Effect of Convective Flow

in addition to the diffusion-limited result, there emerges a multiplicative factor due to flow, which is proportional to the one-third power of the Peclet number Pe = vR/D. In the flow-dominated regime, the capture rate is proportional to. This is to be contrasted with the Smoluchowski result 

Therefore, the presence of strong flows can significantly influence the capture rate of the polymer molecules through a pore. 

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In considering the effect of mass transfer on the boiling of a multicomponent mixture, both the boiling mechanism and the driving force for transport must be examined (17—20). Moreover, the process is strongly influenced by the effects of convective flow on the boundary layer. In Reference 20 both effects have been taken into consideration to obtain a general correlation based on mechanistic reasoning that fits all available data within 15%. 

S. Coriell, R. Sekerka. Effect of convective flow on morphological stability. Physico-Chem Hydrodyn 2 281, 1981. 

EXP AC analyzes an interconnected network of building rooms and ventilation systems. A lumped-parameter formulation is used that includes the effects of inertial and choking flow in rapid gas transienl.s. The latest version is specifically suited to calculation of the detailed effects of explosions in the far field using a parametric representation of the explosive event. A material transport capability models the effects of convection, depletion, entrainment, and filtration of... 

The density change on polymerization is typically about 20%, and this density gradient can cause significant secondary flows and natural convection effects. The experiments cited above for vinyl acetate polymerization were performed in a helical reactor. The centrifugal force in helical reactors induces secondary flows as well. The effects of helical flow have been analyzed, but were found to be less significant than the effects of natural convection [14]. 

Strictly speaking, in this formulation the effective diffusion coefficient, is replaced by an empirical dispersion coefficient, D, to account for the effect of water flow on diffusion. However, in practice, the rate of transpirational water flow is sufficiently slow that dispersion effects are minimal and Eq. (8) can be used without error. This is because the Peclet number (see Sect. F.2) is small. For the same reason, in almost all cases diffusion is the most important process in moving nutrients to the root and the convection term can be omitted entirely. 

The spatial temperature distribution established under steady-state conditions is the result both of thermal conduction in the fluid and in the matrix material and of convective flow. Figure 2. 9.10, top row, shows temperature maps representing this combined effect in a random-site percolation cluster. The convection rolls distorted by the flow obstacles in the model object are represented by the velocity maps in Figure 2.9.10. All experimental data (left column) were recorded with the NMR methods described above, and compare well with the simulated data obtained with the aid of the FLUENT 5.5.1 [40] software package (right-hand column). Details both of the experimental set-up and the numerical simulations can be found in Ref. [8], The spatial resolution is limited by the same restrictions associated with spin... 

Low-permeability passive perimeter gas control systems (Figure 16.7) effectively block gas flow into the areas of concern by using barriers (such as synthetic membranes or natural clays) between the contaminated site and the area to be protected. In the low-permeability system, gases are not collected and therefore cannot be conveyed to a point of controlled release or treatment. The low-permeability system can also alter the paths of convective flow. 

However, the two mechanisms interact and molecular diffusion can reduce the effects of convective dispersion. This can be explained by the fact that with streamline flow in a tube molecular diffusion will tend to smooth out the concentration profile arising from the velocity distribution over the cross-section. Similarly radial dispersion can give rise to lower values of longitudinal dispersion than predicted by equation 4.39. As a result the curves of Peclet versus Reynolds number tend to pass through a maximum as shown in Figure 4.6. 

The effect of air flow past the diffusion tube inlet was studied to simulate ambient convection. The effect of external air flows perpendicular to the diffusion tube for two different CO concentrations is shown in Figure Ik. Little variation was seen in the response over the range 200 - 600 ft/min. Response times to... 

Before leaving this discussion, it is important to note that other forms of Peclet numbers are also possible and may be more appropriate depending on the type of convective influence studied. For example, in the case of oscillatory flows (as in oscillatory viscometers), it is more useful to define the Peclet number as (Rfa/D), where co is the frequency of oscillation. Regardless of the particular definition, the general significance of the Peclet number remains the same, i.e., it compares the effect of convection relative to diffusion. 

Labuntsov (LI), 1956 Heat transfer to falling films (laminar flow) effects of convective heat transfer and inertia forces (neglected in Nusselt theory) considered experimentally and theoretically. 

The study of rotating disk electrode behavior provides a unique opportunity to develop a model that predicts the effect of diffusion and convection on the current. This is one of the few convective systems that have simple hydrodynamic equations that may be combined with the diffusion model developed herein to produce meaningful results. The effect of diffusion is modeled exactly as it has been done previously. The effect of convection is treated by integrating an approximate velocity equation to determine the extent of convective flow during a given At interval. Matter, then, is simply transferred from volume element to volume element in accord with this result to simulate convection. The whole process repeated results in a steady-state concentration profile and a steady-state representation of the current (the Levich equation). 

Srinivasan, V., and W.I. Higuchi. 1990. A model for iontophoresis incorporating the effect of convective solvent flow. Int J Pharm 60 133. 

In gas-solid flows well beyond the Stokes regime, the effect of convective acceleration of the gas surrounding the particle is important. To incorporate this effect into the preceding formulation, modifications of the expressions for the Stokes drag, carried mass, and Basset force in the BBO equation are necessary [Odar and Hamilton, 1964]. The modified BBO equation takes the form [Hansell et al., 1992]... 

The effect of die flow direction on the flow field in mixed convection is further illustrated by the experimental results given in Fig. 9.5. This figure essentially shows... 

In gas-filled windows there are three heat transfer mechanisms conduction and convection through the gas layer and radiation between the surroundings and the glass surfaces. The heat flow by conduction is minimized by using a fairly thick gas layer with a low conductivity. With even thicker layers, the effect of convection becomes important. Conduction and radiation cause similar heat fluxes, with heat transfer coefficients of a few watts per square metre per kelvin. 

R. C. Alkire, H. Deligianni, and J.-B. Ju, Effect of Fluid Flow on Convective Transport in Small Cavities, J. Electrochem. Soc. (Submitted August 1989). 

At higher gas pressures, a buoyancy correction must be made to allow for the volume occupied by the sample this increases with pressure. The mass of gas displaced is given by MPV/RT, where P and V are pressure and volume of gas of molar mass M, and/ is the gas constant. During reactant decompositions, the volume of the residual sample changes for example, the nickel metal product formed on heating nickel oxalate dihydrate occupies only about 10% the volume of the reactant from which it was formed. Other corrections include the contributions from any gas flow in and around the balance mechanism and the effects of convection that increase with pressure. Some specific issues are discussed in the following text ... 

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