Fluid flow convection

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... 

Once a solute molecule reaches a free adsorption site on the surface, actual adsorption takes place (4). If the adsorption processes (1-4) are slow compared with the convective fluid flow through the packed bed the eluted peaks show a non-symmetrical band broadening. Severe tailing can be observed, due to the slower movement of those solute molecules, which penetrate deeper into the pore system. 

Figure 27a shows the SECM image obtained at 0.75 atm after subtracting the image at 0 atm. This image is a visualization of the transport of Ru(NH3)s+ away from the cartilage surface due to convective fluid flow. The... 

Convection Fluid flow driven by vertical temperature differences. 

Another feature of tumors that can have a major impact on the distribution of targeted radiotherapeutics is tumor interstitial fluid pressure. Interstitial fluid pressure results in a pressure gradient that can inhibit the delivery of molecules from the plasma to the extracellular fluid in central regions of a tumor. Tliis pressure gradient is not present in normal tissues because they have a lymphatic system however, tumors do not, creating an additional barrier that must be overcome. Experimental evidence of an elevated interstitial pressure in murine tumor models has been reported by Boucher et al. (1990). As expected, the effect was most apparent at the tumor periphery. Using a mathematical model, the magnitude of this outward convection fluid flow was predicted to be 0.1-0.2 pm/s (Jain and Baxter 1988). 

Figure 9.2 (Left) Convective fluid flow and effect on the waveform, slightly above the critical Rayleigh number. (Right) Fluid flow at Rayleigh numbers greatly exceeding the critical value, where axisymmetric flow is expected. The waveform has a parabolic shape.

One-dimensional reaction-diffusion equations (RD-approach) offer a more adequate model than the rj-approach to account for mass transport in the washcoat. The model calculates spatial variations of concentrations and surface reaction rates inside the washcoat. It assumes that the species flux inside the pores is only due to diffusion (Stutz and Pouhkakos, 2008). Therefore, it neglects the convective fluid flow inside the porous layer, because of very low permeabihty assumption (Stutz and Pouhkakos, 2008). Eventually, each gas-phase species leads to one reaction-diffusion equation in the RD-approach, which is written in the transient form, as (Deutschmann, 2011b Deutschmann et al., 2014 Karadeniz et al., 2013)... 

Choi et al. [104] synthesized ZnO NCs using a continuous-flow microreactor system. The growth mechanism and stability of ZnO NCs were studied by varying the pH value of the aqueous solution and flow conditions. It was found that external forces from convective fluid flow could affect the assembly of ZnO NCs and result in different shapes at pH 13. The ZnO NC assemblies formed particular structures such as a tactoid structure or a semispherical structure via an attachment growth mechanism. The assembly results from a competing interaction between electrostatic force caused by surface charge of NCs and external force from convective fluid flow. This study shows that the external forces from convective fluid flow could be applied to fabricate assembly of functional metal oxides with complex architectures in a continuous-flow microreactor system. 

The mass transfer process within porous yam packages depends on many factors, including sorption (dye/fibre systems, sorption constant), convection (fluid flow... 

The modeling of the current distribution in a general-geometry cell nearly always requires a numerical solution. The following discussion focuses on the thin boundary layer approximation, with the overpotential components lumped within a thin boundary layer which may be of a varying thickness. The Laplace equation for the potential with nonlinear boundary conditions must be solved. Similar considerations typically apply to the more comprehensive solution of the Nernst-Planck equation (10) however, the need to account for the convective fluid flow in the latter case makes the application of the boundary methods more complex. We focus our brief discussion on the most common methods the finite-difference method, the finite-element method, and the boundary-element method, schematically depicted in Fig. 4. Since the finite-difference method is the simplest to implement and the best known technique, it is discussed in somewhat more detail. 

---