Steady state or transient

How fast the concenttation or temperature will change due to a step change at an inlet gives us an idea about the time resolution that is required for a transient solution, and how quickly the reactor will reach steady state. One way to retrieve the time constants is to compare the accumulation term with the dominating transport term. 

Axial transport the ratio of accumulation to convection is written and simplified as dCA/dt AC /Ai C, i T 

This gives the time constant for axial convection as 

As expected, it will take one residence time Llvz for a change in inlet concentration to affect the whole length of the reactor, and it will take R /D for the concentration to diffuse from the center of the reactor to the wall in accordance with the time constants developed in Section 5.1.5. 

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One way to examine the validity of the steady-state approximation is to compare concentration—time curves calculated with exact solutions and with steady-state solutions. Figure 3-10 shows such a comparison for Scheme XIV and the parameters, ki = 0.01 s , k i = 1 s , 2 = 2 s . The period during which the concentration of the intermediate builds up from its initial value of zero to the quasi-steady-state when dcfjdt is vei small is called the pre-steady-state or transient stage in Fig. 3-10 this lasts for about 2 s. For the remainder of the reaction (over 500 s) the steady-state and exact solutions are in excellent agreement. Because the concen-... 

Voltammetry, which determines the steady-state or transient polarization characteristics of electrodes in reactions involving the substance being examined... 

Equation 10.1.1 represents a very general formulation of the first law of thermodynamics, which can be readily reduced to a variety of simple forms for specific applications under either steady-state or transient operating conditions. For steady-state applications the time derivative of the system energy is zero. This condition is that of greatest interest in the design of continuous flow reactors. Thus, at steady state,... 

FRET interactions are typically characterized by either steady-state or transient fluorescence emission signals from the donor or acceptor species. Efficient nonradiative energy transfer results in donor PL loss associated with acceptor gain in photoluminescence intensity (if the acceptor is an emitter). The rate of this energy transfer is related to the intrinsic lifetime of the isolated donor and depends strongly on the donor-acceptor separation distance ... 

The methods of measurement of thermal conductivity can be divided into steady state methods and transient methods. Traditionally, steady state methods were most widely used as they are mathematically more simple, but because, particularly for materials of low conductivity, they can be very time consuming and involve expensive apparatus, non-steady state or transient methods have been developed. These can have experimental advantages once the much more difficult mathematical treatment has been worked out. 

Chemical processes may be classified as batch, continuous or semi-batch and as either steady-state or transient. Although the procedure required for performing mass, or material, balances depends on the type of process, most of the concepts translate directly to all types. 

Catalytic reactors can be classified globally according to their mode of operation under steady state or transient conditions, as indicated in Fig. 4, or according to the contacting/mixing mode, as indicated in Fig. 5 for... 

For all values of the variables studied, the gas-phase dispersion does not show a significant effect on the steady-state or transient characteristics of the liquid-phase or surface concentration. This means that, in modeling three-phase slurry reactors, the gas phase may be assumed to move in plug flow as long as the performance of the reactor is measured in terms of the change in concentration of the liquid phase. 

Steady-state or transient two-dimensional (2D) and three-dimensional (3D) flows in standard geometries involving Cartesian, cylindrical, or spherical coordinates and complex geometries involving BFCs with adaptive grids... 

If the values of all the variables in a process (i.e., all temperatures, pressures, volumes, flow rates) do not change with time, except possibly for minor fluctuations about constant mean values, the process is said to be operating at steady state. If any of the process variables change with time, transient or unsteady-state operation is said to exist. By their nature, batch and semibatch processes are unsteady-state operations (why ), whereas continuous processes may be either steady-state or transient. 

The ammonia produced dissolves to form NH, which is sensed by the ISE. The signal generated by the NH4 produced is proportional to the logarithm of the concentration of urea in the sample. The response may be either steady state or transient. Typically, correction for background potassium is required, since the nonactin ionophore has limited selectivity for ammonium over potassium (Knh4/k = 0.1). Potassium is measured simultaneously with urea and used to correct the output of the urea sensor using the Nicolslcy-Eisenman equation. 

Pre-steady-state (or transient-state) kinetic approaches, allowing the dissection of individual steps and intermediates in an enzymatic reaction, are superior to classical steady-state approaches. Pre-steady-state kinetic methods were first applied to DNA polymerases in late 1980s to early 1990s in classical studies of E. coli Pol I (Klenow fragment, and bacteriophage T7 DNA polymerase. These studies have served as a... 

The MOTIF code is a three-dimensional finite-element code capable of simulating steady state or transient coupled/uncoupled variable-density, variable- saturation fluid flow, heat transport, and conservative or nonspecies radionuclide) transport in deformable fractured/ porous media. In the code, the porous medium component is represented by hexahedral elements, triangular prism elements, tetrahedral elements, quadrilateral planar elements, and lineal elements. Discrete fractures are represented by biplanar quadrilateral elements (for the equilibrium equation), and monoplanar quadrilateral elements (for flow and transport equations). 

Macroscopic, such as the analysis of uptake curves, Wicke-Callanbach methods based on steady-state or transient diffusion cell, time lag method, chromatographic methods, zero length column (ZLC) method, and FR method... 

In reactions occurring within porous catalysts the reactants have to adsorb and diffrise to and from the active centres. Typically this Affusion-sorption behaviour is measured under inert conditions at temperatures well below that at which reactions occur. It is preferable to study catalysts under reaction conditions. Such data can be interpreted by reaction-diffusion-adsorption models, the so-called "Thiele modulus" reproach [1]. The model parameters can be determined by using steady state or transient measurements. 

Finally, to conclude this introduction, and to avoid any possible confusion in the terminology, we wish to define briefly what is an ultramicroelectrode (at least in our sense ). When their interfacial properties are to be considered identical with those of any other electrode of a larger dimension, ultramicroelectrodes must remain much larger than the double layer thickness. This sets a lower dimension of a few tens of A for ultramicroelectrodes.On the other hand, if diffusional steady state voltammetry has to be observed without significant interference of convection, they must be smaller than convective layers, which sets an upper limit of a few tens of /im. Between these limits, all ultramicroelectrodes possess identical intrinsic physico-chemical properties. However, their behavior (viz. ohmic drop, steady state or transient currents, etc) obviously depends on the medium and the time-scale considered. ... 

The mechanisms of mass transport can be divided into convective and molecular flow processes. Convective flow is either forced flow, for example, in pipes and packed beds, or natural convection induced by temperature differences in a fluid. For diffusive flow we have to distinguish whether we have molecular diffusion in a free fluid phase or a more complicated effective diffusion in porous solids. Like heat transport, diffusion may be steady-state or transient. 

Pick s second law of diffusion is for a non-steady state or transient conditions in which dCj/t 0. Using Crank s model [23] for the rectangular element shown in Figure 4.1 yields the fundamental differential equations for the rate of concentration. Consider the central plane as the reference point in the rectangular volume element and assume that the diffusing plane at position 2 moves along the x-direction at a distance x-da from position 1 and x-Hdi to position 3. Thus, the rate of diffusion that enters the volume element at position 1 and leaves at position 3 is... 

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