Particle-enhanced convection

Sundararajan et al. [131] in 1999 calculated the slurry film thickness and hydrodynamic pressure in CMP by solving the Re5molds equation. The abrasive particles undergo rotational and linear motion in the shear flow. This motion of the abrasive particles enhances the dissolution rate of the surface by facilitating the liquid phase convective mass transfer of the dissolved copper species away from the wafer surface. It is proposed that the enhancement in the polish rate is directly proportional to the product of abrasive concentration and the shear stress on the wafer surface. Hence, the ratio of the polish rate with abrasive to the polish rate without abrasive can be written as... 

Particles enhance mass transfer in laminar flow for natural convection. Good fit with correlation of Ray et ak, Inti. J. Heat Mass Transfer, 41, 1693 (1998). = g A... 

In a continuous system, the band of drying material is transported in a serpentine fashion through the fluidized bed of sorbent particles. Heat required for moisture release from the sorbent to fluidizing air is supplied by immersed heaters. The use of fluidized beds of active particles enhances not only the convective but also material-sorbent, sorbent-sorbent, and sorbent-heater contact heat/mass transfer rates. Comparison of the fluid bed dryer with inert sorbent with the cylinder dryer is given in Table 12.1. 

Convection heat transfer is dependent largely on the relative velocity between the warm gas and the drying surface. Interest in pulse combustion heat sources anticipates that high frequency reversals of gas flow direction relative to wet material in dispersed-particle dryers can maintain higher gas velocities around the particles for longer periods than possible ia simple cocurrent dryers. This technique is thus expected to enhance heat- and mass-transfer performance. This is apart from the concept that mechanical stresses iaduced ia material by rapid directional reversals of gas flow promote particle deagglomeration, dispersion, and Hquid stream breakup iato fine droplets. Commercial appHcations are needed to confirm the economic value of pulse combustion for drying. 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

Some researchers have noted that this approach tends to underestimate the lean phase convection since solid particles dispersed in the up-flowing gas would cause enhancement of the lean phase convective heat transfer coefficient. Lints (1992) suggest that this enhancement can be partially taken into account by increasing the gas thermal conductivity by a factor of 1.1. It should also be noted that in accordance with Eq. (3), the lean phase heat transfer coefficient (h,) should only be applied to that fraction of the wall surface, or fraction of time at a given spot on the wall, which is not submerged in the dense/particle phase. This approach, therefore, requires an additional determination of the parameter fh to be discussed below. 

For G/S particle systems, enhancement in convective heat transfer is achieved at the expense of increased pressure drop in moving the gas at higher velocities. A measure of the relative benefit of enhanced heat transfer to added expenditure for fluid movement can be approximated by an effectiveness factor, E, defined as the ratio of the heat transfer coefficient to some kind of a pressure drop factor. For G/S systems in which particles are buoyed by the flowing gas stream, this pressure drop factor is expressed by the Archimedes number Ar, and E can be written... 

An extremely effective means of enhancing heat removal from a reactor is to make use of fluidized-bed technology (3). Heat transfer coefficients for gaseous systems are increased to values of around 600 W/m2K or more by virtue of the very efficient convective-regenerative particle transport mechanism of heat transfer. Further... 

The particle convection is in general important in the overall bed-to-surface heat transfer. When particles or particle clusters contact the surface, relatively large local temperature gradients are developed. This rate of heat transfer can be enhanced with increased surface renewal rate or decreased cluster residence time in the convective flow of particles in contact with the surface. The particle-convective component hpc can be expressed by the following equation, which is an alternative form of Eq. (12.39) ... 

When the particle is moving relative to the suspending fluid, transport of heat or matter is enhanced by convective diffusional processes. Under conditions where the particle exists in a rarified medium (Kn 0), the heat and mass tranfer relations are modified to account for surface accommodation or sticking of colliding molecules and the slippage of gas around the particle. 

MakCay, A. J., Deen, D. F., and Szoka, F. C., Jr. (2005), Distribution in brain of liposomes after convection enhanced delivery modulation by particle charge, particle diameter, and presence of steric coating, Brain Res., 1035,139-153. 

In these materials, mass transport inside particles occurs not only by diffusion but also by convecdon. Nir and Pismen (ref. 1) showed that the effectiveness factor of a catalyst (slab geometry) for 1 order isothermal reacdon, working in the intermediate regime increases due to intraparticle convective flow. The enhancement of catalyst effectiveness can be quantified by E= doAl(], shown in Fig. 1. This pioneering work was later extended to other kinetic laws (refs. 2-4). 

---