Transient mass transfer

M. Younas, S. Druon-Boequet, and J. Sanchez, Experimental and theoretical mass transfer transient analysis of copper extraction using hoUow fiber membrane contactors, J. Membr. Sci 382 (2011) 70-81. 

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... 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

Carbon dioxide gas diluted with nitrogen is passed continuously across the surface of an agitated aqueous lime solution. Clouds of crystals first appear just beneath the gas-liquid interface, although soon disperse into the bulk liquid phase. This indicates that crystallization occurs predominantly at the gas-liquid interface due to the localized high supersaturation produced by the mass transfer limited chemical reaction. The transient mean size of crystals obtained as a function of agitation rate is shown in Figure 8.16. 

Gal-Or and Hoelscher (G5) have recently developed a fast and simple transient-response method for the measurement of concentration and volumetric mass-transfer coefficients in gas-liquid dispersions. The method involves the use of a transient response to a step change in the composition of the feed gas. The resulting change in the composition of the liquid phase of the dispersion is measured by means of a Clark electrode, which permits the rapid and accurate analysis of oxygen or carbon dioxide concentrations in a gas, in blood, or in any liquid mixture. 

Part 1. Presentation of the model. Int J Heat Mass Transfer 47 3375-3385 Tiselj I, Hetsroni G, Mavko B, Mosyak A, Pogrebnyak E, Segal Z (2004) Effect of axial conduction on the heat transfer in micro-channels Int J Heat Mass Transfer 47 2551-2565 Triplett KA, Ghiaasiaan SM, Abdel-Khalik SI, Sadowski DL (1999) Gas-liquid two-phase flow in microchannels. Part I. Two-phase flow patterns. Int J Multiphase Flow 25 377-394 Tsai J-H, Lin L (2002) Transient thermal bubble formation on polysihcon micro-resisters. J Heat Transfer 124 375-382... 

We have considered thermodynamic equilibrium in homogeneous systems. When two or more phases exist, it is necessary that the requirements for reaction equilibria (i.e., Equations (7.46)) be satisfied simultaneously with the requirements for phase equilibria (i.e., that the component fugacities be equal in each phase). We leave the treatment of chemical equilibria in multiphase systems to the specialized literature, but note that the method of false transients normally works quite well for multiphase systems. The simulation includes reaction—typically confined to one phase—and mass transfer between the phases. The governing equations are given in Chapter 11. 

Measurements Using Liquid-Phase Reactions. Liquid-phase reactions, and the oxidation of sodium sulfite to sodium sulfate in particular, are sometimes used to determine kiAi. As for the transient method, the system is batch with respect to the liquid phase. Pure oxygen is sparged into the vessel. A pseudo-steady-state results. There is no gas outlet, and the inlet flow rate is adjusted so that the vessel pressure remains constant. Under these circumstances, the inlet flow rate equals the mass transfer rate. Equations (11.5) and (11.12) are combined to give a particularly simple result ... 

Curing of Polyimlde Resin. Thermoset processing involves a large number of simultaneous and interacting phenomena, notably transient and coupled heat and mass transfer. This makes an empirical approach to process optimization difficult. For instance, it is often difficult to ascertain the time at which pressure should be applied to consolidate the laminate. If the pressure is applied too early, the low resin viscosity will lead to excessive bleed and flash. But if the pressure is applied too late, the diluent vapor pressure will be too high or the resin molecular mobility too low to prevent void formation. This example will outline the utility of our finite element code in providing an analytical model for these cure processes. 

Cao, Y., and Faghri, A., 1991, Performance characteristics of a thermal energy storage module a transient PCM/forced convection conjugate analysis, hit. J. Heat Mass Transfer, 34 93—101. 

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... 

For a number of flow situations, the mass-transfer rate can be derived directly from the equation of convective diffusion (see Table VII, Part A). The velocity profile near the electrode is known, and the equation is reduced to a simpler form by appropriate similarity transformations (N6). These well-defined flows, therefore, are being exploited increasingly by electrochemists as tools for the kinetic characterization of electrode reactions. Current distributions at, or below, the limiting current, transient mass transfer, and other aspects of these flows are amenable to analysis. Especially noteworthy are the systematic investigations conducted by Newman (review until 1973 in N7 also N9b, N9c, H6b and references in Table VII), by Daguenet and other French workers (references in Table VII), and by Matsuda (M4a-d). Here we only want to comment on the nature of the velocity profile near the electrode, and on the agreement between theory and mass-transfer experiment. 

One really may need an inherently transient LES to capture all these details. The finer the grid for such a LES, the more reliably the local transient conditions may be taken into account in reproducing this turbulent mass transfer process (while ignoring the issue of supplying the heat for the dissolution which may also depend on a proper representation of the turbulent-flow field). An additional important issue is how many particles have to be tracked for a proper representation of the transient spatial distribution of the particles over the vessel. 

Using Equation (13), the external mass transfer coefficient at 723 K was calculated to be 60 cm/s. Since the reactor operating conditions at th s temperature (723 K, slightly above atmospheric pressure, 247 cm /s) were very similar to those of our transient chemisorption experiments, the external mass transfer coefficient calculated above was used for the simulations. 

However, one must be careful because in an LMXB the optical emission from the accretion disk (whether in the outer, cool regions or as reprocessed X-ray emission) can outshine the companion by a large factor. This makes spectral lines difficult to measure and also complicates the ellipsoidal light curve technique. The ideal systems to study are therefore transient systems, which undergo periods of active mass transfer (often for a few weeks to a few months) before lapsing into quiescence, where there is little to no mass transfer. During quiescence, the companion is still distorted by the gravity of the neutron star, hence the flux variations still occur, but without any contamination by the accretion disk. There is a relatively new approach similar to this that... 

Condensation is generally a transient operation in which, as discussed by Ueda and Takashima(106), simultaneous heat and mass transfer are further complicated by the effects of spontaneous condensation in the bulk gaseous phase. After the creation of supersaturation in the vapour phase, nucleation normally occurs which may be homogeneous in special circumstances, but more usually heterogeneous. This process is followed by both crystal growth and agglomeration which lead to the formation of the final crystal product. As a rate process, the condensation of solids from vapours is less well understood than vaporisation(98). Strickland-Constable(107) has described a simple laboratory technique... 

Response time. In the literature, response time is usually specified as the time taken for the electrode to reach > 90% of the output. Typical response times are around 30 sec. A fast response time is critical when one is measuring transient phenomena such as oxygen respiration rates in tissue or suspended cells and dynamic measurements of the volumetric mass transfer coefficient in bioreactors. 

J. P. Owejan, T. A. Trabold, D. L. Jacobson, et al. In situ investigation of water transport in an operating PEM fuel cell using neutron radiography. Part 2. Transient water accumulation in an interdigitated cathode flow field. International Journal of Heat Mass Transfer 49 (2006) 4721-4731. 

Magnussen, B.F. etal. Kameleon II A Transient, 3-Dimensional Computer Program for Fluid Flow, Heat- and Mass Transfer. NTH/SINTEF. Norwegian Institute of Technology (NTH). Trondheim, Norway Division of Thermodynamics. 

One temporal concept to be borne in mind in this context is whether the (bio)chemical reactions and mass transfer separations taking place at the active microzone (one or both of which, by definition, take place simultaneously with detection) are simultaneous or sequential relative to each other. Whether such processes take place at the same or a different time has a marked effect on the sensor performance and type of transient signal obtained. 

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 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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