Vertical transport

Detailed consideration of the interaction between particles and fluids is given in Volume 2 to which reference should be made. Briefly, however, if a particle is introduced into a fluid stream flowing vertically upwards it will be transported by the fluid provided that the fluid velocity exceeds the terminal falling velocity o of the particle the relative or slip velocity will be approximately uq. As the concentration of particles increases this slip velocity will become progressively less and, for a slug of fairly close packed particles, will approximate to the minimum fluidising velocity of the particles. (See Volume 2, Chapter 6.) 

The evidence from practical studies of vertical transport is that the contribution of the solids to the pressure gradient in the pipeline is attributable predominantly to the weight of the particles. Because the density of the particles ps is much greater than that of the gas, this additional pressure gradient can be written  

The conveying of fine particles in vertical pipes of diameters 25 mm, 50 ram, and 75 mm has been studied by BoOTHROYD He measured tiie pressure gradient in the pipeline, and found that tiie frictional pressure drop was less than that for air alone in the 25 mm pipe, but was greater in the larger pipes. This effect was attributed to the fact that the extent to which the fluid turbulence was affected by the presence of the particles was markedly influenced by pipe size. 

Sinclair and JaCKSON have presented a theoretical relation between pressure gradient and the flowrates of gas and solids over the whole range of possible conditions for both cocurrent and countercurrent flow. It predicts marked segregation of gas and particles in the radial direction. 

Miller and Gidaspow have studied transport of 75 /xm catalyst particles in a 75 nim diameter vertical pipe. The flow was characterised by a dilute rising core and a dense annular region at the walls which tended to move downwards. The fractional volumetric concentration of the solids was from 0.007 to 0.04 in the core and up to 0.25 in the annular region. 

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Nested wells can also be used to analyze multilayer aquifer flow. There are many situations involving interaquifer transport owing to leaky boundaries between the aquifers. The primary case of interest involves the vertical transport of fluid across a horizontal semipermeable boundary between two or more aquifers. Figure 4 sets out the details of this type of problem. Unit 1 is a phraetic aquifer, bound from below by two confined aquifers, having semipermeable formations at each interface. 

It is known from experience with vertical pneumatic transport that the influence of weight prevails at low velocities, but as the velocity increases friction gains importance. Therefore, in the calculation of the pressure loss one must find not only the weight of the solids, which could be set up theoretically, but also an empirical relationship for vertical transport from the measured data. A correlation of the pressure-loss coefficient for vertical pneumatic conveyance according to data measured by Flatow " has been developed by Weber, and the result is... 

Due to the nonuniforra velocity and pressure distribution along the y-axis, the particles remain separate and floating in the gas stream. In a vertical transportation the force /) , is obviously zero, because then the particles do not tend to fall and gather on the bottom of the tube. The force cannot be included in the drag force because the drag force pushes the particles forward in the direction of the j -axis, whereas does not affect the particles but the gas itself. 

The flow behaviour of suspensions of coarse particles is completely different in horizontal and vertical pipes. In horizontal flow, the concentration of particles increases towards the bottom of the pipe, the degree of non-uniformity increasing as the velocity of flow is decreased. In vertical transport, however, axial symmetry is maintained with the solids evenly distributed over the cross-section. The two cases are therefore considered separately. 

Durand<62) has also studied vertical transport of sand and gravel of particle size ranging between 0.18 mm and 4.57 mm in a 150 mm diameter pipe, and Worster and Denny 63 conveyed coal and gravel in vertical pipes of diameters 75, 100, and 150 mm. They concluded that the pressure drop for the slurry was the same as for the water alone, if due allowance was made for the static head attributable to the solids in the pipe. 

Bucket elevators are suited to vertical transport of sticky and abrasive materials. With buckets 20 x 20 in. capacity can reach 1000 cuft/hr at a speed of 100 ft/min, but speeds to 300 ft/min are used. 

Transport and dijfusion. With the exception of N2, O2, Ar, and numerous other long-lived species that are well-mixed in the bulk of the atmosphere, horizontal and vertical transport are closely coupled with chemical reactions in controlling atmospheric trace-substance concentrations. 

