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Diffusion convective

It follows from (6.19) that C remains constant during the motion of a liquid particle. If C = Q in the bulk of the flow and = 0 at the surface, no solution of Eq. (6.19) can be found that would satisfy these conditions. Therefore, by analogy with the theory of a viscous boundary layer, there should exist near the surface a thin diffusion boundary layer of thickness Sq, in which the concentration changes from Q to C. Inside this layer, the partial y-derivatives (along the normal to the surface) would be much greater then the x-derivatives (along the tangent to the surface). [Pg.112]

Recall that the thickness of a viscous boundary layer is estimated by the expression [2] [Pg.112]

In the diffusion boundary layer, we have d Cfdx d C/dy, so the equation of convective diffusion in the layer becomes  [Pg.113]

Consider the diffusion process at an infinite fiat wall [3, 4], Estimate the thickness of the diffusion boundary layer. For simplicity, assume the process to be stationary. It is known from the theory of a viscous boundary layer that v/u S /L, therefore u8C/8x vdC/dy. Since Sd Su, the structure of velocity in diffusion layer is equal to the velocity in the immediate vicinity of the wall [Pg.113]

Our thickness estimation requires the knowledge of the concentration C . If the process is diffusion-controlled, then C = 0. Another example is the surface of a material dissolvable in liquid. If dissolution occurs much faster than removal of dissolved substance into to the bulk of the liquid, then C , = C at, where Cjat is the equUibrium concentration of dissolved substance near the surface. The values of C for mixed heterogeneous reactions and penetrable surfaces will be determined later on in the relevant sections. [Pg.113]

The net rate of the electrochemical process is given by the maximum rate of mass transport. The transport processes are rate-determining. Conversely, K 1 implies [Pg.17]

The concentration is constant in the entire electrolytic solution. The net rate is governed by the rate of the heterogeneous reaction and given by fcbC . [Pg.17]

The total flux of ions of the species n in a stirred electrolyte is  [Pg.17]

The last term on the right side represents the flux due to migration of ions in the electric field which is characterized by the vector E. It follows from Eq. 7 at steady state  [Pg.17]

The system of equations 19 has to be solved for the given electrolytic solution under the condition of approximate neutrality in the bulk. [Pg.17]


Splelman L A and Friedlander S K 1974 Role of the electrical double layer In particle deposition by convective diffusion J. Colloid. Interfaoe. Sol. 46 22-31... [Pg.2851]

The finite element results obtained for various values of (3 are compared with the analytical solution in Figure 2.27. As can be seen using a value of /3 = 0.5 a stable numerical solution is obtained. However, this solution is over-damped and inaccurate. Therefore the main problem is to find a value of upwinding parameter that eliminates oscillations without generating over-damped results. To illustrate this concept let us consider the following convection-diffusion equation... [Pg.61]

Petera, J., Nassehi, V. and Pittman, J.F.T., 1989. Petrov-Galerkiii methods on isoparametric bilinear and biquadratic elements tested for a scalar convection-diffusion problem. Ini.. J. Numer. Meth. Heat Fluid Flow 3, 205-222,... [Pg.68]

Morton, K. W., 1996. Numerical Solution of Convection Diffusion Problems, Chapman Hall, London. [Pg.109]

According to the chemical theory of olfaction, the mechanism by which olfaction occurs is the emittance of particles by the odorous substances. These particles are conveyed to the olfactory epithelium by convection, diffusion, or both, and dkecdy or indkectly induce chemical changes in the olfactory receptors. [Pg.292]

Under conditions of limiting current, the system can be analyzed using the traditional convective-diffusion equations. For example, the correlation for flow between two flat plates is... [Pg.66]

Example Consider the equation for convection, diffusion, and reaction in a tiihiilar reactor. [Pg.476]

Hyperbolic Equations The most common situation yielding hyperbohc equations involves unsteady phenomena with convection. Two typical equations are the convective diffusive equation... [Pg.481]

The effect of using upstream derivatives is to add artificial or numerical diffusion to the model. This can be ascertained by rearranging the finite difference form of the convective diffusion equation... [Pg.481]

Another method often used for hyperbohc equations is the Mac-Cormack method. This method has two steps, and it is written here for the convective diffusion equation. [Pg.481]

