Transient processes

Other Models for Mass Transfer. In contrast to the film theory, other approaches assume that transfer of material does not occur by steady-state diffusion. Rather there are large fluid motions which constantiy bring fresh masses of bulk material into direct contact with the interface. According to the penetration theory (33), diffusion proceeds from the interface into the particular element of fluid in contact with the interface. This is an unsteady state, transient process where the rate decreases with time. After a while, the element is replaced by a fresh one brought to the interface by the relative movements of gas and Uquid, and the process is repeated. In order to evaluate a constant average contact time T for the individual fluid elements is assumed (33). This leads to relations such as... 

Differential and Integral Balances. Two types of material balances, differential and integral, are applied in analyzing chemical processes. The differential mass balance is valid at any instant in time, with each term representing a rate (i.e., mass per unit time). A general differential material balance may be written on any material involved in any transient process, including semibatch and unsteady-state continuous flow processes ... 

For any transient process that begins at time t and is terminated at a later time tp, the general integral material balance equation has the form... 

In a possible hypothesis, Smirnov et al. have proposed that a transient process such as [MX4]3- + [MXj] - —> [MX,] 2- + [MXJs- is the electrically conducting process. Their concept may he similar to the dynamic dissociation model. 

In electrochemical systems, transient processes are of major practical significance because they are an efficient route for studying electrode reactions and phenomena (see Chapter 12). In addition, transient measurements are useful for analytical purposes (see Chapter 23). 

Concentration gradients in the electrolyte layer next to the electrode surface will develop or change as a result of the primary electrode reaction. Therefore, the current associated with these changes is faradaic, although it is also transient and falls to zero when adjustment of the concentration profile is complete. Unlike other transient processes, these processes, can be described in a quantitative way (Sections 11.2 and 11.3). The transition times of such processes as a rule are longer than 1 s. 

This equation holds only at short times when thickness 5. is small compared to the steady-state dilfnsion-layer thickness 5j.(, which will be attained under given experimental conditions, particularly when the solntion is stirred. As soon as attains the value of 5,.(, the transitory processes end and a steady state is attained there is no fnr-ther change in concentration distribution with time (Fig. 11.3a). It follows from Eq. (11.7) that the transition time of the transient process... 

The transient process continues until thickness 5. has attained the value of diffusion-layer thickness corresponding to the applicable experimental conditions. Hence, we obtain for the duration of this transitory process,... 

The model approximates the transient process of heat injection or extraction by... 

This formula can be used as an approximation of the transient process under the condition that... 

Of course, in free-convection mass transfer the transition time is dependent on the density difference generated at the electrode. The dimensionless time variable of the transient process is... 

Laser flash photolysis techniques offer the possibility of examining in detail the transient processes responsible for the photostabilizing effect discussed above. The triplet lifetimes are frequently too short, even for this technique however, they can still be estimated using as a probe the quenching by 1-methyl-naphthalene, which leads to the formation of its easily detectable triplet. The optical absorbance due to the 1-methylnaphthalene triplet (Aft) produced as a result of energy transfer is related to the Stern-Volmer slope by equation 5, where N stands for... 

The transient processes under discussion here must be described in terms of elementary steps, and the relative rates of the steps will change as conditions change during transients. 

The extruder would operate for several hours to days at steady state, and then for no apparent reason It would flow surge for several hours. After a period of time, the extruder would return to a steady-state operation and would remain there until the cycle repeated. Problem diagnosis was impossible without transient process data. Moreover, molten resin would frequently flow out the vent, especially during times of unsteady-state operation. 

However, it is possible to directly or indirectly measure the mass flux (mass flow) of conversion gas. Several authors have measured the mass loss of the fuel bed as function of primary air velocities and biofuel [12,33,38,53] by means of a balance. Most of them have used the over-fired batch conversion concept. They utilise the relationship illustrated by Eq. 16 (formulised in amounts instead of flows) above and the assumption that no ash is entrained. As a consequence, the mass loss of the batch bed with time equals the conversion gas. In the simple three-step model [3], an assumption of steady state is made, which is not relevant for batch studies. If it is practically possible, the method of using a balance to measure the conversion gas rate is especially appropriate for transient processes, that is, batch processes. 

The ultrasonic irradiation of a solution induces acoustic cavitation, a transient process that promotes chemical activity. Acoustic cavitation is generated by the growth of preexisting nuclei during the alternating expansion and compression cycles of ultrasonic waves. For example, in aqueous liquid, temperatures as high as 4300 K and pressures over 1000 atm are estimated to exist within... 

Study of transient processes utilizes the three-electrode cell design. One type of three-compartment electrochemical cell is shown in Figure 6.16. Other designs can be found in the literature (e.g.. Ref. 54). 

Fig. 13.1 Ignition transient process by conductive, convective, and radiative heat.

Is it a transient process or does it reach a steady state ... 

There are no solutions for transfer with the generality of the Hadamard-Rybczynski solution for fluid motion. If resistance within the particle is important, solute accumulation makes mass transfer a transient process. Only approximate solutions are available for this situation with internal and external mass transfer resistances included. The following sections consider the resistance in each phase separately, beginning with steady-state transfer in the continuous phase. Section B contains a brief discussion of unsteady mass transfer in the continuous phase under conditions of steady fluid motion. The resistance within the particle is then considered and methods for approximating the overall resistance are presented. Finally, the effect of surface-active agents on external and internal resistance is discussed. 

The theories of transient processes leading to steady detonation waves have been concerned on the one hand with the prediction of the shape of pressure waves which will initiate, described in Section VI, A of Ref 66, and on the other hand with the pressure leading to the formation of such.an initiating pulse, described in Section VI, B. In Section V it was shown that the time-independent side boundary conditions are important in determining the characteristics of steady, three-dimensional waves. It now becomes necessary to take into consideration time-dependent rear boundary conditions. For one-dimensional waves, the side boundary conditions are not involved... 

The first term on the right-hand side of Eq. (257) is provided by the quasisteady model, whereas the second represents the contribution of the transient process. Measurements of the mass transfer coefficients from the dissolution of the wall of a tube into a turbulent liquid having Schmidt numbers as large as 10s could be correlated with the expression [56]... 

Schmidt number, ShocSc1/3, as the experiment does. The transient term leads to a too strong dependence, ShocSc1/2. In addition, one can easily verify that, for sufficiently large values of the Schmidt number, the term in Eq. (257) due to the transient process has the dominant contribution to the value of the mass transfer coefficient and that the values predicted are much too large. 

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