Computational mass transport

The only way to know if your computational model is functioning properly is to test it against an analytical solution. This is done by first choosing an analytic solution that has boundary conditions close to those that will be modeled computationally. 

Then run the computational model on the same conditions as the analytical solution was applied. The result will be a direct, apples-to-apples comparison that will let you know how your computational solution is performing in the planned application. Then, you are ready to move on to the more complex boundary conditions of the application. 

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Chapter 7 Computational Mass Transport. Computational mass transport is a more flexible solution technique that still requires verification with an analytical solution. A short description of some of the more prevalent techniques applied to mass transport is provided in this chapter. 

The response given in equation (6.12) is precisely the output that one would get from the standard computational mass transport program that uses control volumes... 

Let US return to the discussion of computational transport routines, where each computational cell is the equivalent of a complete mix reactor. If we are putting together a computational mass transport routine, we could simply specify the size of the cells to match the diffusion/dispersion in the system. The number of well-mixed cells in an estuary or river, for example, could be calculated from equation (6.44), assuming a small Courant number. Then, the equivalent longitudinal dispersion coefficient for the system would be calculated from equation (6.44), as well, for a small At (At was infinitely small in equation 6.44) ... 

Solve Example 2.2 with a computational mass transport routine under the following conditions ... 

Test your computational mass transport routine before tackling this problem, with a known solution of some problem that has similar characteristics in time and space. Show this test when you write up your answer to the problem. 

Then in Section 10.3, we address the problem of computing mass transport coefficients in porous materials called zeolites. Zeolites are materials with a wide range of applications, such as petrochemical separation, water purification, and catalysis. Understanding and predictably computing mass transport coefficients for a variety of molecules in these molecular sieves instruct optimal use of the appropriate zeolite for an application. We describe the methodology used to compute... 

Schuck P 1996 Kinetics of iigand binding to receptors immobiiized in a poiymer matrix, as detected with an evanescent wave biosensor, i. A computer simuiation of the influence of mass transport Biophys. J. 70 1230-49... 

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. 

The ratio of the observed reaction rate to the rate in the absence of intraparticle mass and heat transfer resistance is defined as the elFectiveness factor. When the effectiveness factor is ignored, simulation results for catalytic reactors can be inaccurate. Since it is used extensively for simulation of large reaction systems, its fast computation is required to accelerate the simulation time and enhance the simulation accuracy. This problem is to solve the dimensionless equation describing the mass transport of the key component in a porous catalyst[l,2]... 

In a finite difference model, the differential equation representing mass transport (Eqn. 20.24 or 20.25) is converted into an approximate, algebraic form that can readily be evaluated using a computer. A derivative of concentration in space evaluated between nodal points (/, J) and (7 + 1, J), for example, can be written,... 

Once the value of cM(ro, t) (which for simplicity will be denoted as from now on) is known, any physical quantity of the system can be computed. In particular, the incoming diffusive (or mass transport) flux ... 

Glaser, R. W. (1993). Antigen-antibody binding and mass transport by convection and diffusion to a surface a two-dimensional computer model of binding and dissociation kinetics, Anal. Biochem., 213, 152-161. 

A second cause of irreproducibility is not maintaining constant flow or rotation rate during analysis. Since convection is such an efficient form of mass transport, small variations in cu or Vf can cause /um to vary greatly. The variation in flux caused by a poor-quality pump can be negated if the solution is delivered from a well-observed constant-head tank. Vigilance is recommended in the absence of computer feedback systems,. 

The Brunauer type I is the characteristic shape that arises from uniform micro-porous sorbents such as zeolite molecular sieves. It must be admitted though that there are indeed some deviations from pure Brunauer type I behavior in zeoHtes. From this we derive the concept of the favorable versus an unfavorable isotherm for adsorption. The computation of mass transfer coefficients can be accompHshed through the construction of a multiple mass transfer resistance model. Resistance modehng utilizes the analogy between electrical current flow and transport of molecular species. In electrical current flow voltage difference represents the driving force and current flow represents the transport In mass transport the driving force is typically concentration difference and the flux of the species into the sorbent is resisted by various mechanisms. 

Darling, E. M., Jr. Computer Modeling of Transportation-Generated Air Pollution. A State-of-the-Art Survey. Final Report. DOT-TSC-OST-72-20. Cambridge, Mass. Transportation Systems Center, 1972. 131 pp. 

The terminology of computational techniques is descriptive, but one needs to know what is being described. Table 7.1 lists some common terms with a definition relative to mass transport. Most computational techniques in fluid transport are described with control volume elements, wherein the important process to be computed is the transport across the interfaces of small control volumes. The common control volumes are cubes, cylindrical shells, triangular prisms, and trapezoidal prisms, although any shape can be used. We will present the control volume technique. 

Over the last four decades or so, transport phenomena research has benefited from the substantial efforts made to replace empiricism by fundamental knowledge based on computer simulations and theoretical modeling of transport phenomena. These efforts were spurred on by the publication in 1960 by Bird et al. (6) of the first edition of their quintessential monograph on the interrelationships among the three fundamental types of transport phenomena mass transport, energy transport, and momentum transport. All transport phenomena follow the same pattern in accordance with the generalized diffusion equation (GDE). The unidimensional flux, or overall transport rate per unit area in one direction, is expressed as a system property multiplied by a gradient (5)... 

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