Flow rate transport parameters

From the general flow equations transport parameters can be derived in terms of the phenomenological coefficients if a proper choice of forces appertaining to a specified experimental situation is made. We shall distinguish between transport of ions in an applied external electrical field and mass transport in diffusion and sedimentation at zero electrical current. As usual, transport parameters will be defined as the rate of motion of ions or electroneutral components per unit applied force. 

The two steps in the removal of a particle from the Hquid phase by the filter medium are the transport of the suspended particle to the surface of the medium and interaction with the surface to form a bond strong enough to withstand the hydraulic stresses imposed on it by the passage of water over the surface. The transport step is influenced by such physical factors as concentration of the suspension, medium particle size, medium particle-size distribution, temperature, flow rate, and flow time. These parameters have been considered in various empirical relationships that help predict filter performance based on physical factors only (8,9). Attention has also been placed on the interaction between the particles and the filter surface. The mechanisms postulated are based on adsorption (qv) or specific chemical interactions (10). 

Where large samples of reactant are used and/or where C02 withdrawal is not rapid or complete, the rates of calcite decomposition can be controlled by the rate of heat transfer [748] or C02 removal [749], Draper [748] has shown that the shapes of a—time curves can be altered by varying the reactant geometry and supply of heat to the reactant mass. Under the conditions used, heat flow, rather than product escape, was identified as rate-limiting. Using large ( 100 g) samples, Hills [749] concluded that the reaction rate was controlled by both the diffusion of heat to the interface and C02 from it. The proposed models were consistent with independently measured values of the transport parameters [750—752] whether these results are transfenable to small samples is questionable. 

Dispersion depends on several experimental factors, such as volume of sample injected, length, inner diameter, and geometrical configuration to the space of the transportation tube [and the reactor(s), if there is any], and flow rate of the carrier. If all other variables are constant, then dispersion depends on the following parameters [8] ... 

Reverse-Osmosis Experiments. All reverse-osmosis experiments were performed with continuous-flow cells. Each membrane was subjected to an initial pure water pressure of 2068 kPag (300 psig) for 2 h pure water was used as feed to minimize the compaction effect. The specifications of all the membranes in terms of the solute transport parameter [(Dam/ 6)Naci]> the pure water permeability constant (A), the separation, and the product rate (PR) are given in Table I. These were determined by Kimura-Sourirajan analysis (7) of experimental reverse-osmosis data with sodium chloride solution at a feed concentration of 0.06 m unless otherwise stated. All other reverse-osmosis experiments were carried out at laboratory temperature (23-25 °C), an operating pressure of 1724 kPag (250 psig), a feed concentration of 100 ppm, and a feed flow rate >400 cmVmin. The fraction solute separation (/) is defined as follows ... 

Downcomer Choke Flooding This is also called downcomer entrance flood or downcomer velocity flood. A downcomer must be sufficiently large to transport all the liquid downflow. Excessive friction losses in the downcomer entrance, and/or excessive flow rate of gas venting from the downcomer in counterflow, will impede liquid downflow, initiating liquid accumulation (termed downcomer choke flooding) on the tray above. The prime design parameter is the downcomer top area. Further down the downcomer, gas disengages from the liquid and the volumes of aerated liquid downflow and vented gas... 

Summarizing this short discussion it has to be stated, that up to now experiments providing absolute numbers of kf during protein adsorption in fluidized beds are not available, the interpretations are based on correlations derived for small ions. As ion exchange with fluidized resins is performed at much higher Reynolds numbers and mostly is not limited by particle side transport, the validity of the correlations for proteins has to be proven. Nevertheless, the influence of bed expansion at increased linear flow rate cannot be neglected and fluid side mass transport should be considered as a system parameter governing the sorption process in a fluidized bed under certain conditions. 

A dynamic model for on-line estimation and control of a fixed bed catalytic reactor must be based on a thorough experimental program. It must be able to predict the measured experimental effects of the variation of key variables such as jacket temperature, feed flow rate, composition and temperature on the dynamic behaviour of the reactor this, in turn, requires the knowledge of the kinetic and "effective" transport parameters involved in the model. 

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