Convection-controlled case

In cases where the mass transport conditions reach a steady state, e.g. with a microelectrode where spherical diffusion dominates (Section 11.2.4) or with a rotating disc electrode where hydrodynamic convection controls the diffusion layer thickness (Section 11.2.5), the current-voltage curve takes the form of a sigmoidal wave (Figure 11.7). The voltammogram is described by equation (11.2.49) when the kinetics are reversible. If however the... 

A large Biot Number means that conduction controls the energy transfer to/from the plastic and large temperature gradients will exist in the plastic. A small Biot Number means that convection is the dominant factor. The above analysis was for conduction heat transfer (B, - oo). When the plastic moulding is taken out of the mould we need to check the value of B,. In this case... 

Anodic shipping voltammetry (ASV) is the most widely used form of stripping analysis, hi this case, the metals are preconcenhated by elechodeposition into a small-volume mercury electrode (a tiiin mercury film or a hanging mercury drop). The preconcenhation is done by catiiodic deposition at a controlled tune and potential. The deposition potential is usually 0.3-0.5 V more negative than E° for the least easily reduced metal ion to be determined. The metal ions reach die mercury electrode by diffusion and convection, where diey are reduced and concentrated as amalgams ... 

Besides the convective fluxes, the diffusive fluxes on the control volume faces have to be determined. As apparent from Eq. (33), an expression for dO/dsc containing the nodal values of O is needed. In the case of an orthogonal grid aligned with the axes of a Cartesian coordinate frame, the expression... 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

There are three types of mass transport processes within a microfluidic system convection, diffusion, and immigration. Much more common are mixtures of three types of mass transport. It is essential to design a well-controlled transport scheme for the microsystem. Convection can be generated by different forces, such as capillary effect, thermal difference, gravity, a pressurized air bladder, the centripetal forces in a spinning disk, mechanical and electroosmotic pumps, in the microsystem. The mechanical and electroosmotic pumps are often used for transport in a microfluidic system due to their convenience, and will be further discussed in section 11.5.2. The migration is a direct transport of molecules in response to an electric field. In most cases, the moving... 

The process of steady flame propagation into a premixed system is depicted in Figure 4.12 for a moving control volume bounding the combustion region <5r. The heat loss in this case is only considered to the duct wall. With h as the convection heat transfer coefficient, the loss rate can be written as... 

Dissolution can be described as a mass transfer process. Although mass transfer processes commonly are under the combined influence of both thermodynamics and hydrodynamics, usually one of these prevails in terms of the overall dissolution process (1-3). Hydrodynamics is predominant for the overall dissolution rate if the mass transfer process is mainly controlled by convection and/or diffusion, as is usually the case for poorly soluble substances. This is of great... 

Diffusive crystal dissolution means that crystal dissolution is controlled by diffusion, which requires high interface reaction rate and absence of convection. In nature, diffusive crystal dissolution is rarely encountered, because there is almost always fluid flow, or crystal falling or rising in the fluid. That is, crystal dissolution in nature is often convective dissolution, which is discussed in the next section. One possible case of diffusive crystal dissolution is for crystals on the roof or floor of a magma chamber if melt produced by dissolution does not sink or rise. For these... 

Central differences are applied to diffusion problems, and upwind differences are applied to convective problems, but most cases have both diffusion and convection. This conundrum led Spaulding (1972) to develop exponential differences, which combines both central and upwind differences in an analytical solution of steady, one-dimensional convection and diffusion. Consider a control volume of length Ax, in a flow fleld of velocity U, and transporting a compound, C, at steady state with a diffusion coefficient, D. Then, the governing equation inside of the control volume is a simphflcation of Equation (2.14) ... 

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