). Crashed borides form chains of particles of rod and strip morphology. It is seen that boride strips are often splitted for three ones (Fig. 5b). Preliminary qualitative X-ray microanalysis shows that borides are compounds containing, except boron and titanium, all the additives added specially like Al, Si, Zr, and present in the basic BT1-0 alloy like Fe, 0 and possibly C. Matrix is pure in comparison with original BT1-0 alloy. It consists of Ti, Al, Si, and Zr only. 

Diffusion Wake. Mass Exchange of Liquid With Chains of Particles 207... 

Chains of Particles or Drops at High Peclet Numbers... 

If the particles are highly conductive with respect to the solution (metal), this metal is not directly accessible for the current the double layer must be passed two times. If the concentration of metal particles (fill factor) is increased, the measured voltage will not necessarily decrease that depends on metal/solution impedance and therefore also the frequency. Above a certain particle concentration, there will be a sharply increased probability of a direct contact chain of particles throughout the measured volume segment, the segment will be short-circuited. 

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