Slip flow effect

The next section will first show the importance of flow in a concrete modelling problem such as the slip flow effect on the efficiency of a permanent mechanically mixed reactor. Then the characterization of the combined flow models where the slip flow occurs will be presented. 

The Slip Flow Effect on the Efficiency of a Mechanically Mixed Reactor in a Permanent Regime... 

In the study of Fan, et al. [If], a numerical simulation of gaseous flows in microchannels by the DSMC was carried out. Several unique features were obvious to maintain a constant mass flow, the mean streamwise velocity at the walls was found to increase to make up for the density drop caused by the pressure decrease in the flow direction, which is in contrast to the classical PoisueUe flow. In addition, the velocities at the walls were found to be nonzero and to increase in the streamwise direction, which highlights the slip-flow effect due to rarefaction. The results of the DSMC simulations were validated by an analytical solution in the slip regime. It was observed that the two results showed remarkable agreements. 

Multidimensional Effects. In the previous section, we studied the wall effect on the shear factor. To give a full account of the wall effects, we now look at the no-slip flow effect posed by the containing wall (multidimensional effect) on the total pressure drop. For simplicity, let us rewrite the normalized pressure drop factor, fv, based on the permeability of the medium rather than the particle diameter,... 

While slip-flow effects are mostly expected to have an impact on flow behavior on the submicrometer scale, there is another phenomenon that may lead to deviations from the usual model predictions on a larger length scale. On a solid surface exposed to an electrolyte, charges may accumulate, causing the formation of a... 

Kn = 0.01-0.1 Slip flow rarefaction effects that can be modeled with a modified continuum theory with wall slip taken into consideration... 

Since the middle of the 1990s, another computation method, direct simulation Monte Carlo (DSMC), has been employed in analysis of ultra-thin film gas lubrication problems [13-15]. DSMC is a particle-based simulation scheme suitable to treat rarefied gas flow problems. It was introduced by Bird [16] in the 1970s. It has been proven that a DSMC solution is an equivalent solution of the Boltzmann equation, and the method has been effectively used to solve gas flow problems in aerospace engineering. However, a disadvantageous feature of DSMC is heavy time consumption in computing, compared with the approach by solving the slip-flow or F-K models. This limits its application to two- or three-dimensional gas flow problems in microscale. In the... 

XlylmnkT/ird ), or h = [TT[i 2RTI2p), as long as substituting the gap-dependent viscosity rather than the bulk viscosity. Because the effective viscosity decreases as the Knudsen number enters the slip flow and transition flow ranges, and thus the mean free path becomes smaller as discussed by Morris [20] on the dependence of slip length on the Knudsen number. 

Having established that wall slip occurs but is not dominant, the procedure is to estimate the value of v, and hence calculate a corrected flow rate by subtracting the slip flow from the measured flow rate. In general it is found that the slip velocity increases with tw and decreases with d, although in some cases vs is independent of dt. Consequently, it can be seen from equation 3.66 that the effect of slip decreases as d, increases, and becomes negligible at very large diameters. 

The other approach is to scale up the genuine flow, then add the slip flow for the appropriate pipe diameter. Scale up of the genuine flow can be done as described in Section 3.3 or Section 3.4. In order to assess the flow due to wall slip in the pipe, it is necessary to have information about the variation of vs with tw and dt unless it is assumed that the pipe is large enough for the effect of slip to be negligible. If slip velocity data are available, implying that the apparent fluidity plots are also available, then it would be easier to use these plots directly. 

Various nonequilibrium and slip flow models have been proposed as improvements on the homogeneous equilibrium flow model. See, for example, Henry and Fauske (Trans. ASME J. Heat Transfer, 179-187 [May 1971]). Nonequilibrium and slip effects both increase... 

Figure 3.30 shows clearly the effect of m and z on the reactant transformation degree for a SPMR. Only for a zero-order kinetics process, does the slip flow not affect the degree of the reactant transformation. For other Xf values, each graphic construction based on Fig. 3.30 shows the same rules of evolution (at m<0.5, z and X increase simultaneously, and, when n increases, X increases slowly for m>0.5, X keeps a constant value determined by z). When the PM core of SPMR is exchanged with a CFM model, we obtain a special SPMR type in which the performances can be appreciated by the model developed above. 

Figure 3.30 The effect of the perfect mixing region dimension and of the slip flow degree on the SPMR conversion (reaction order n = 0, 0.5, 1, 1.5, 2 X , = 0.9).

In the SFA experiments there is no way to determine whether shear occurs primarily within the film or is localized at the interface. The assumption, made by experimentalists, of a no-slip flow boundary condition is invalid when shear localizes at the interface. It has also not been possible to examine structural changes in shearing films directly. MD simulations offer a way to study these properties. Simulations allow one to study viscosity profiles of fluids across the slab [21], local effective viscosity inside the solid-fluid interface and in the middle part of the film [28], and actual viscosity of confined fluids [29]. Manias et al. [28] found that nearly all the shear thinning takes place inside the adsorbed layer, whereas the response of the whole film is the weighted average of the viscosity in the middle and inside the interface. Furthermore, MD simulations also allow one to examine the structures of thin films during a shear process, resulting in an atomic-scale explanation [12] of the stick-slip phenomena observed in SFA experiments of boundary lubrication [7]. 

Another study, [17], used helium as their working fluid and carried out the experiments in 51.25 X 1.33 micrometer microchannels. They showed that, as long as the Knudsen number is in the slip flow range, the Navier-Stokes equations are still applicable and the discontinuities at the boundaries need to be represented by the appropriate boundary conditions. They obtained the following formula for the mass flow rate including the slip effects... 

Heat convection for gaseous flow in a circular tube in the slip flow regime with uniform temperature boundary condition was solved in [23]. The effects of the rarefaction and surface accommodation coefficients were considered. They defined a fictitious extrapolated boundary where the fluid velocity does not slip by scaling the velocity profile with a new variable, the shp radius, pj = l/(l + 4p.,Kn), where is a function of the momentum accommodation coefficient, and defined as p, =(2-F,j,)/F,j,. Therefore, the velocity profile is converted to the one used for the... 

Equation (40) shows that the optimum hydraulic diameter decreases at lower temperatures. Thus, microscale effects may be more important in low temperature applications, such as in heat exchangers of cryocoolers. However, temperature has little effect on the relative importance of slip flow. The mean free path of gas molecules is given by... 

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