Motion solid

Gas Stripping. Heat transfer is a combination of direct and indirect The solids motion is achieved by agitation and the bed is partially flu-... 

That steps involving atomic or molecular motion can be rate determining, even in fluids, is well known through diffusion limited reaction rates and the solvent cage effect. In solids, motion more subtle than translational diffusion can be influential, and cases of rotational diffusion control are familiar [7],... 

Many theoretical and experimental studies carried out in the past deal with the study of the solid motion inside a rotary cylinder, drum or kiln [1-8]. Saeman s model, developed in 1951, is undoubtedly the first attempt for modelling such motion [1] this mechanistic model is widely... 

This paper presents the first experimental results for the solid motion inside a pilot-scale rotary kiln. Such data are useful to enable efficient pyrolysis reactions inside a rotary kiln to be carried out, through the prediction of residence time and material hold-up, and the evaluation of different surfaces and temperature profiles according to the operating conditions. In the first part, the pilot-scale rotary kiln and the principle of the experiments will be described. An original dynamic solid motion model will be presented in the second part, this dynamic model is derived from the original static model of Seaman [1], The static and dynamic experimental results are finally compared with the simulated results. 

For the numerical implementation, the component concentration balances are rewritten in terms of the solid motion leading to... 

Therein, nF wF is the so-called filter velocity. Note that c wF is added to the ion velocities to get the velocities relative to the solid motion. 

Solids motion in A. Ingram and Tracking molten polymer... 

The attrition of solid particles is an unavoidable consequence of the intensive solids motion resulting from the presence of bubbles in the fluidized bed. The attrition problem is especially critical in processes where the bed material needs to remain unaltered for the longest possible time, as in fluidized-bed reactors for heterogeneous catalytic gas-phase reactions. Catalyst attrition is important in the economics of such processes and may even become the critical factor. 

Solids motion was observed in the spout for different solids and gas flow rates, different positions of the distributor and different angles and sizes of the spout. 

The regions with fine dotted lines are inoperable when solids motion is initiated only by gravity and drag forces. However, these regions may become operable when the particles are motivated by other forces such as magnetic, mechanical, or electrical. 

Figure 2.1 Pictorial representations of elastic waves in solids. Motions of groups of atoms ate depicted in these cross-sectional views of plane elastic waves propagating to the right. Vertical and horizontal displacements are exaggerated for clarity. Typical wave speeds, Vp, are shown below each sketch, (a) Bulk longitudinal (compressional) wave in unbounded solid, (b) Bulk transverse (shear) wave in unbounded solid, (c) Surface acoustic wave (SAW) in semi-infinite solid, where wave motion extends below the surface to a depth of about one wavelength, (d) Waves in thin solid plates.

Chapter 4 is devoted to the description of stochastic mathematical modelling and the methods used to solve these models such as analytical, asymptotic or numerical methods. The evolution of processes is then analyzed by using different concepts, theories and methods. The concept of Markov chains or of complete connected chains, probability balance, the similarity between the Fokker-Plank-Kolmogorov equation and the property transport equation, and the stochastic differential equation systems are presented as the basic elements of stochastic process modelling. Mathematical models of the application of continuous and discrete polystochastic processes to chemical engineering processes are discussed. They include liquid and gas flow in a column with a mobile packed bed, mechanical stirring of a liquid in a tank, solid motion in a liquid fluidized bed, species movement and transfer in a porous media. Deep bed filtration and heat exchanger dynamics are also analyzed. 

In calculating temperature distribution in the dilute phase, solid motion must be accounted for. Solid motion in the dilute phase is shown in Sections II and VI. Laboratory-scale fluid beds exhibit a circulating flow of solid particles with ascending central core and descending peripheral region. The enthalpy balances for both ascending and descending zcHies for the steady state are... 

Fluidization refers to the state of solid particles in a suspended condition owing to the flow of fluid, gas, and/or liquid. Contact schemes of fluidized bed systems can be classified on the basis of the states of solid motion. For a batch-solids system, the fluid at a low velocity merely percolates through the voids between packed particles, while the particles remain motionless. The solids in this case are in the fixed bed state. With an increase in the fluid velocity, particles move apart and become suspended the bed then enters the fluidization state. The fluidization characteristics vary, depending on whether gas, liquid, or gas-liquid is the fluidizing medium. 

Lin JS, Chen MM, Chao BT (1985) A Novel Radioactive Particle Tracking Facility for Measurement of Solids Motion in Gas Fluidized Beds. AIChE J 31(3) 465-473... 

Other interesting treatments of the solid motion have been developed in which the motion of the solid s atoms is described by quantum mechanics [Billing and Cacciatore 1985, 1986]. This has been done for a harmonic solid in the context of treatment of the motion of the molecule by classical mechanics and use of a TDSCF formalism to couple the quantum and classical subsystems. The impetus for this approach is the fact that, if the entire solid is treated as a set of coupled harmonic oscillators, the quantum solution can be evaluated directly in an operator formalism. Then, the effect of solid atom motion can be incorporated as an added force on the gas molecule. Another advantage is the ability to treat the harmonic degrees of freedom of the solid and the harmonic electron -hole pair excitations on the same footing. The simplicity of such harmonic degrees of freedom can also be incorporated into the previously defined path-integral formalism in a simple manner to yield influence functionals (Feynman and Hibbs 1965). 

S. Limtrakul et al.. Solids motion and holdup profiles in liquid fluidized beds, Chem. Eng. Sci., 60, 1889-1900 (2005). 

Wang, S. J., T. Dyakowski, and M. S. Beck, An Application of Electrical Capacitance Tomography to Measure Gas-Solid Motion in a Fluidized Bed, AIChE Symposium Series, National Heat Transfer Conf., Houston, Ed, M. S. El-Genk, 92, 310, Aug. 3-6, 1996, pp. 155-160. 

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