Turbulence solid-liquid

Equihbrium concentrations which tend to develop at solid-liquid, gas-liquid, or hquid-liquid interfaces are displaced or changed by molecular and turbulent diffusion between biilk fluid and fluid adjacent to the interface. Bulk motion (Taylor diffusion) aids in this mass-transfer mechanism also. 

Table 5.1 shows that, with the boundary conditions present in most environmental flows (i.e., the Earth s surface, ocean top and bottom, river or lake bottom), turbulent flow would be the predominant condition. One exception that is important for interfacial mass transfer would be very close to an interface, such as air-solid, solid-liquid, or air-water interfaces, where the distance from the interface is too small for turbulence to occur. Because turbulence is an important source of mass transfer, the lack of turbulence very near the interface is also significant for mass transfer, where diffusion once again becomes the predominant transport mechanism. This will be discussed further in Chapter 8. 

There is diffusion of salt away from both the solid-liquid interface and the vapor-liquid interface, in each case toward the brine. Water moves counterflow to the salt. Heat must transfer from solid to liquid to gas through stagnant films at the solid surface and through the turbulent liquid. An additional resistance to the formation of ice exists at the ice surface, where water molecules must orient themselves and find positions of low energy before being incorporated into the crystal lattice. When inadequate ice surface or foreign particles exist in the freezer, nucleation may control or affect the rate of ice production. 

Shamlou, P. A., and Titchener-Hooker, N., Turbulent aggregation and breakup of particles in liquids in liquids in stirred vessels, in "Processing of Solid-Liquid Suspensions" (P. A. Shamlou Ed.), pp. 1-25. Butterworth-Heinemann Ltd, Oxford (1993). 

System with random fluxes is defined as the nonequilibrium system where the fluxes of substance, heat, etc. change randomly. One can cite numerous examples of such systems turbulent gas-liquid systems with intensive heat/mass transfer, turbulent fluids containing dispersed solids, etc. In the case of pore formation, such situation is realized when the heat fluxes change randomly because of air fluidization or mechanical mixing. All macroscopic measured parameters of stationary turbulent flows, like their pressure, temperature, excess (free) energy, entropy, etc. do not change with time, while their values and directions in different spots of the flows can vary significantly. 

D. Turbulent, vertical wetted wall column with ripples tfsw = = 0.00814ivriv i2e. J1 30 (iSE. ) < 1200 > l / Nsh e = = 0.023tf 8tfs [E] For gas systems with rippling. Fits 5-18-B for ( 2P ) = 1000 / [E] Rounded approximation to include ripples. Includes solid-liquid mass-transfer data to find V6 coefficient on NSc- May use A 83. Use for liquids. See also Table 5-19. [85] [138] p. 213... 

Ham et al. (1990) used Eqs. (30) and (31) and estimated the values of the solid phase dispersion coefficient using the experimental results on transition in solid-liquid fluidized beds. However, the estimated values of deviate from the experimental values of obtained by Dorgelo et al. (1985). It may be noted that the RTD based experimental values includes gross nonidealities in addition to the turbulent dispersion. 

Impeller Reynolds number = pND /p Impeller Reynolds number at Vjs for solid-liquid suspensions = Nj D /v Particle Reynolds number in a turbulent... 

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

The application of CFD in the modeling of solid-liquid mixing is fairly recent. In 1994, Bakker et al. developed a two-dimensional computational approach to predict the particle concentration distribution in stirred vessels. In their model, the velocity field of the liquid phase is first simulated taking into account the flow turbulence. Then, using a finite volume approach, the diffusion-sedimentation equation along with the convective terms is solved, which includes Ds, a... 

At certain conditions agglomeration also takes place in turbulently moving liquid suspensions. This is the case if, for example, a small amount of a second liquid is added as a binder. This component must be able to adhere to the solid particles in the suspension but must be immiscible with the suspending liquid. After its addition, spherical agglomerates form during a suitable movement of the liquid. Figure 86(a) to (h) shows schematically apparatuses that were successfully used for agglomeration in suspension. 

The enhancement of mass transfer in the solid/liquid system is a frequent stirring operation. It should be remembered, that many salts must be dissolved in the liquid, to prepare a salt solution or to initiate a chemical reaction. In order that the dissolution process proceeds rapidly, the whole surface of the solid particles must be wetted as completely as possible by the liquid and the liquid flow should be turbulent, so that the boundary layer on the liquid side is small and the transfer of the dissolved material to the bulk of the liquid proceeds rapidly. 

Langlois WE (1964) Slow Viscous Flow. Macmillan, New York Laux H (1998) Modeling of dilute and dense dispersed fluid-particle flow. Dr Ing Thesis, Norwegian University of Science and Technology, Trondheim, Norway Lawler MT, Lu P-C (1971) The role of lift in radial migration of particles in a pipe flow. In Zandi 1 (ed) Advances in Solid-Liquid Flow in Pipes and its Apphcations. Pergamon Press, Oxford, Chap 3, pp. 39-57 Lee SL (1987) Particle drag in a dilute turbulent two-phase suspension flow. Int J Multiphase Flow 13(2) 247-256... 

FIGURE 11.1 A generalized flow scheme that indicates the fundamental elements of LC-MS-based bioanalysis. Abbreviations LLE = liquid-liquid extraction SPE = solid-phase extraction RAM = restricted-access media TEC = turbulent flow liquid chromatography API = atmospheric-pressure ionization APCI = atmospheric-pressure chemical ionization ESI = electrospray ionization SQMS = single-quadrupole mass spectrometry TQMS = triple-quadrupole mass spectrometry TOF = time-of-flight Q-TOF = quadrupole TOF. (Reprinted from Ackermann et al. [4], with permission from John Wiley Sons, Inc.)... 

Slurry bubble column reactor for methanol and other hydrocarbons productions from synthesis gas is an issue of interest to the energy industries throughout the world. Computational fluid dynamics (CFD) is a recently developed tool which can help in the scale up. We have developed an algorithm for computing the optimum process of fluidized bed reactors. The mathematical technique can be applied to gas solid, liquid-solid, and gas-liquid-solid fluidized bed reactors, as well as the LaPorte slurry bubble column reactor. Our computations for the optimum particle size show that there is a factor of about two differences between 20 and 60 pm size with maximum granular-like temperature (turbulent kinetic energy) near the 60 pm size particles. 

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