Fluid particles, mechanism

Currently available limited experimental data do not permit the formulation of generalized predictive expressions even for macroscopic quantities like drag coefficient and wall correction factors. Thus, the empirical correlations presented herein must be regarded as somewhat tentative in their scope, and extrapolations beyond their ranges of applicability must be treated with reserve. Finally, it is hoped that this review will stimulate further interest in this hitherto somewhat neglected field of non-Newtonian fluid/particle mechanics. 

Reiss H 1977 Scaled particle theory of hard sphere fluids Statistical Mechanics and Statistical Methods in Theory and Application ed U Landman (New York Plenum) pp 99-140... 

C. A. Lapple and co-workers, Fluid and Particle Mechanics, University of Delaware, Newark, Del., 1956, p. 292. 

FIG. 6-61 Terminal velocities of spherical particles of different densities settling in air and water at 70°F under the action of gravity. To convert fhs to m/s, multiply by 0.3048. (From Lapple, etal.. Fluid and Particle Mechanics, University of Delaware, Newark, 1951, p. 292. )... 

This subsection is concerned with the application of particle mechanics (see Sec. 5, Fluid and Particle Mechanics ) to the design and apphcation of dust-collection systems. It includes wet collectors, or... 

In processes where new powder feed has a much smaller particle size than the smallest granular product, the feed powder can be considered as a continuous phase which can nucleate to form new granules [Sastry Fuerstenau, Powder Tech., 7, 97 (1975)]. The size of the nuclei is then related to nucleation mechanism. In the case of nucleation by spray, the size of the nuclei is of the order of the droplet size and proportional to cos0, where 0 is binder fluid-particle contact angle (see Fig. 20-67 of Wetting section). 

When the length scale approaches molecular dimensions, the inner spinning" of molecules will contribute to the lubrication performance. It should be borne in mind that it is not considered in the conventional theory of lubrication. The continuum fluid theories with microstructure were studied in the early 1960s by Stokes [22]. Two concepts were introduced couple stress and microstructure. The notion of couple stress stems from the assumption that the mechanical interaction between two parts of one body is composed of a force distribution and a moment distribution. And the microstructure is a kinematic one. The velocity field is no longer sufficient to determine the kinematic parameters the spin tensor and vorticity will appear. One simplified model of polar fluids is the micropolar theory, which assumes that the fluid particles are rigid and randomly ordered in viscous media. Thus, the viscous action, the effect of couple stress, and... 

Bubble and drop breakup is mainly due to shearing in turbulent eddies or in velocity gradients close to the walls. Figure 15.11 shows the breakup of a bubble, and Figure 15.12 shows the breakup of a drop in turbulent flow. The mechanism for breakup in these small surface-tension-dominated fluid particles is initially very similar. They are deformed until the aspect ratio is about 3. The turbulent fluctuations in the flow affect the particles, and at some point one end becomes... 

In the general case, the direction of movement of the particle relative to the fluid may not be parallel with the direction of the external and buoyant forces, and the drag force then creates an angle with the other two. This is known as two-dimensional motion. In this situation, the drag force must be resolved into two components, which complicates the treatment of particle mechanics. This presentation considers only the one-dimensional case in which the lines of action of all forces acting on the particle are collinear. 

Handley, D., Doraisamy, A., Butcher, K. L., and Franklin, N. L. Trans. Inst. Chem. Eng. 44 (1966) T260. A study of the fluid and particle mechanics in liquid-fluidised beds. 

When considering boundary conditions, a useful dimensionless hydrodynamic number is the Knudsen number, Kn = X/L, the ratio of the mean free path length to the characteristic dimension of the flow. In the case of a small Knudsen number, continuum mechanics will apply, and the no-slip boundary condition assumption is valid. In this formulation of classical fluid dynamics, the fluid velocity vanishes at the wall, so fluid particles directly adjacent to the wall are stationary, with respect to the wall. This also ensures that there is a continuity of stress across the boundary (i.e., the stress at the lower surface—the wall—is equal to the stress in the surface-adjacent liquid). Although this is an approximation, it is valid in many cases, and greatly simplifies the solution of the equations of motion. Additionally, it eliminates the need to include an extra parameter, which must be determined on a theoretical or experimental basis. 

In practice, this model is oversimplified since the exciting wake shedding is by no means harmonic and is itself coupled with the shape oscillations and since Eq. (7-30) is strictly valid only for small oscillations and stationary fluid particles. However, this simple model provides a conceptual basis to explain certain features of the oscillatory motion. For example, the period of oscillation, after an initial transient (El), becomes quite regular while the amplitude is highly irregular (E3, S4, S5). Beats have also been observed in drop oscillations (D4). If /w and are of equal magnitude, one would expect resonance to occur, and this is one proposed mechanism for breakage of drops and bubbles (Chapter 12). 

We focus our attention on a packet of fluid, or a fluid particle, whose size is small compared to the length scales over which the macroscopic velocity varies in a particular flow situation, yet large compared to molecular scales. Consider air at room temperature and atmospheric pressure. Using the ideal-gas equation of state, it is easily determined that there are approximately 2.5 x 107 molecules in a cube that measures one micrometer on each side. For an ordinary fluid mechanics problem, velocity fields rarely need to be resolved to dimensions as small as a micrometer. Yet, there are an enormous number of molecules within such a small volume. This means that representing the fluid velocity as continuum field using an average of the molecular velocities is an excellent approximation. 

For banks of in-line tubes,/for isothermal flow is obtained from Fig. 6-43. Average deviation from available data is on the order of 15 percent. For tube spacings greater than 3Dt, the charts of Gram, Mackey, and Monroe (Tram. ASME, 80, 25-35 [1958]) can be used. As an approximation, the pressure drop can be taken as 0.32 velocity head (based on Vm ) per row of tubes (Lapple, et al., Fluid and Particle Mechanics, University of Delaware, Newark, 1954). 

By integrating these equations over time, the position of any fluid particle with a given initial condition can be predicted at any time t. This approach is different from the common approach in fluid mechanics where flow is described in terms of velocity fields. However, by following the motion of the fluid we obtain a physically more profound understanding of mixing. 

Results demonstrate that when agitators are switched the slope of the pathline becomes discontinuous. We will see later in this chapter how this mechanism may produce an essentially stochastic response in the Lagrangian sense. Aref termed this chaotic advection, which he suggested to be a new intermediate regime between turbulent and laminar advection. The chaos has a kinematic origin, it is temporal—that is, along trajectories associated with the motion of individual fluid particles. Chaos is used in the sense of sensitivity of the motion to the initial position of the particle, and exponential divergence of adjacent trajectories. 

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