Mechanism, convective transport

To derive an approximate solution we start by transforming the space variable x to one that moves by the convective transport mechanism— i.e., a coordinate that remains fixed with the solute motion when diffusion can be neglected. This coordinate will be denoted by and is... 

The Nusselt number represents the relation between the forced or free convective transport mechanism and the conductive heat transport within the boundary layer of the fluid flow. 

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

The concentration boundary layer forms because of the convective transport of solutes toward the membrane due to the viscous drag exerted by the flux. A diffusive back-transport is produced by the concentration gradient between the membranes surface and the bulk. At equiUbrium the two transport mechanisms are equal to each other. Solving the equations leads to an expression of the flux ... 

First order parameters affecting dispersion stem from meteorological conditions. These, as much as any other consideration, determine how a stack is to be designed for air pollution control purposes. Since the operant transport mechanisms are determined by the micro-meteorological conditions, any attempt to predict ground-level pollutant concentrations is dependent on a reasonable estimate of the convective and dispersive potential of the local air. The following are meteorological conditions which need to be determined ... 

We have so far assumed that the atoms deposited from the vapor phase or from dilute solution strike randomly and balHstically on the crystal surface. However, the material to be crystallized would normally be transported through another medium. Even if this is achieved by hydrodynamic convection, it must nevertheless overcome the last displacement for incorporation by a random diffusion process. Therefore, diffusion of material (as well as of heat) is the most important transport mechanism during crystal growth. An exception, to some extent, is molecular beam epitaxy (MBE) (see [3,12-14] and [15-19]) where the atoms may arrive non-thermalized at supersonic speeds on the crystal surface. But again, after their deposition, surface diffusion then comes into play. 

Many investigators consider neutralization as a poorly understood process in the gas phase. While in the best possible cases it may be considered as a homogeneous second-order process, detailed experimentation in specific cases sometimes fails to establish that (Freeman, 1968 Meisels, 1968). At low dose rates and low gas pressures, wall effects can be seen as a major inhibiting factor, as most neutralizations would then be expected to occur on the walls. Coating the wall with specific chemicals has not lead to a uniform conclusion. On the other hand, wall effects are also present at high dose rates. In such cases, and with gas pressure greater than about 0.1 atm, normal positive ions cannot reach the walls if the size of the vessel is 10 cm or more (Freeman, 1968). Even for electrons, it is hard. Large-scale convection is supposed to be the chief transport mechanism this, however, is difficult to establish experimentally. 

The most serious causes of error are (i) wave and peak distortion caused by excessively fast scan rates, which are themselves caused by diffusion being an inefficient mass transport mechanism, (ii) current maxima caused by convective effects as the mercury drop forms and then grows, and (iii) IR drop, i.e. the resistance of the solution being non-zero. Other causes of error can be minimized by careful experimental design. 

The transport mechanisms that operate in distribution and elimination processes of drugs, drug-carrier conjugates and pro-drugs include convective transport (for example, by blood flow), passive diffusion, facilitated diffusion and active transport by carrier proteins, and, in the case of macromolecules, endocytosis. The kinetics of the particular transport processes depend on the mechanism involved. For example, convective transport is governed by fluid flow and passive diffusion is governed by the concentration gradient, whereas facilitated diffusion, active transport and endocytosis obey saturable MichaeUs-Menten kinetics. 

Polymer network structure is important in describing the transport through biomedical membranes [139, 140]. The mechanism of diffusion in membranes may be that of pure diffusion or convective transport depending on the mesh size of the polymer network. With this in mind, polymer membranes are typically divided into three major types described below [141]. 

Macroporous membranes - these are membranes containing large pores. The pore size is usually between 0.1 and 1 pm. Convective transport through the pore space is the mechanism of diffusion in this case. 

Nonporous gel membranes - these membranes do not contain a porous structure and thus diffusion occurs through the space between the polymer chains (the mesh). Obviously in this case, molecular diffusion rather than convective transport is the dominant mechanism of diffusion in these membranes. 

The most significant effect of a convective-diffusive transport mechanism is to counteract the tendency of the electronation-current density to reduce the interfacial concentration of electron acceptors to zero. Further, since the interfacial concentration of electron acceptors then remains at a value above that given by the diffusion-based equations, a transition time, indicated by a rapid potential variation, need not be attained. 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

When a solute is transferred from a solid into a high-pressure gas, it is then taken downstream in the bulk fluid by convective transport. Depending on turbulence, the solute may travel further by other mass-transport mechanisms such as dispersion. Dispersion spreads the solute axially and radially in a cylindrical stet. Eaton and Akgerman [30] considered both axial and radial effects in a model for the desorption of heavy organics, from carbon, by a dense gas. 

Examples of dimensionless groups that specify ratios of transport mechanisms are listed next in Table II and depend on the size and shape of the domain. The Peclet numbers for heat (Pet) and solute (Pes) and momentum (Re) transport are ratios of scales for convective to diffusive transport and depend on the magnitudes of the velocity field and the length scale for the diffusion gradient. Boundary layers form at large Peclet numbers (Pet or Pes) or Reynolds numbers (Re). The fonnation of a boundary layer at a large Re is particularly important in crystal growth from the melt, because the low... 

The physical factors include mechanical stresses and temperature. As discussed above, IFP is uniformly elevated in solid tumors. It is likely that solid stresses are also increased due to rapid proliferation of tumor cells (Griffon-Etienne et al., 1999 Helmlinger et al., 1997 Yuan, 1997). The increase in IFP reduces convective transport, which is critical for delivery of macromolecules. The temperature effects on the interstitial transport of therapeutic agents are mediated by the viscosity of interstitial fluid, which directly affects the diffusion coefficient of solutes and the hydraulic conductivity of tumor tissues. The temperature in tumor tissues is stable and close to the body temperature under normal conditions, but it can be manipulated through either hypo- or hyper-thermia treatments, which are routine procedures in the clinic for cancer treatment. 

An extremely effective means of enhancing heat removal from a reactor is to make use of fluidized-bed technology (3). Heat transfer coefficients for gaseous systems are increased to values of around 600 W/m2K or more by virtue of the very efficient convective-regenerative particle transport mechanism of heat transfer. Further... 

The concept of critical flux ( Jcrit) was introduced by Field et al. [3] and is based on the notion that foulants experience convection and back-transport mechanisms and that there is a flux below which the net transport to the membrane, and the fouling, is negligible. As the back transport depends on particle size and crossflow conditions the Jcrit is species and operation dependent. It is a useful concept as it highlights the... 

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