The materials leaving containment are source terms for offsite convective-diffusion transport calculations. Codes. such as CRAC-2 calculate atmospheric diffusion with different probabilities of meteorological conditions to estimate the radiological health effects and costs. [Pg.237]

Another approach to modeling the particle-collection process is based on the convective diffusion equation... [Pg.1228]

H. Steady-State Convective Diffusion with Simultaneous First-Order Irreversible... [Pg.295]

The estimation of the diffusional flux to a clean surface of a single spherical bubble moving with a constant velocity relative to a liquid medium requires the solution of the equation for convective diffusion for the component that dissolves in the continuous phase. For steady-state incompressible axisym-metric flow, the equation for convective diffusion in spherical coordinates is approximated by... [Pg.347]

For very small values of Reynold s numbers (negligible convective diffusion), elementary calculations lead to... [Pg.373]

A more rigorous treatment takes into account the hydrodynamic characteristics of the flowing solution. Expressions for the limiting currents (under steady-state conditions) have been derived for various electrodes geometries by solving the three-dimensional convective diffusion equation ... [Pg.91]

Example 8.8 Explore conservation of mass, stability, and instability when the convective diffusion equation is solved using the method of lines combined with Euler s method. [Pg.288]

This velocity profile is commonly called drag flow. It is used to model the flow of lubricant between sliding metal surfaces or the flow of polymer in extruders. A pressure-driven flow—typically in the opposite direction—is sometimes superimposed on the drag flow, but we will avoid this complication. Equation (8.51) also represents a limiting case of Couette flow (which is flow between coaxial cylinders, one of which is rotating) when the gap width is small. Equation (8.38) continues to govern convective diffusion in the flat-plate geometry, but the boundary conditions are different. The zero-flux condition applies at both walls, but there is no line of symmetry. Calculations must be made over the entire channel width and not just the half-width. [Pg.290]

Radial motion of fluid can have a significant, cumulative effect on the convective diffusion equations even when Vr has a negligible effect on the equation of motion for V. Thus, Equation (8.68) can give an accurate approximation for even though Equations (8.12) and (8.52) need to be modified to account for radial convection. The extended versions of these equations are... [Pg.302]

The convective diffusion equations for mass and energy are given detailed treatments in most texts on transport phenomena. The classic reference is... [Pg.309]

The appropriateness of neglecting radial flow in the axial momentum equation yet of retaining it in the convective diffusion equation is discussed in... [Pg.309]

This section derives a simple version of the convective diffusion equation, applicable to tubular reactors with a one-dimensional velocity profile V (r). The starting point is Equation (1.4) applied to the differential volume element shown in Figure 8.9. The volume element is located at point (r, z) and is in the shape of a ring. Note that 0-dependence is ignored so that the results will not be applicable to systems with significant natural convection. Also, convection due to is neglected. Component A is transported by radial and axial diffusion and by axial convection. The diffusive flux is governed by Pick s law. [Pg.310]

Thermal runaway. Temperature control in a tubular polymerizer depends on convective diffusion of heat. This becomes difficult in a large-diameter tube, and temperatures may rise to a point where a thermal runaway becomes inevitable. [Pg.496]

Include the radial velocity term in the convective diffusion equation and plot streamlines in the reactor. [Pg.500]

Solution The problem requires solution of the convective diffusion equation for mass but not for energy. Rewriting Equation (8.71) in dimensionless form gives... [Pg.500]

The unsteady version of the convective diffusion equation is obtained just by adding a time derivative to the steady version. Equation (8.32) for the convective diffusion of mass becomes... [Pg.534]

Axial Dispersion. Rigorous models for residence time distributions require use of the convective diffusion equation. Equation (14.19). Such solutions, either analytical or numerical, are rather difficult. Example 15.4 solved the simplest possible version of the convective diffusion equation to determine the residence time distribution of a piston flow reactor. The derivation of W t) for parabolic flow was actually equivalent to solving... [Pg.558]


See other pages where Diffusion convective is mentioned: [Pg.110]    [Pg.511]    [Pg.156]    [Pg.434]    [Pg.481]    [Pg.481]    [Pg.2006]    [Pg.1227]    [Pg.295]    [Pg.332]    [Pg.347]    [Pg.273]    [Pg.269]    [Pg.272]    [Pg.291]    [Pg.292]    [Pg.293]    [Pg.310]    [Pg.318]    [Pg.336]    [Pg.498]    [Pg.534]   
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