Viscous flow mechanism

Furtheron, the dispersed droplets are the smaller the closer to unity the viscosity ratio of the components is (62-64). Their sizes decrease also if the first normal stress difference of the dispersed phase becomes smaller than that of the matrix (61). The droplet size, moreover, is influenced by the tendency to further break down of elongated particles due to capillary instabilities (61) as well as by coalescence via an interfacial energy driven viscous flow mechanism. All these procedures and dependences affect the structure formation within their typical time scales (61,62). 

For the viscous flow mechanism, Frenkel (1945) found that... 

By insertion of Af, obtained from equation (5.176) and obtained from using equation (5.169) and (5.171) into equation (5.175), a single equation for the total flux of the diffusive and viscous flow mechanisms is obtained ... 

It is of interest that of the various postulated mechanisms none has passed from the literature direct electronic excitation, frictional processes, and viscous flow mechanisms continue to arouse interest, and even tribochemical mechanisms, discarded by Bowden and Yoffe, have remained alive within the same laboratory in new guise (Chapter 9). 

Equations 3.S.b-4 to 6 can also be combined to give a single equation containing only the total flux resulting from both diffusive and viscous flow mechanisms ... 

Poiseuille (viscous flow) mechanism occurs when the average pore diameter is bigger than the average free path of fluid molecules. In this case, the collisions among the different molecules are more frequent than those among the molecules and the porous wall as a consequence no separation takes place [12]. 

The viscous flow mechanism, which was first proposed by Frenkel," can be operative in the sintering of viscous materials like glass. If the material follows the behaviour of a Newtonian fluid, the neck growth and shrinkage kinetics are expressed as follows. 

It is worthwhile at this point to remind the reader that the above conclusion for Knudsen diffusion is valid as long as the pressure is low or the capillary size is very small. When the capillary size is larger or the pressure is higher, the viscous flow will become important and the flow will be resulted due to the combination of the Knudsen and viscous flow mechanisms. This will be discussed in Sections 7.5 and 7.6. 

To describe the transition flux when the Knudsen and viscous flow mechanisms are operating inside a unconsolidated medium, we assume that the flux is additive (Kraus et al., 1953), that is the transition flux is the sum of the viscous flux (eq. 7.5-28a) and the Knudsen flux (eq. 7.4-36) ... 

DoC . Thus, if the experimental data of time lag versus concentration Cq shows a decrease with concentration, it could point to the fact that the apparent diffusivity is a function of concentration, but it says nothing about the mechanism of transport of molecules through the medium. We will show later that the viscous flow mechanism and the adsorbing gas situations also give rise to the behaviour of a decrease of time lag for the concentration (pressure) of the supply reservoir. 

We have shown the essential features of the time lag in Section 12.2 using the simple Knudsen diffusion as an example, and a direct method of obtaining the time lag in Section 12.3. The diffusion coefficient dealt with in the Frisch s method in Section 12.3 is concentration dependent. In this section we will deal with a case where the transport through the porous medium is a combination of the Knudsen diffusion and the viscous flow mechanism. We shall see below that this case will result in an apparent diffusion coefficient which is concentration dependent, and hence it is susceptible to the Frisch s analysis as outlined in the Section 12.3. This means that the results of equations (12.3-21) are directly applicable to this case. 

The viscous flow mechanism is important when the pressure of the system is reasonably high. When this is the case, the constitutive flux equation describes a combined transport of Knudsen diffusion and viscous flow as ... 

The removal of water from aqueous salt solutions by reverse osmosis, as in seawater desalination with cellulose acetate membranes or nylon hollow fibers, is believed to occur primarily by a diffusive transport mechanism for both water and solutes. On the other hand, in the use of membranes for the removal of water fiom aqueous solutions containing higher molecular weight solutes, such as the ultrafiltration of protein solutions, the solvent is believed transported by a viscous flow mechanism within the pores of the membrane and solute molecules are convected with the solvem in the huger pores." "... 

On the basis of the linearity of curve M in Figure 6 and following the literature suggestions [32], it may be assumed that the viscous flow mechanism in pure DME, and other solvents like this one, would be a single thermally activated process. These conjectures are probably supported by the fact that DME molecules would scarcely... 

On the basis of the above observation, Schultz and Asunmaa developed the following transport mechanism. They made an assumption that the low-density and the noncrystalUnc region of the polymer that fills the space between the circular cells is incorporated into the unit cell as its part. Those spaces (between the unit cells) were therefore assumed to be vacant. In reverse osmosis operation these vacant spaces are filled only with water, and this water is assumed to be more ordered than the ordinary water under strong influence from the polymeric material. This water flows by the viscous flow mechanism through channels that arc formed by connecting the vacant spaces. Suppose r is the effective radius of this pore (m), np is the number of the pore in a unit area (1/m ), p is the pressure drop across the membrane (Pa), 17 is the water viscosity (Pa s), L is the effective layer thickness (m), and r is the tortuosity factor (-), the volumetric... 

The respective values of Ep and Ep p calculated from Fig.5 are about 4.8 Kcal/mole and 2.3 l cal/mole respectively the low activation energy of the isothermal process being indicative of a viscous flow mechanism while.the relatively higher value of Ep j is comparable with those generally found in diffusive processes (17-19). The concept of apparent activation energies for transport in a temperature gradient arises from the different dissolution enthalpies of the permeant on opposite partition sides. From the definition of enthalpy it follows that... 

From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then the re-forming of bonds with new neighbors as large numbers of atoms or molecules move relative to one another upon removal of the stress, they do not return to their original positions. The mechanism of this deformation is different for crystalline and amorphous materials. For crystalline solids, deformation is accomplished by means of a process called slip, which involves the motion of dislocations as discussed in Section 7.2. Plastic deformation in noncrystalline solids (as well as liquids) occurs by a viscous flow mechanism, which is outlined in Section 12.10. 

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