Mass transport phenomena Convection

What characterises the different incubation steps is the time required to reach thermodynamic equilibrium between an antibody and an antigen in the standard format of microtitre plates. In fact the volume used in each of the incubation steps has been fixed between 100 and 200 pL to be in contact with a surface area of approx. 1 cm2 where the affinity partner is immobilised. The dimensions of the wells are such that the travel of the molecule from the bulk solution to the wall (where the affinity partner is immobilised) is in the order of 1 mm. It must be taken into account that the generation of forced convection or even of turbulence in the wells of a microtitre plate is rather difficult due to the intrinsic dimensions of the wells [10]. Indeed, even if some temperature or shaking effects can help the mass transport from the solution to the wall, the main mass transport phenomenon in these dimensions is ensured by diffusion. 

Ary given catalytic material can be abstracted based on the same underlying similar architecture — for ease of comparison, we describe the catalytic material as a porous network with the active centers responsible for the conversion of educts to products distributed on the internal surface of the pores and the external surface area. Generally, the conversion of any given educt by the aid of the catalytic material is divided into a number of consecutive steps. Figure 11.13 illustrates these different steps. The governing transport phenomenon outside the catalyst responsible for mass transport is the convective fluid flow. This changes dramatically close to the catalyst surface from a certain boundary onwards, named the hydrodynamic boundary layer, mass transport toward and from the catalyst surface only takes place... 

There is, as yet, no complete theory to explain the phenomenon of polarographic maxima which is manifested by the observed current overshooting the limiting current. The causes are convective mass transport in the solution and adsorption. Three types of maximum have been identified [61] ... 

Concentration polarization Convective transport and retention of solutes by the membrane results in an accumulation of species at wall. Local concentrations, C , are higher than in the bulk, Cb, and a back-diffusion from near the wall into the bulk liquid phase takes place. This is the so-called "concentration polarization" phenomenon (Fig. 12.1). A simple mass balance leads to the classical equation ... 

The transfer of heat in a fluid may be brought about by conduction, convection, diffusion, and radiation. In this section we shall consider the transfer of heat in fluids by conduction alone. The transfer of heat by convection does not give rise to any new transport property. It is discussed in Section 3.2 in connection with the equations of change and, in particular, in connection with the energy transport in a system resulting from work and heat added to the fluid system. Heat transfer can also take place because of the interdiffusion of various species. As with convection this phenomenon does not introduce any new transport property. It is present only in mixtures of fluids and is therefore properly discussed in connection with mass diffusion in multicomponent mixtures. The transport of heat by radiation may be ascribed to a photon gas, and a close analogy exists between such radiative transfer processes and molecular transport of heat, particularly in optically dense media. However, our primary concern is with liquid flows, so we do not consider radiative transfer because of its limited role in such systems. 

Concerning mass transfer modeling across nanofiltration membranes, the transport mechanisms occiuring are convection, diiiusion, and electromigration (when the solutes are charged). Taking into account the polarization concentration phenomenon, which can occm dming the filtration operation (and thus the increase of the concentration at the membrane interface C ), the solute real retention (l reai) can be calculated from the observed retention by ... 

An effort or a flow, which is a gate for communicating with the exterior, can be imposed (or supplied) by an external system (another dipole or dipole assembly, for instance). An example of external effort is when a force is imposed on a mass placed in a gravitational field. An external flow may correspond to the convection phenomenon, when a fluid transporting an object imposes its own velocity. 

It was shown that for certain system parameters given by a critical Reynolds number, there is a possibility of propagation of the specific flow structures inside the liquid layer. The convection cells, which can appear, are similar to those observed in the Ryleigh-Benard experiment [9]. Such phenomenon can be very important for some air-water-phospholipid systems such as the pulmonary surfactant present in the natural mass exchanger - the lungs. The hydrodynamic system described in the piq er can be a very useful tool for explanation of convective diffusion-reaction transport process in case of interaction of allergens with pulmonary epithelium, causing atopy. 

The above equations, based on the conservation of mass for chemical transport, yield the convection-dispersion-sorption equation CDSE (Eq. 3.41 and its variations), which is widely used in industrial applications, including dyeing. Many researchers call the term (D d ddx ) in Eq. 3.41b either dispersion or diffusion, and D is usually treated as a constant. In the context of this analysis, dispersion is used to describe this phenomenon, and the diffusion is considered a special case of dispersion when the velocity of the fluid is zero. 

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