Mass micro-models

Most microfluidic microdialysis systems consist of a two-compartment system with a sample flow channel and perfusion flow channel separated by the microdialysis membrane. A two-compartment cocurrent mass transport model of microdialysis is shown in Fig. 3. For this micro-dialysis system, molecules inside the sample channel are dialyzed across the membrane into the perfusion flow channel. Again, this system may be modeled by balancing the sample and perfusion convective fluxes with the diffusion of analyte across the membrane. Assuming the overall permeability is constant, K, over the diffusion path, the mass transfer along the membrane diffusional area. A, can be described as... 

The authors [13] also proposed a multiphase mass transport model for toluene nitration, the details of, which are given in Fig. 2.4. It is based on the formation of a thin aqueous film aroimd the hydrophilic catalyst particles, which are dispersed in toluene medium. The model also accounted for the existence of vapor phase over the liquid-liquid-solid reaction medium. The major mass transfer resistances are offered by the liquid film around the catalyst particles and in the catalyst pores. The aqueous film and the liquid in the pores constitute the micro environment necessary to facilitate the desired level of lattice transformation in the catalyst particles. Figure 2.4 also shows the concept of the microenvironment within and around the catalyst particle. These studies have demonstrated that shape selectively effect of zeolite Beta catalyst is significantly enhanced by the specific microenvironment created within and around the catalyst particles. This has significantly enhanced the para-selectivity from 0.7 to 1.5. The microenvironment has also improved the accessibility of reactant molecules to the catalyst active sites. 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

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... 

For a micro-channel connected to a 100 pm T-junction the Lockhart-Martinelli model correlated well with the data, however, different C-values were needed to correlate well with all the data for the conventional size channels. In contrast, when the 100 pm micro-channel was connected to a reducing inlet section, the data could be fit by a single value of C = 0.24, and no mass velocity effect could be observed. When the T-junction diameter was increased to 500 pm, the best-fit C-value for the 100 pm micro-channel again dropped to a value of 0.24. Thus, as in the void fraction data, the friction pressure drop data in micro-channels and conventional size channels are similar, but for micro-channels, significantly different data can be obtained depending on the inlet geometry. 

Qu W, Mudawar I (2002) Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks. Int J Heat Mass Transfer 45 3933-3945 Qu W, Mudawar I (2004) Measurement and correlation of critical heat flux in two-phase micro-channel heat sinks. Int J Heat Mass Transfer 47 2045-2059 Quiben JM, Thome JR (2007a) Flow pattern based two-phase pressure drop model for horizontal tubes. Part I. Diabatic and adiabatic experimental study. Int. J. Heat and Fluid Flow. 28(5) 1049-1059... 

ReveUin R, Thome J. (2008) A theoretical model for the prediction of the critical hat flux in heated micro-channel. Int. J. Heat and Mass Transfer 51 1216-1225 Roach GM, Abdel-Khahk SI, Ghiaasiaan SM, Dowling MF, Jeter SM (1999) Low-flow critical heat flux in heated microchannels. Nucl Sd Eng 131 411 25 Robinson AJ, Judd RL (2001) Bubble growth in a uniform and spatially distributed temperature field. Int J Heat Mass Transfer 44 2699-2710... 

The present model takes into account how capillary, friction and gravity forces affect the flow development. The parameters which influence the flow mechanism are evaluated. In the frame of the quasi-one-dimensional model the theoretical description of the phenomena is based on the assumption of uniform parameter distribution over the cross-section of the liquid and vapor flows. With this approximation, the mass, thermal and momentum equations for the average parameters are used. These equations allow one to determine the velocity, pressure and temperature distributions along the capillary axis, the shape of the interface surface for various geometrical and regime parameters, as well as the influence of physical properties of the liquid and vapor, micro-channel size, initial temperature of the cooling liquid, wall heat flux and gravity on the flow and heat transfer characteristics. 

The quasi-one-dimensional model of flow in a heated micro-channel makes it possible to describe the fundamental features of two-phase capillary flow due to the heating and evaporation of the liquid. The approach developed allows one to estimate the effects of capillary, inertia, frictional and gravity forces on the shape of the interface surface, as well as the on velocity and temperature distributions. The results of the numerical solution of the system of one-dimensional mass, momentum, and energy conservation equations, and a detailed analysis of the hydrodynamic and thermal characteristic of the flow in heated capillary with evaporative interface surface have been carried out. 

The processes in a cooling system of electronic devices with high power density can be modeled as follows. The coolant with temperature T2.0 and pressure F2.0 enters into the micro-channel from the tank (5) (Fig. 10.2). The mass capacity of the liquid in the tank (5) is large enough, therefore the heat flux from the micro-channel... 

The quasi-one-dimensional model used in the previous sections for analysis of various characteristics of fiow in a heated capillary assumes a uniform distribution of the hydrodynamical and thermal parameters in the cross-section of micro-channel. In the frame of this model, the general characteristics of the fiow with a distinct interface, such as position of the meniscus, rate evaporation and mean velocities of the liquid and its vapor, etc., can be determined for given drag and intensity of heat transfer between working fluid and wall, as well as vapor and wall. In accordance with that, the governing system of equations has to include not only the mass, momentum and energy equations but also some additional correlations that determine... 

In this work, the MeOH kinetic model of Lee et al. [9] is adopted for the micro-channel fluid dynamics analysis. Pressure and concentration distributions are investigated and represented to provide the physico-chemical insight on the transport phenomena in the microscale flow chamber. The mass, momentum, and species equations were employed with kinetic equations that describe the chemical reaction characteristics to solve flow-field, methanol conversion rate, and species concentration variations along the micro-reformer channel. 

Fig. 2 shows a schematic diagram of a micro-channel of reformer section to be examined in this study. A multi-physics computer-aided numerical model framework integrating kinetics, mass transport, and flow dynamics in micro-channel reactors has been established. 

For fast reactions Da becomes large. Based on that assumption and standard correlations for mass transfer inside the micro channels, both the model for the micro-channel reactor and the model for the fixed bed can be reformulated in terms of pseudo-homogeneous reaction kinetics. Finally, the concentration profile along the axial direction can be obtained as the solution of an ordinary differential equation. 

Performing this reaction primarily served as a model to show the feasibility of micro flow processing for soHd/Hqnid reactions [19]. In a similar way as for catalyzed gas-phase reactions, micro-reactor processing was expected to show benefits in terms of mass and heat transfer. Particularly this relates to transfer enhancement when using porous media. 

The cyclohexene hydrogenation is a well-studied process especially in conventional trickle-bed reactors (see original citations in [11,12]) and thus serves well as a model reaction. In particular, flow-pattern maps were derived and kinetics were determined. In addition, mass transfer can be analysed quantitatively for new reactor concepts and processing conditions, as overall mass transfer coefficients were determined and energy dissipations are known. In lieu of benchmarking micro-reactor performance to that of conventional equipment such as trickle-bed reactors, such a knowledge base facilitates proper, reliable and detailed comparison. 

GL 16] ]R 12] ]P 15] Using a simple thin-film model for mass transfer, values for the overall mass transfer coefficient were determined for both micro-channel processing and laboratory trickle-bed reactors [11]. The value for micro-reactor processing (fCL = 5-15 s ) exceeds the performance of the laboratory tool Ki a = 0.01-0.08 s ) [11, 12], However, more energy has to be spent for that purpose (see the next section). 

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