Transport flow heterogeneity

Normally, crystals do not exhibit convective flow and, therefore, mixing by convection at atomic dimensions is not possible. As a consequence, diffusive transport and heterogeneous reactions are the only processes which can be anticipated at this point. 

Just as one considers two regions of flow for homogeneous media, so one may have molecular or Knudsen transport for heterogeneous media. 

Hutson, J.L., and R.J. Wagenet. 1995. A multiregion model describing water flow and solute transport in heterogeneous soils. Soil Sci. Soc. Am. J. 59 743-751. 

Philip, J.R. 1986. Issues in flow and transport in heterogeneous porous media. Transp. Por. Media 1 319-338. 

Feyen, J., Jacques, D., Timmerman, A., and Vanderborght, J. Modelling water flow and solute transport in heterogeneous soils A review of recent approaches. Joumal-of-Agricultural-Engineering-Research 70[3], 231-256. 1998. 

The most frequent disposal of most of the polymer-based heterogeneous materials family takes place by the dispersed phase/matrix mode. So the dispersed phase components may be identified by the finite size of each of their domains, being surrounded by the continuous matrix. Both the size and the geometry of the particles featuring the dispersed phase together with their surface properties govern the transport phenomenon across the interphase between the dispersed particles and the continuous matrix. According to the interface approach defined in the previous section, it is obvious that the domain size and its distribution confine the interfacial volume available for effective transport flows between the matrix and the disperse phase. 

R.A. Greenkorn, Flow Phenomena in Porous Media, Marcel Dekker, NY, 1983. C.N. Satterfield, Mass Transport in Heterogeneous Catalysis, MIT Press, Cambridge, 1970. 

There were several studies of hydraulic transport in the 1950s, sparked off particularly by an interest in the economic possibilities of transportation of coal and other minerals over long distances. Newitt et al.p2) working with solids of a range of particle sizes (up to 5 fim) and densities (1180-4600 kg/m3) in a 25 mm diameter pipe, suggested separate correlations for flow with a bed deposit and tor conditions where the particles were predominantly in heterogeneous suspension. 

Sand of mean diameter 0.2 mm is to be conveyed by water flowing at 0.5 kg/s in a 25 mm ID horizontal pipe, 100 nt long. What is the maximum amount of sand which may be transported in this wav if the head developed by the pump is limited to 300 kN/m2 Assume fully suspended heterogeneous flow. 

There is a substantial weight of evidence for the cytoskeleton being responsible for the force production and control of cell locomotion. This view has not yet been accepted unanimously. However, an alternative hypothesis continues to be argued which states that membrane cycling is the motive force driving cell locomotion (Bretscher, 1987). One of the predictions of the membrane flow hypothesis is that there should be a discernible flow of lipid from the front to the rear of the cell. Lipid flow has proven very difficult to study, because of the lack of suitable methods to label single lipid molecules and the heterogenous behavior of membrane-associated proteins. The observation that particles were transported rearward when they bound... 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

Helmig R., Class H., et al. Architecture of the modular program system MUFTE-UG for simulating multiphase flow and transport processes in heterogeneous prous media. 1998 MathematischeGeologie2 123-131. 

This study was carried out to simulate the 3D temperature field in and around the large steam reforming catalyst particles at the wall of a reformer tube, under various conditions (Dixon et al., 2003). We wanted to use this study with spherical catalyst particles to find an approach to incorporate thermal effects into the pellets, within reasonable constraints of computational effort and realism. This was our first look at the problem of bringing together CFD and heterogeneously catalyzed reactions. To have included species transport in the particles would have required a 3D diffusion-reaction model for each particle to be included in the flow simulation. The computational burden of this approach would have been very large. For the purposes of this first study, therefore, species transport was not incorporated in the model, and diffusion and mass transfer limitations were not directly represented. 

---