POC/ Th (mol C/dpm is the ratio on sinking particles and is the decay constant of " Th (0.029 d ). This approach makes no assumptions about residence times, although it implicitly assumes that sinking biogenic particles are the principal carriers of " Th atoms, that the POC/ Th ratio on sinking particles can be measured, that steady state applies and that horizontal and vertical transport of " Th via advection of water are negligible. 

Gustafsson O, Buesseler KO, Geyer WR, Moran SB, Gschwend PM (1998) An assessment of the relative importance of horizontal and vertical transport of particle-reactive chemicals in the coastal ocean. Cont Shelf Res 18 805-829... 

Bates TS, Hamilton SE, Cline JP. 1984. Vertical transport and sedimentation of hydrocarbons in the central main basin of Puget Sound, Washington. Environ Sci Technol 18 299-305. 

Knowlton has cautioned on the difference between small diameter and large diameter systems for pressure losses. The difference between these systems is especially apparent for dense phase flow where recirculation occurs and wall friction differs considerably. Li and Kwauk (1989, 1989) have also studied the dense phase vertical transport in their analysis and approach to recirculating fluid beds. Li and Kwauk s analysis included the dynamics of a vertical pneumatic moving bed upward transport using the basic solid mechanics formulation. Some noncircular geometries were treated including experimental verification. The flows have been characterized into packed and transition flows. Accurate prediction of the discharge rates from these systems has been obtained. 

Stier P, Feichter J, Kinne S, Kloster S, Vignati E, Wilson J, Ganzeveld L, Tegen I, Werner M, Balkanski Y, Schulz M, Boucher O, Minikin A, Petzold A (2005) The aerosol-climate model ECHAM5-HAM. Atmos Chem Phys 5 1125-1156 Tanabe S, Tatsukawa R (1983) Vertical transport and residence time of chlorinated hydrocarbons in the open ocean water column. Journal of the Oceanographical Society of Japan 39 53-62 Tiedtke M (1989) A comprehensive mass flux scheme for cumulus parameterization in large scale models. Mon WeaRev 117 1779-1800... 

It should also be noted that Chen et al. (2001) used a model with a vertical transport component and they do not specify which height the fluxes they report refer to. 

Aerosol surface area is likely to be variable even within a remote marine air mass. Previous MBL aerosol studies describe changes in aerosol concentration and composition due to entrainment from the free troposphere (Bates et al., 1998, 2001 Covert et al., 1998). Raes et al. (1997) found an observable link between vertical transport patterns and aerosol variability in the MBL specifically in the Aitken mode (<0.2/u.m). Hence entrainment of aerosol from the free troposphere appears to occur frequently, even in remote MBL air masses. In addition, aerosols have the capacity to travel great distances in the free troposphere, before being entrained into the MBL. 

Sigg, L., M. Sturm, and D. Kistler (1987), "Vertical Transport of Heavy Metals by Settling Particles in Lake Zurich , Limnol. Oceanogr. 32, 112-130. 

Richardson, 1. F. and Smith, 1. W. Trans. Inst. Chem. Eng. 40 (1962) 13. Heat transfer to liquid fluidised systems and to suspensions of coarse particles in vertical transport. 

The synthesis, destruction, and vertical transport of organic matter in the marine environment all have important implications for the produc-... 

Sorption/desorption is the key property for estimating the mobility of organic pollutants in solid phases. There is a real need to predict such mobility at different aqueous-solid phase interfaces. Solid phase sorption influences the extent of pollutant volatilization from the solid phase surface, its lateral or vertical transport, and biotic or abiotic processes (e.g., biodegradation, bioavailability, hydrolysis, and photolysis). For instance, transport through a soil phase includes several processes such as bulk flow, dispersive flow, diffusion through macropores, and molecular diffusion. The transport rate of an organic pollutant depends mainly on the partitioning between the vapor, liquid, and solid phase of an aqueous-solid phase system. 

The depth of the mixed layer is important for two reasons. First, phytoplankton can be carried out of the photic zone and, hence, halt net primary production if the mixed layer is deeper than the photic zone. Second, the bottom of the mixed layer marks the upper limit to which density stratification in the thermocline inhibits upward vertical transport of nutrients. If the photic zone extends into the thermocline, phytoplankton... 

A series of field and laboratory experiments identified the spatial redistribution of contaminants by surface runoff and contamination of the subsurface by vertical transport of colloids. These findings demonstrate that colloidal-mediated transport of contaminants is a major environmental hazard. 

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