Laminar flows continued determination

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

Write out the continuity, Navier-Stokes, and energy equations in cylindrical coordinates for steady, laminar flow with constant fluid properties. The dissipation term in the energy equation can be ignored. Using this set of equations, investigate the parameters that determine the conditions under which similar" velocity and temperature fields will exist when the flow over a series of axisymmetrie bodies of the same geometrical shape but with different physical sizes is considered. 

The film is laminar, but waves are on the surface. If laminar flow m this wavy regime (30[Pg.1225]

The basis of this method is the measurement of permeability of a packed bed of powder to a laminar gas flow. The determination of permeability can be made either at continuous, steady-state... 

In continuous centrifugation, the centrifugal force and flow rate must be controlled to provide sufficient time for solid or denser liquids to sediment before being carried out with the supernatant but not so long as to underutilize the rotor-throughput capacity. With information on liquid volume within the rotor and assuming laminar flow, the maximum flow rate can be determined from eqn [8]. Alternatively, if the rotor i -factor and the particle sedimentation coefficient are known, the minimum residence time required for pelleting can be calculated from eqn [11],... 

Hydrodynamic and interfacial flow In addition to the wettability, the interfacial state is determined by hydrodynamics of the system. As noted previously (12) the flow profiles in the region of an interface during its displacement are not well known. It is these flows which affect the supply and/or depletion of surfactant to the interface, as well as the flow of the interface itself. Two extreme cases can be envisaged (a) a fully flowing interface, described by Dussan (8), which results from shear forces imposed on the interface by the interaction of the the two laminar flow profiles in the two liquid phases, (b) a non-flowing interface (12). A non-flowing interface would exhibit interfacial properties dependent on the time lapse since its formation and subsequent deformations. A flowing interface would exhibit a dynamic value of interfacial tension, since fresh interface would be formed continuously. 

For nonisothermal systems a general differential equation of conservation of energy will be considered in Chapter 5. Also in Chapter 7 a general differential equation of continuity for a binary mixture will be derived. The differential-momentum-balance equation to be derived is based on Newton s second law and allows us to determine the way velocity varies with position and time and the pressure drop in laminar flow. The equation of momentum balance can be used for turbulent flow with certain modifications. 

Fig. 7.2. Schematic diagram of the apparatus. Each solution, one corresponding to one stable stationary state and the other to the other stationary state, is stored in one of two continuous-stirred tank reactors (CSTR) and pumped at a determined and variable rates through the laminar flow reactor (LFR), where they are brought in contact with each other in a sharp well-defined boundary. For the remainder of the definitions see the text. Prom [1]...

Nonfractionating continuous inlet. An inlet in which gas flows from a gas stream being analyzed to the mass spectrometer ion source without any change in the conditions of flow through the inlet or by the conditions of flow through the ion source. This flow is usually viscous flow, such that the mean free path is very small in comparison with the smallest dimension of a traverse section of the channel. The flow characteristics are determined mainly by collisions between gas molecules, i.e., the viscosity of the gas. The flow can be laminar or turbulent. 

Measurements of kinetic parameters of liquid-phase reactions can be performed in apparata without phase transition (rapid-mixing method [66], stopped-flow method [67], etc.) or in apparata with phase transition of the gaseous components (laminar jet absorber [68], stirred cell reactor [69], etc.). In experiments without phase transition, the studied gas is dissolved physically in a liquid and subsequently mixed with the liquid absorbent to be examined, in a way that ensures a perfect mixing. Afterwards, the reaction conversion is determined via the temperature evolution in the reactor (rapid mixing) or with an indicator (stopped flow). The reaction kinetics can then be deduced from the conversion. In experiments with phase transition, additionally, the phase equilibrium and mass transport must be taken into account as the gaseous component must penetrate into the liquid phase before it reacts. In the laminar jet absorber, a liquid jet of a very small diameter passes continuously through a chamber filled with the gas to be examined. In order to determine the reaction rate constant at a certain temperature, the jet length and diameter as well as the amount of gas absorbed per time unit must be known. 

An important question for the design of continuous flow systems is When can the classic perfectly mixed assumption (ideal CSTR) be used in a continnons flow stirred tank reactor The blend time concept can be used here. If the blend time is small compared to the residence time in the reactor, the reactor can be considered to be well mixed. That is because the residence time is proportional to the characteristic chemical reaction time. A 1 10 ratio of blend time to reaction time is often used, but often, larger values result because the mixer must do other jobs, which lead to even smaller blend times. Frequently, residence time distributions are used to determine whether a reactor is well-mixed. It is usually easy to achieve well-mixed conditions in continuous flow, turbulent stirred vessels unless the reactions are very fast, such as acid-base neutralizations. Even in laminar systems the blend time can be made much less than the required residence time for the chemical reaction mainly because required residence times are so long for high viscosity reactants. For discussions of residence time distribution analysis, see Chapter 1, Levenspiel (1972), and Nauman (1982). 

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