Particle eddy interaction with

The total energy dissipation from the eddy, which equals the total work performed by the eddy on the particle during the particle-eddy interaction, is thus obtained by integrating Eq. (6.198) with respect to t... 

The number of theoretical plates is proportional to the column length and inversely proportional to the particle size. The advantage of using small particles is that they distribute flow more uniformly and, as a result, reduce the eddy diffusion, term A in the Van Deemter equation. However, the smaller particles increase the diffusional resistance of the solvent as well as the pressure drop (for a given flow rate). Choosing the flow rate is a critical parameter in developing an HPLC method. Low flow rates allow the analyte sufficient time to interact with the stationary phase and will affect both the B and C terms of the Van Deemter equation. 

When the eddy size is (i) smaller than (ii) but not too small as to have very low energy content, its interaction with the particle is significant. Such interaction can lead to higher rates of mass transfer provided the eddy frequency is also high. For multiphase systems, these eddies are also responsible for breakage of drops/bubbles (Section 7A.5.1 and Fig. 7A.11). 

McLaughlin [141] used the one-way coupling approach to simulate the motion of aerosol particles in a turbulent channel flow. The particle Reynolds number was smaller than unity for most of the particles although some particles occasionally attained Reynolds numbers larger than unity as a result of interaction with unusually strong eddies. 

In the same way that relative length scales of eddies and blobs affect the breakup of blobs, in multiphase flows the relative response times of particles and eddies determine how particles interact with eddies (Tang et al., 1992). Although we do not discuss this issue in detail, it is important to recognize two things (1) the relevant length scales for multiphase flows can be much more difficult to scale accurately because of the complicated interactions between turbulence and particles and (2) where tracer particles are used in experiments, the scales of motion that can be observed are a function of the particle size and characteristic response time. 

Clearly, this simplification in terms of time scales is not the complete story. This can be illustrated by Balachandar s (2009) analysis of particles setding under turbulent flow conditions when a particle continuously experiences accelerations in varying directions as a result of the interaction with turbulent eddies. WhenTpj/Tt< 1, the gravitational acceleration competes with the Kolmogorov acceleration jif, where t denotes... 

FIGURE 16 Schematic representation of the origins of zone-broadening behavior and mass transfer effects of a polypeptide or protein due to Brownian motion, eddy diffusion, mobile phase mass transfer, stagnant fluid mass transfer, and stationary-phase interaction transfer as the polypeptide or protein migrated through a column packed with porous particles of an interactive HPLC sorbent. 

A new on-line approach to SPE is the use of so-called turbulent flow chromatography which combines rapid mobile phase linear velocities with larger particle sizes this approach was discussed in Section 3.5.9 in the context of breakdown of the conventional (van Deemter) rate theory. Whether or not the flow can truly be described as turbulent (Ayrton 1998), there is no question that eddies are formed that enhance the interactions of smaller molecules with the stationary phase. In contrast the large proteins and other biopolymers have rates of mass transfer from the liquid to stationary phase (C term in the van Deemter equation) that are too... 

A perennial problem in multiphase reactors is scale-up, that is, how to achieve the desired results in a large-scale reactor based on the observations made in the laboratory unit, which remains elusive due to complexities associated with transport-kinetic coupling [14]. The success of scale-up of trickle-bed reactors is based on the ability to understand and quantify the transport-kinetic interactions at the particle scale level (or single eddy scale), the interphase transport at the particle and reactor scales, and the flow pattern of each phase and phase contacting pattern and their changes with the changes in reactor scale and operating conditions [1]. 

For describing the rate of a chemical conversion one generally needs to consider the rates with which the reactants are transported towards each other, and combine these with the intrinsic rate of the chemical reaction itself The combination of these effects can best be considered on the "intermediate scale", that is the scale of large eddies or dispersed particles, mostly on the order of 1 to 10 mm. The essential transport phenomena are mixing and mass transfer, which have been described for a number of configurations in Chapter 4, The principles of the interaction between physical and chemical phenomena will be described in more general terms, which are applicable to most types of reactors. In this chapter volume element models are presented for mixing combined with chemical reaction, and for mass transfer combined with chemical reaction. 

Actually, the behavior of solid particles in the flow field is quite complex, depending on the structure of turbulence. Of interest in this respect is the ejection sequence viewed by Corino and Brodkey (1969) in their study of single-phase flow. The interaction of fluid eddies with particles is more likely as the size of the particles is decreased. This injection sequence could well keep the large particles at the center of the pipe and concentrate the smaller particles that follow the turbulence more closely in the wall region. Figure 4-12 shows the relative sizes of particles and eddies. 

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